CN106846413A - The device and method that three-dimensional tree-shaped rectangular coordinate system is built and image space is demarcated - Google Patents
The device and method that three-dimensional tree-shaped rectangular coordinate system is built and image space is demarcated Download PDFInfo
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Abstract
Put and embodiment the present invention relates to a kind of simply and intuitively three-dimensional tree shape dress, the present apparatus can rapidly and accurately build three-dimensional cartesian rectangular coordinate system, build space geometrical element point, line, surface, body, characterize coordinate of the space geometrical element in three-dimensional cartesian coordinate system, judge the geometrical relationship between geometric element, the spatial relationship of capture apparatus and device is built, and the caliberating device demarcated as image space.Present apparatus simple structure, the global formation accuracy of manufacture is high, it is flexible using combination, present apparatus tool has been widely used and application field, can be as the operation device in geometry teaching, it is also possible to used as the structure and caliberating device of the space coordinates of three-dimensional scanner and motion capture system based on image etc..Specific implementer's case is based on geometry principle, with reference to the advantage of apparatus of the present invention, illustrating in detail operation and application method of the present apparatus in its concrete function.
Description
Technical field
The device and method demarcated with image space, the present apparatus are built the present invention relates to a kind of three-dimensional tree-shaped rectangular coordinate system
Can be as the device for building coordinate system and image space demarcation.Concrete function includes：Three-dimensional cartesian rectangular coordinate system is built,
Space geometrical element point, line, surface, body are built, coordinate of the space geometrical element in three-dimensional cartesian coordinate system is characterized, geometry is judged
Geometrical relationship between element, builds the spatial relationship of capture apparatus and device, and uncalibrated image space.Category three dimensions is sat
Mark the foundation of system, geometric element coordinate sign in a coordinate system, the judgement of space geometry relation, capture apparatus and device space
The structure of relation, and the technical field that image space is demarcated and parsed.
Background technology
At present, in teaching, scientific research and engineering in practice, lack a kind of directly perceived, image, quickly and easily set up three-dimensional flute card
The device of your rectangular coordinate system, can both build space geometrical element point, line, surface, body, it is also possible to judge the geometry between them
Relation, can characterize the coordinate of geometric element in the rectangular coordinate system set up again.
In addition, when image space two-dimensional analysis are carried out or plane motion catches, it is necessary to camera or video camera（Hereinafter referred to as
Capture apparatus or equipment）Primary optical axis and a certain reference or plane of movement keep perpendicular or parallel relation.If it cannot be guaranteed that vertical
Or parallel relation, then the image for shooting can produce certain systematic error when according to perpendicular or parallel Automated generalization data；
When carrying out three dimension laser scanning surreying and three-dimensional motion seizure, the existing image space caliberating device overwhelming majority is belonging to
Various plane reference plates, therefore construct Descartes's rectangular coordinate system of two dimension, i.e.,Z=0（Or constant）Plane.Due to clapping
The manufacturing process deviation of equipment, the refraction error and CCD lattice position errors of incident ray when by each lens etc. are taken the photograph,
All there is nonlinear geometry distortion in actual optical system, so that there is geometric distortion between actual image point and theoretical picture point.
It is usually nonlinear which results in the conversion between real space and image space, thus in scaling board planeXWithY
The coordinate precision in the two directions can be guaranteed, but vertical with scaling boardZThe coordinate precision in direction not necessarily can guarantee that；
Again because the camera lens of capture apparatus is mostly sphere, the presence of aberration causes the light of edge part than the light of central part
Serious refraction and bending are easily produced, if still being demarcated to image space using two-dimensional calibrations plate, so as to increased in mirror
The error of coordinate of the object space in head edge region, and then influence image space parsing precision.This also causes the mirror of capture apparatus
Head edge region than central area with greater need for demarcation, and should using three dimensions caliberating device.
The content of the invention
It is an object of the invention to provide a kind of simple, image, intuitively three-dimensional tree shape dress is put and embodiment, can quickly,
Three Cartesian coordinates are built exactly, space geometrical element point, line, surface, body is built, and determine space geometrical element in three-dimensional
Coordinate in rectangular coordinate system is characterized, and judges the geometrical relationship between geometric element, and the space for building capture apparatus and device is closed
System, and uncalibrated image space.
The device that three-dimensional tree-shaped rectangular coordinate system of the present invention is built and image space is demarcated is using following technology
What scheme was realized：
Apparatus of the present invention（Hereinafter referred to as device）Symmetrical mounting and asymmetric unit can be divided into.So-called symmetrical mounting, refers to all
Attached spheroid（Hereinafter referred to as attached ball）Size it is identical, and to main body ball（Hereinafter referred to as cue ball）The distance of the centre of sphere also phase
Deng, and respectively connect attached ball all equal with the length of connecting rod of cue ball and all relative cue ball centre of sphere of each attached ball and connecting rod forms center pair
Title relation.Symmetrical mounting is by a cue ball, a cylinder（Or cuboid）Base, six attached balls of same size, respectively
Forecourt, rear ball, left ball, right ball, upper ball, lower ball, seven（Six roots of sensation geometric parameter is identical）The part of connecting rod four constitutes.It is asymmetric
The size dimension that device refers mainly to each attached ball is differed, or connection cue ball and attached ball connecting rod size it is unequal, or attached ball number
Amount is less than six.The conventional asymmetric unit of one of which is main by a cue ball, a cylinder（Or cuboid）Base, five
Individual attached ball, respectively forecourt, rear ball, left ball, right ball, upper ball, the six roots of sensation（Five geometric parameters are identical）The part group of connecting rod four
Into.Symmetrical mounting than this asymmetric unit increase an attached spheroid and a connecting rod, advantage is symmetrical configuration, it is attractive in appearance and
One index point is provided more when demarcating and parse image space, and for building three-dimensional cartesian rectangular coordinate system, builds space
Geometric element point, line, surface, body and judge geometrical relationship between them, and characterize space geometrical element in three-dimensional rectangular coordinate
Coordinate in system, the two devices are without this qualitative difference.The concrete structure of symmetrical and asymmetric unit is shown in accompanying drawing 1 to 4.
The further design feature description of above two device：Above-mentioned cue ball, base, six（Or five）Individual attached ball, seven（Six）Root
Connecting rod can use the materials such as metal, plastics, glass, macromolecule.Under（Or it is main）Ball downside is fixed by connecting rod with base, base
Bottom is embedded in annular magnet.Other six（Or five）Individual attached ball is separately fixed at the front, back, left, right, up of cue ball by connecting rod
And downside（Or without downside）.Cue ball has through hole in three mutually perpendicular directions being connected with connecting rod, and attached ball connects with connecting rod
There is through hole on the direction for connecing, base also has through hole on the direction being connected with connecting rod, and all clear size of opening are identical.Through-hole diameter
Size more than or equal to 1 micron to be less than or equal to 1 meter.Attached bulb diameter is more than 1 times of through-hole diameter, and cue ball diameter is attached
1 times of bulb diameter and more than, connecting rod overall diameter be 1.1 times of through-hole diameter and more than, the length of lower ball and base connecting rod and outward
Diameter be respectively 1 times of attached bulb diameter and the above and 1.1 times and more than, base round diameter（Or the square length of side）More than cue ball
4 times of diameter, substructure height be 6 times of through-hole diameter and more than, the diameter of the magnet that goes in ring be not less than 8 times of through-hole diameter and with
On, the diameter of the magnet that goes in ring is not more than cup dolly diameter or the square base length of side, and the height of the magnet that goes in ring is not higher than base
Highly.Six（Or five）The size of individual attached ball can be with identical or differ, connection cue ball and the six of attached ball（Or five）The hollow company of root
Bar physical dimension can be with identical or differ, the 7th（Or six）The geometric parameter of root with other six（Or five）Root connecting rod can phase
Deng, it is also possible to it is unequal.Present apparatus global formation, it is ensured that forecourt, cue ball are with rear ball center's line on link centerline, it is ensured that
Left ball, cue ball are with right ball center's line on link centerline, it is ensured that upper ball, cue ball and lower ball（Or without lower ball）With base center
Line on link centerline, and ensure front-rear linkage, left linkages, upper and lower strut center line it is orthogonal.And forecourt,
Left ball, upper outer surface of ball brush color consistent with other spheroids or inconsistent respectively.
The method that three-dimensional tree-shaped rectangular coordinate system of the present invention is built and image space is demarcated is following technical scheme reality
Existing：A kind of method that three-dimensional tree-shaped rectangular coordinate system is built and image space is demarcated, by the origin of coordinates, reference axis and coordinate are flat
Face, builds three-dimensional cartesian rectangular coordinate system；
The described device cue ball centre of sphere is the origin of coordinates of coordinate system；
The origin of coordinates can determine that straight line with the centre of sphere of any one attached ball, can set up the reference axis of coordinate system,XAxle positive direction
Forecourt centre of sphere direction is pointed to from the cue ball centre of sphere,YAxle positive direction points to left ball centre of sphere direction from the cue ball centre of sphere,ZAxle positive direction is from master
The ball centre of sphere points to upper ball centre of sphere direction, and three axles meet right-handed helix relation, and offside is respectivelyX, Y, ZThree negative semiaxis；
The cue ball centre of sphere not on the same line, the front/rear ball centre of sphere, the left/right ball centre of sphere, it is determined thatXOYPlane namely horizontal plane；No
The cue ball centre of sphere on the same line, the front/rear ball centre of sphere, the up/down ball centre of sphere, determinationZOXPlane namely sagittal plane；Not same
The cue ball centre of sphere, the left/right ball centre of sphere on straight line, the up/down ball centre of sphere, it is determined thatYOZPlane namely coronal-plane；
Based on the origin of coordinates, three reference axis and three coordinate planes build three-dimensional cartesian rectangular coordinate system；
Based on the origin of coordinates, any two reference axis and the coordinate plane determined by its build two-dimentional Descartes's rectangular coordinate system；
Based on the origin of coordinates and any one reference axis, one-dimensional cartesian coordinate system, i.e. number axis are built；
Based on the origin of coordinates, zero dimension cartesian coordinate system, i.e. point are built.
Further, also including building point, line, surface, body space geometrical element, the structure point, line, surface, body space are several
What element comprises the following steps：
（1）, device the cue ball centre of sphere, build a geometric point in three dimensions；One each attached ball centre of sphere of device, point
Geometric point that Gou Jian be in three dimensions；
（2）, one laser beam pass sequentially through two cue ball centre ofs sphere of device, build the straight line in three dimensions；One dress
Each reference axis put, builds the straight line in three dimensions respectively；One centre of sphere of any two ball of device, builds
Straight line in three dimensions；Cross space not on straight line a bit, build the parallel lines of this straight line；Cross not on straight line
Space a bit, builds point to the vertical line of this straight line；
（3）, be not arranged on the same straight line three cue ball centre ofs sphere of device, build a plane of three dimensions；Two devices
The cue ball centre of sphere builds the 3rd cue ball centre of sphere of device outside straight line, with straight line, builds a plane of three dimensions；Three
Two straight lines for intersecting vertically that the cue ball centre of sphere of individual device builds, build a plane of three dimensions；Four masters of device
Two of ball centre of sphere structure intersect vertically or parallel straight line, build a plane of three dimensions；Four cue ball balls of device
The heart is respectively the four of rectangle summits, builds a plane of three dimensions；One each coordinate surface of device, respectively
Build a plane in three dimensions；One three ball centre of sphere not on the same line of device, builds three-dimensional space respectively
Between in a plane；
（4）, four devices not at grade the cue ball centre of sphere, build a tetrahedron of three dimensions；Not same
Five and the cue ball centre of sphere of apparatus above in plane, build a polyhedron of three dimensions；Eight cue ball centre ofs sphere of device
Respectively one the eight of cuboid summits, build a cuboid of three dimensions；One device not at grade
Four and the above ball centre of sphere, build respectively one individual in three dimensions.
Further, the coordinate also including point, line, surface, body geometric element in three-dimensional cartesian coordinate system is characterized, described
The coordinate of point, line, surface, body geometric element in three-dimensional cartesian coordinate system is characterized and comprised the following steps：
（1）, coordinate characterizing method of the point in three-dimensional cartesian rectangular coordinate system：Build a three-dimensional cartesian rectangular co-ordinate
System, upright projection is made by point to three axles of coordinate system respectively, and the distance of subpoint to the origin of coordinates is the exhausted of coordinate a little
To value, the positive and negative semiaxis of reference axis is respectively at according to subpoint, coordinate is respectively positive and negative value；
（2）, coordinate characterizing method of the straight line in three-dimensional cartesian rectangular coordinate system：Build a three-dimensional cartesian rectangular co-ordinate
System, optional 2 points from straight line, according to step（1）Described method, provides this 2 points of coordinates in a coordinate system, then profit respectively
With the determination method of the space line introduced in analytic geometry, coordinate side of the straight line in three-dimensional cartesian rectangular coordinate system is given
Journey；
（3）, coordinate characterizing method of the plane in three-dimensional cartesian rectangular coordinate system：Build a three-dimensional cartesian rectangular co-ordinate
System, optionally not conllinear 3 points from plane, according to step（1）Described method, provides this 3 points in a coordinate system respectively
Coordinate, using the determination method of the space plane introduced in analytic geometry, provides plane in three-dimensional cartesian rectangular coordinate system
Equation in coordinates；
（4）, coordinate characterizing method of the body in three-dimensional cartesian rectangular coordinate system：Build a three-dimensional cartesian rectangular co-ordinate
System, chooses three summits, such as step respectively from polyhedral each surface successively（3）Described method, provides each surface
Plane equation, it is the area of space surrounded by the inequation group of these planes that the coordinate of body is characterized.
Further, also including point and point, Points And lines, point and face, put and body, straight line and straight line, straight line and face, straight line and
Body, face and face, face and body, the judgement of body and body space geometry relation；Described point and point, Points And lines, point and face, point and body,
Straight line and straight line, straight line and face, straight line and body, face and face, face and body, the judgement of body and body space geometry relation are as follows：
（1）, using building point, line, surface, the side for building the geometric point in three dimensions described in body space geometrical element step
Whether method, builds two points in three dimensions, be zero according to the distance between two points, and the geometry of decision space point and point is closed
System be overlap or from；The method characterized using coordinate of the point in three-dimensional cartesian rectangular coordinate system, provides two points respectively
Coordinate, according to two points coordinate it is whether identical, decision space point and point geometrical relationship be overlap or from；
（2）, using building point, line, surface, the side for building the geometric point in three dimensions described in body space geometrical element step
The method of the straight line in method and structure three dimensions, builds the point and straight line in three dimensions respectively, builds
Straight line in three dimensions, whether according to point on this straight line, the geometrical relationship of decision space point and straight line is that point is online
It is upper or online outer；Cross and a little make vertical line to straight line, whether the distance of foundation point to intersection point is zero, the geometry of decision space point and straight line
Relation is on line or online outer point；Coordinate characterizing method and straight line using point in three-dimensional cartesian rectangular coordinate system is three
The method that coordinate in dimension Descartes's rectangular coordinate system is characterized, provides the equation of coordinate and straight line a little respectively, according to the seat of point
Whether mark meets the equation of straight line, and the geometrical relationship of decision space point and straight line is on line or online outer point；
（3）Using the geometric point built in three dimensions built described in point, line, surface, body space geometrical element step
Whether with a method for plane, the point and a plane in three dimensions are built respectively, sentence according to point on that plane
The geometrical relationship for determining spatial point and straight line is put on the whole or outside face；Cross and a little make vertical line to plane, according to point to intersection point away from
Whether from being zero, the geometrical relationship of decision space point and plane is put on the whole or outside face；It is straight in three-dimensional cartesian using putting
The coordinate characterizing method of coordinate characterizing method and plane in angular coordinate system in three-dimensional cartesian rectangular coordinate system, is given respectively
Whether the coordinate of point and the equation of plane, the geometry pass of the equation of plane, decision space point and plane is met according to the coordinate of point
System is point on the whole or outside face；
（4）, using building point, line, surface, the geometric point built in three dimensions described in body space geometrical element step
And the method for building an individuality of three dimensions, the point and individual, a foundation composition body in three dimensions are built respectively
Each surface regional relation that space is split, the position relationship on each surface of decision-point and body；If point is located at constitutes body
Each surface surround space, then put in vivo；If point is located on each surface for constituting body, put on body；If point is not
Positioned at constitute body each surface surround space, then body do not include point, i.e., point and body be from relation；Using point in three-dimensional
The coordinate characterizing method of coordinate characterizing method and body in Descartes's rectangular coordinate system in three-dimensional cartesian rectangular coordinate system, point
The inequation group on each surface of coordinate and body a little is not given, and whether the coordinate according to point can make the inequality side of cuboid
, less than zero, equal to zero or more than zero, decision-point is in cuboid, on cuboid or rectangular external for journey group；
（5）, using building point, line, surface, the straight line built in three dimensions described in body space geometrical element step
Method, builds two straight lines in three dimensions, selects three points being not arranged on the same straight line on this two straight lines, builds three-dimensional
A plane in space, using step（3）Described method, it is known that the 4th point judges empty on that plane or outside face
Between the geometrical relationship of straight line and straight line be coplanar or antarafacial；
1., two straight lines are coplanar line, judge between two straight lines geometrical relationship be overlap, it is parallel, intersect, intersect vertically, such as
Step（2）Whether whether described method, according to 2 points on straight line on another straight line, judge two coplanar lines
Overlap；2 points on straight line are made vertical line to another straight line respectively, are a rectangle with two intersection points according to this 2 points
Whether is four summits, judges that two coplanar lines are parallel or intersecting；Two intersection points overlap, and judge two vertical phases of coplanar line
Hand over；
2., two straight lines are different surface beeline, judge between two straight lines that geometrical relationship is that antarafacial is vertical or general antarafacial relation：Select this
Three points being not arranged on the same straight line on two straight lines, build a plane in three dimensions, not on that plane straight
Line makees upright projection to this plane, and whether is the former straight line according to projection line in plane, judges that the geometry of two former straight lines is closed
It is antarafacial vertical relation or general antarafacial relation to be；Simultaneously and the straight line that all intersects vertically of two different surface beelines is that two antarafacials are straight
The common vertical line of line；
（6）, coordinate characterizing method using straight line in three-dimensional cartesian rectangular coordinate system, two sides of straight line are given respectively
Journey, according to the equations of two straight lines, the geometrical relationship of decision space straight line and straight line is coplanar, antarafacial, overlap, it is parallel, intersecting,
Intersect vertically, antarafacial is vertical or general antarafacial；Determine the common vertical line of different surface beeline；
（7）, using build point, line, surface, the straight line built in three dimensions described in body space geometrical element step and
One method of plane, builds the straight line and a plane in three dimensions respectively, and straight line makees upright projection to this plane,
Space line and projection line overlap, the geometrical relationship of decision space straight line and plane be straight line planar；Space line and throwing
Hachure intersects, and the geometrical relationship of decision space straight line and plane is that straight line and plane are intersecting；Projection line is degenerated to a subpoint,
The geometrical relationship of decision space straight line and plane is that straight line and plane intersect vertically；Space line is parallel with projection line, judges empty
Between straight line be straight line parallel with plane with the geometrical relationship of plane, the distance between straight line and projection straight line are straight line and plane
Distance；Coordinate characterizing method and plane using straight line in three-dimensional cartesian rectangular coordinate system is in three-dimensional cartesian rectangular co-ordinate
Coordinate characterizing method in system, provides the equation of straight line and plane respectively, according to straight line and the equation of plane, decision space straight line
With the geometrical relationship of plane be straight line in face, straight line and plane intersect, intersect vertically, and straight line is parallel with plane；
（8）, using build point, line, surface, the straight line built in three dimensions described in body space geometrical element step and
The method of one individuality, builds the straight line and an individuality in three dimensions, such as step respectively（7）Described method, according to straight
Whether line intersects with polyhedron arbitrary surfaces, the geometrical relationship of decision space straight line and body be it is intersecting or from；Such as step（5）Or
（6）Described method, straight line and polyhedral seamed edge overlap or straight line is on polyhedral surface, decision space straight line and body it is several
What relation is space line on body；Coordinate characterizing method and body using straight line in three-dimensional cartesian rectangular coordinate system is three
Coordinate characterizing method in dimension Descartes's rectangular coordinate system, provides the inequation on the equation of straight line and each surface of body respectively
Group, according to linear equation and the relation of the inequation group on each surface of body, the geometrical relationship of decision space straight line and body is
Straight line and the cross, straight line of body phase on the border of body or with body phase from；
（9）, using a side for plane for building point, line, surface, structure three dimensions described in body space geometrical element step
Method, builds two planes in three dimensions, and four points in a plane do upright projection, four points to another plane respectively
All it is zero to distance between intersection point, the geometrical relationship of decision space plane and plane is to overlap；Four points between intersection point away from
From all equal and be all not equal to homonymy of zero, and four points positioned at another plane, the geometrical relationship of decision space plane and plane
It is parallel；The geometrical relationship of the straight line in four intersection point another planes of composition, decision space plane and plane is vertical phase
Hand over；Four points are unequal to the distance between intersection point, although or distance it is all equal, four points are located at the two of another plane
The geometrical relationship of side, decision space plane and plane is intersecting；
（10）, using building point, line, surface, a plane of structure three dimensions described in body space geometrical element step
Method, builds two planes in three dimensions, and three points on two straight lines that will intersect in a plane are respectively to another
Individual plane makees vertical line, and for two former straight lines in itself, the geometrical relationship of decision space plane and plane is to overlap to two projection lines；Hang down
Foot can only build straight line, and the geometrical relationship of decision space plane and plane is to intersect vertically；Intersection point build two it is intersecting
Straight line, and two straight line parallels that this two intersecting projection lines build with original three points respectively, decision space plane and plane
Geometrical relationship be parallel；Intersection point build two intersecting straight lines, and this two intersecting projection lines respectively with original three structures
At least a pair is not parallel in two straight lines built, and the geometrical relationship of decision space plane and plane is intersecting；
（11）, coordinate characterizing method using plane in three-dimensional cartesian rectangular coordinate system, the equation of two planes is given respectively,
According to plane equation, the geometrical relationship of decision space plane is that plane and plane overlap, and intersects, intersects vertically, parallel；
（12）, using build point, line, surface, a plane of structure three dimensions described in body space geometrical element step and
The method of one individuality, builds the plane and an individuality in three dimensions, such as step respectively（7）、（8）、（9）Described side
Any one surface of method, plane and cuboid is intersected, and the geometrical relationship of decision space plane and body is intersecting；Plane and rectangular
The geometrical relationship of any one surface coincidence of body, decision space plane and body is plane on body；Plane not with cuboid
Any one surface is intersecting or overlaps, the geometrical relationship of decision space plane and body be from；Using plane in three-dimensional cartesian
The coordinate characterizing method of coordinate characterizing method and body in rectangular coordinate system in three-dimensional cartesian rectangular coordinate system, is given respectively
The inequation group on each surface of the equation of plane and the inequation group on each surface of body, foundation plane equation and body
The geometrical relationship of relation, decision space plane and body be plane and body phase hand over, plane on the border of body or with body phase from；
（13）, using building point, line, surface, the individuality built in three dimensions described in body space geometrical element step
Method, builds two individualities in three dimensions, using step（4）Described method, each summit of a cuboid is all located at
Inside another cuboid, the geometrical relationship of decision space body and body is to include；Using step（7）、（8）、（9）Described side
Method, each surface of an individuality can overlap with an another individual surface, and the geometrical relationship of decision space body and body is body
Closed with body weight；Using step（12）Described method a, cuboid is mutually given with any one surface of another cuboid
It is no, the geometrical relationship of decision space body and body be it is intersecting or from；Using coordinate of the body in three-dimensional cartesian rectangular coordinate system
Characterizing method, provides the inequation group on each surface of two individualities respectively, the inequation group on each surface of foundation body
The geometrical relationship of relation, decision space body and body be include, overlap, intersecting or from.
Further, the demarcation of the structure and image space also including capture apparatus and device spatial relationship, it is included such as
Lower step：
（1）, capture apparatus and device spatial relationship structure：
1., capture apparatus primary optical axis is vertical with any coordinate plane of device, by capture apparatus observe an attached ball with
Cue ball forms concentric circles, the i.e. distance positioned at upper and lower, right position attached ball to cue ball and distinguishes equal, the primary optical axis of capture apparatus
On this attached ball, cue ball, the line of the attached ball of offside, the primary optical axis of capture apparatus is perpendicular to the attached ball positioned at left upper, right position
The coordinate plane of structure；
2., two capture apparatus primary optical axis are mutually perpendicular to：Using the 1. described method of step, the primary optical axis of two capture apparatus respectively with
One the two of device mutually perpendicular coordinate plane is vertical, and the primary optical axis of two capture apparatus is orthogonal；
3., capture apparatus primary optical axis is parallel with the coordinate plane of device：Beam of laser is entered from the attached ball in side of two devices successively
Enter, by the cue ball centre of sphere, passed from the attached ball of offside, the coordinate plane that two devices build be at least a pair it is parallel to each other,
Using the 1. described method of step, the primary optical axis of the capture apparatus not coordinate parallel with another device in a device
Plane, equipment primary optical axis is parallel to coordinate plane parallel with first device in another device；
4., two capture apparatus primary optical axis are mutually perpendicular to：Step 3. as described in method, two equipment primary optical axis are respectively parallel to two
The a pair of parallel coordinate plane of device, the primary optical axis of two capture apparatus is parallel to each other；
（2）The demarcation of image space：
1., capture apparatus can be one, two or many, the optional digital camera of equipment or video camera；
2., at uncalibrated image space, can be using one, two or multiple device is demarcated；The conventional combination of multiple devices has
Four plane combinations and eight Spatial Couplings of device of device；
3., image space demarcates conventional method：According to the conversion dimension of image space to real space, using the mark of image space
The method that to determine step 1. and 2. described, selects appropriate number of caliberating device and capture apparatus；Set up on a caliberating device
Two dimension or three-dimensional cartesian rectangular coordinate system；Projection laser beam, using step（1）Described method, builds capture apparatus and mark
Determine the spatial relationship of device；The image for shooting is obtained, the algorithm of and center identification circular by image procossing finds the master of device
Ball and each the two-dimensional pixel coordinate of attached ball centre of sphere on image；By the design size and the situation of Spatial Coupling of each device, really
Determine the coordinate of each cue ball and each attached ball in the rectangular coordinate system of the real space for building；Set up by linearly or nonlinearly equation group
Transformation relation between them；According to the method for solving of linearly or nonlinearly equation group, coordinate is set up linearly or nonlinear transformation
Coefficient, demarcated the transformation matrix of image space；According to different capture apparatus imaging models, derive equipment inside and
External parameter matrix, demarcates the parameters of capture apparatus；
4., the transformation matrix of coordinates of uncalibrated image space and two-dimensional space, using the 3. described side of the demarcating steps of image space
Method, determines the transformation parameter needed in scaling method, sets up coordinate conversion relation, the transformation matrix in uncalibrated image space；Foundation
Different capture apparatus imaging models, can also derive the inside and outside parameter matrix of capture apparatus, demarcate capture apparatus
Parameters；
5., the transformation matrix of coordinates of uncalibrated image space and three dimensions, using the 3. described side of the demarcating steps of image space
Method, determines the transformation parameter needed in scaling method, sets up transformation relation, the transformation matrix in uncalibrated image space；According to different
Capture apparatus imaging model, can derive the inside and outside parameter matrix of equipment, demarcate the parameters of capture apparatus.
Beneficial effects of the present invention：
The present invention has obvious advanced compared with background technology, there is provided a kind of simply and intuitively three-dimensional tree shape dress is put and real
Apply scheme, can quickly and accurately build three-dimensional cartesian rectangular coordinate system, build space geometrical element point, line, surface, body and
Judge the geometrical relationship between them, determine that coordinate of the space geometrical element in three-dimensional cartesian coordinate system is characterized, and use
Apparatus of the present invention are demarcated and parse image space.Specific implementer's case is based on geometry principle, is filled with reference to the present invention
The advantage put, illustrating in detail apparatus of the present invention and is closed in the structure of three-dimensional system of coordinate, the structure of space geometrical element and geometry
The judgement of system, characterize space geometrical element coordinate in a coordinate system and its relation and shot using multiple devices and Duo Tai
Equipment is demarcated to image space.
Brief description of the drawings
Fig. 1, be provided with cylinder base symmetrical mounting top view.
The front view of Fig. 2, symmetrical mounting.
The front view of Fig. 3, asymmetric unit.
Fig. 4, be provided with cuboid base symmetrical mounting top view.
The upward view of Fig. 5, cylinder base.
The upward view of Fig. 6, cuboid base.
The inventory of reference is as follows shown in each figures of Fig. 1 ~ Fig. 6：
1. cue ball, 2. forecourt, 3. after ball, 4. left ball, 5. right ball, 6. goes up ball, 7. plays ball, 8. front rod, 9. after connect
Bar, 10. left connecting rod, 11. right connecting rods, 12. upper connecting rods, 13. lower links, 14. base connecting rods, 15. bases, 16. annulars
Magnet.
The structure schematic diagram of Fig. 7 cuboids.
Shown in figure, round dot 1-8：8 devices；12 straight lines：12 beam laser；Round dot 1-4 builds lower surface；5-8 builds
Upper surface；1st, 2,6,5 preceding surface is built；4th, surface after 3,7,8 structures；1st, 4,5,8 left surface is built；2nd, 3,7,8 right table is built
Face.
The relation schematic diagram of Fig. 8 points and lines in space（Point is outside straight line）.
Shown in figure, 1-4 round dots：4 devices；2 straight lines：2 beam laser；
Round dot 1-3：Build the device of geometrical relationship；Round dot 4：Servicing unit.
The top view of Fig. 9 spatial points and plane relation（Point is outside plane）.
Figure a：Subpoint（That is round dot 10）In rectangle inside region；Figure b：In rectangle exterior lateral area；
Shown in figure, round dot 1-10：10 devices；6 straight lines：6 beam laser；Round dot 1-5：Build the device of geometrical relationship；Circle
Point 10：Point subpoint planar（5,10 overlap on top view）；Round dot 6-10：
Servicing unit；Solid line：Build the laser beam of geometrical relationship；Dotted line：Secondary laser beams.
The top view of Figure 10 space lines and linear relation（Different surface beeline）.
Figure a：General different surface beeline；Figure b：Antarafacial is vertical；
Shown in figure, round dot 1-11：11 devices；6 straight lines：6 beam laser；Round dot 1-4：Build the device of geometrical relationship；Circle
Point 5：Point subpoint planar（4,5 overlap on top view）Round dot 5-11：Servicing unit；Solid line：Build geometrical relationship
Laser beam；Dotted line：Secondary laser beams.
Specific embodiment
Operation principle of the present invention is described in detail below in conjunction with specific embodiment.
By the CAD design present apparatus, the structural requirement of device is met, and use device integral forming method is meeting design
The present apparatus is generated under required precision.The function of the present apparatus, one is to build a three-dimensional cartesian rectangular coordinate system；Two is to build sky
Between geometric element point, line, surface, body；Three is the coordinate for characterizing space geometrical element in three-dimensional cartesian coordinate system, i.e., in a structure
Determine that space point, line, surface and the three-dimensional coordinate of body are characterized in the three-dimensional cartesian coordinate system built, setting up geometric element space coordinates expires
The equation and relation of foot；Four is the geometrical relationship between decision space geometric element；Five is uncalibrated image space；Using the present invention
Device, by carrying out the conversion of image space and real space, determines that transformation matrix of coordinates comes uncalibrated image space.By parsing
Image can obtain three-dimensional coordinate of any pixel in real space on image, it is possible to achieve the actual geometry of subject is special
Levy measurement, such as between the length and space line between the size and profile, spatial point of object the quantitative measurment of angle and
Quantitative coordinate sign of complex space geometrical relationship etc..
（One）Build three-dimensional cartesian rectangular coordinate system
1. the origin of coordinates is built
The present apparatus can build a three-dimensional cartesian rectangular coordinate system, and the wherein centre of sphere of cue ball can be former as the coordinate of coordinate system
Point, referred to asOPoint.
2. reference axis is built
The origin of coordinates can determine that straight line with the centre of sphere of any one attached ball, so as to set up the reference axis of coordinate system, includingX, Y, ZThree positive and negative semiaxis in direction, can be referred to as positive and negativeOX, OY, OZAxle, whereinXAxle positive direction is to refer to from the cue ball centre of sphere
To forecourt centre of sphere direction,YAxle positive direction is to point to left ball centre of sphere direction from the cue ball centre of sphere,ZAxle positive direction is to refer to from the cue ball centre of sphere
Upward ball centre of sphere direction, and three axles meet right-handed helix relation.
3. coordinate plane is built
Any three centre ofs sphere of spheroid chosen not on the same line a, it may be determined that coordinate plane.Choose not same
The cue ball centre of sphere, the front/rear ball centre of sphere on straight line, the left/right ball centre of sphere, it may be determined that a plane, referred to asXOYPlane, or level
Face；Choose the cue ball centre of sphere, the front/rear ball centre of sphere not on the same line, the up/down ball centre of sphere, can determine that a plane, referred to asZOXPlane, or sagittal plane；Choose the cue ball centre of sphere, the left/right ball centre of sphere not on the same line, the up/down ball centre of sphere, it may be determined that
One plane, referred to asYOZPlane, or coronal-plane.Determine plane according to the coplanar attached ball centre of sphere of four and the above, then may be used
To improve the accuracy demarcated and parse image space plane.
4. three-dimensional cartesian rectangular coordinate system is built
Based on the origin of coordinates, three reference axis and three coordinate planes build a three-dimensional cartesian rectangular coordinate system.Based on seat
Mark origin, the orthogonal reference axis of any two and the coordinate plane determined by two orthogonal reference axis, build a two-dimentional flute
Karr rectangular coordinate system；Based on the origin of coordinates and any one reference axis, an one-dimensional cartesian coordinate system, i.e. number axis are built；
The origin of coordinates is based only upon, a zero dimension cartesian coordinate system, i.e., one point is built.
（Two）Build the geometric elements such as space point, line, surface, body
The device can be combined in the case where laser line generator is aided with and use, can build space point, line, surface, body with
And the geometrical relationship for judging between them.By laser beam, it is also possible to extend reference axis, coordinate plane and the sky for building space
Between yardstick.
1. one, space point is built
One the cue ball centre of sphere or the attached ball centre of sphere of device, can be used as a geometric point in three dimensions.It is being not particularly illustrated
In the case of, a point refers mainly to the cue ball centre of sphere of device, similar below.
2. space straight line is built
Gained knowledge according to geometry, 2 points can determine straight line, the i.e. line of any two device cue ball centre of sphere, can build three
Straight line in dimension space, and the line distance of the two centre ofs sphere is the distance between 2 points on straight line.
Specific embodiment：At least need two devices and a laser line generator.（1）Conventional method：Take two dresses
Put, be respectively placed on two transparent platforms in space（Hereinafter referred to as platform）, as two points in space.By rotation
Second platform, any one axle that the laser beam for launching a laser line generator can be successively from two devices passes through（X、Y
OrZ）.Now laser beam is the straight line that two devices build, and two cue ball centre ofs sphere of device are on this straight line；（2）
Specific process：Two devices are positioned in identical platform, by rotationZAxle adjusts two devices, makes laser beam successively from it
XAxle orYAxle passes through.Now laser beam is the straight line that two devices build, and two cue ball centre ofs sphere of device are at this
On bar straight line；（3）Any one reference axis of device is taken, straight line can be built；（4）Take one any the two of device
The centre of sphere of individual ball, can build straight line；（5）If point is outside straight line, can cross outside straight line and a little build directly by following proposal
The vertical line of line：Two devices are taken, is respectively placed on two platforms in space, as two points in space.It is a branch of to swash
Light passes sequentially through the cue ball centre of sphere of the two devices, constructs straight line.A laser line generator separately is taken, makes beam of laser
Can be by the 3rd deviceXOrYAxle, and produced with the straight line for building before and only produce an intersection point.Take the 4th dress
Put, be placed on this platform, keep the cue ball centre of sphere locus of the 3rd device constant, by rotating 3rd device and adjustment the
Four positions of device, make the 4th device cue ball centre of sphere be located on the intersection point of two beam laser, and two beam laser are respectively from itXWithYAxle passes through, then the cue ball centre of sphere of the 4th device is intersection point of the point to straight line, and the line of third and fourth device cue ball centre of sphere builds
Straight line intersected vertically with the straight line for building before；（6）If point is outside straight line, can be crossed outside straight line a bit by following proposal
Build the parallel lines of straight line：Two devices are taken, is respectively placed on two platforms in space, as the first of space and
2 two points.Beam of laser passes sequentially through the cue ball centre of sphere of the two devices, constructs straight line.Foundation crosses straight line outer
Point builds the vertical line method of straight line, and the 3rd device is done into vertical line to the straight line for having built, and the 4th is placed in the position of intersection point
Individual device, the third and fourth two devices build Article 2 straight line, along Article 2 straight-line pass one laser beam.Cross first or
The two devices change in coordinate axis direction vertical with straight line crosses 3rd device vertical with Article 2 straight line by three beams of laser beam
Change in coordinate axis direction by the 4th beam laser beam, and the third and fourth beam laser beam is intersecting and only one of which intersection point, on intersection point
Place the 5th device, and allow the third and fourth laser beam from two vertical reference axis while passing through, then first, fourth, three
With five devices or third and fourth, two and five device constitute a rectangle, i.e. the 3rd and the 5th device build straight line be exactly first
The parallel lines of bar straight line.
3. a plane in space is built
Gained knowledge according to geometry, any three points on the same line can not determine a plane, or two intersect or parallel
Straight line can also determine a plane.
Specific embodiment：At least need three devices and two laser line generators.（1）Conventional method：Take first and second
Two devices, are respectively placed on two platforms in space, used as two points in space.Take a laser line generator hair
Beam of laser is penetrated, passes through any one axle of laser beam successively from two devices（X、YOrZ）Pass through.Now, first and second liang
Individual device constructs the straight line in space.Second laser line generator transmitting laser beam is taken, makes laser beam from second
An axle in device in remaining two axle passes through, and takes the 3rd device, is positioned on the 3rd platform, adjusts the 3rd position of platform
Put, the second beam laser is passed through the 3rd any one axle of device（X、YOrZ）.Now, second and third two devices construct sky
Between Article 2 straight line, due to this deviceX、Y、ZThree axles are vertical two-by-two, then understand this article of straight line phase vertical with straight line
Hand over.From geometric knowledge, two is intersecting or parallel straight line can determine a plane, then this two beams laser constructs one only
One plane for existing, three cue ball centre ofs sphere of device are on that plane.To make this plane more directly perceived, the 3rd can be respectively taken
Laser line generator launches laser beam, and the axle from first device in remaining two axle passes through, and takes the 4th line laser hair
Raw device transmitting laser beam, the axle from the 3rd device in remaining two axle passes through, and ensures the third and fourth beam laser in sky
Between in one and only one intersection point, take the 4th device, be placed on four platformses, regulation four platformses position makes the 4th
The cue ball centre of sphere of individual device has two axles simultaneously by Article 3 and Article 4 laser beam on intersection point.Because this device hasX、Y、ZThree axles feature perpendicular to each other, then understand the Article 3 straight line that is built by third and fourth device and by the four, the one device structures
The Article 4 straight line built is vertical, and first and third straight line is parallel to each other, and second, four straight lines are parallel to each other, and opposite side distance two-by-two
Equal, four laser beams construct a rectangle.This four beams laser formed rectangle build plane on, four masters of device
The ball centre of sphere is on that plane.The space plane of structure can realize the diminution and amplification of plane by the movement of device.（2）It is special
Different directions or tendencies method：Three devices are positioned in identical platform, by adjust three positions of device, make two beam laser beams according toXAxle,YAxle（OrYAxle,XAxle）Order pass through from neighboring devices two-by-two successively, then build two of two laser beams intersect vertically straight
Line constructs a plane for uniquely existing, and three cue ball centre ofs sphere of device are on that plane.To make this plane more directly perceived, can
So that the never two neighboring device of third and fourth Shu Jiguang differenceXAxle,YAxle（OrYAxle,XAxle）Pass through, and two beam laser have and
Only one intersection point, the 4th device is also disposed in identical platform, adjusts the 4th position of device, makes its cue ball centre of sphere
On intersection point, andXAxle,YAxle passes through third and fourth laser beam simultaneously.Understand, then four laser beams form a rectangle, four
Device is located at four summits of rectangle, and in the plane for building, four cue ball centre ofs sphere of device are on that plane for this rectangle.（3）
One each coordinate surface of device, can build a plane in three dimensions respectively.（4）One device not same
Three ball centre ofs sphere on straight line, can build a plane in three dimensions respectively.
4. it is individual that space one is built
Gained knowledge by geometry, four points at grade are not assured that the body in space.In three dimensions, most
Common body is exactly cuboid, if the length of side of cuboid is all equal, then it is exactly square.Body in the present invention refers mainly to many
Face body, i.e., surround the body for forming and occupying certain space by multiple polygon planes.Specific embodiment mainly for polyhedron,
By taking cuboid as an example, for the body of spatial complex, can be using similar construction method.
Specific embodiment：Need eight devices and 12 laser line generators；
（1）Conventional method：The process of specifically setting up of lower surface builds rectangle with above-described using four devices, determines plane
In conventional method it is identical, lower surface has used first to the 4th device, has used four laser line generators, produces respectively
First to the 4th beam laser, constructs rectangle, and four cue ball centre ofs sphere of device are four summits of rectangular undersurface；Separately take four
Laser line generator, produces the 5th to the 8th beam laser, respectively from first to the 4th in device upwards in the lower section of lower surface
Pass through in a remaining axle, then four beam laser are each perpendicular to lower surface；The the 5th to the 8th device separately is taken, four lines has been reused and has been swashed
Optical generator, produces the 9th to the 12nd beam laser respectively, and rectangle, and the 5th to the are built using with lower surface identical method
A remaining axle of eight devices is passed through respectively by the 5th to the 8th beam laser, then the 9th to the 12nd beam laser constructs rectangle, the
Five to the 8th cue ball centre ofs sphere of device are four summits of rectangular top surface.Because this device hasX、Y、ZThree axles hang down two-by-two
Straight the characteristics of, therefore the 5th to the 8th beam laser must be perpendicular to upper surface, laser beam corresponding with upper and lower surface forms rectangle respectively,
The surface of front, rear, left and right four of cuboid is constructed, 12 beam laser are 12 seamed edges of cuboid.By above-mentioned side
Method, using eight devices, 12 beam laser of auxiliary construct cuboid, with six square surfaces, eight summits, 12 ribs
Side.See Fig. 7.
（2）Specific process：The process of specifically setting up of lower surface builds rectangle with above-described using four devices, it is determined that
Specific process in plane is identical, and lower surface has used first to the 4th device, has used four laser line generators, respectively
The first to the 4th beam laser is produced, rectangle is constructed, four cue ball centre ofs sphere of device are four summits of rectangular undersurface；Separately take
Four laser line generators, the 5th to the 8th beam laser is produced in the lower section of lower surface upwards, respectively from first to the 4th dress
PutZAxle passes through, then four beam laser are each perpendicular to lower surface；The the 5th to the 8th device separately is taken, four line lasers have been reused
Generator, produces the 9th to the 12nd beam laser respectively, and rectangle, and the 5th to the 8th are built using with lower surface identical method
DeviceZAxle is passed through respectively by the 5th to the 8th beam laser, then the 9th to the 12nd beam laser constructs rectangle, the 5th to the 8th
The cue ball centre of sphere of individual device is four summits of rectangular top surface.5th to the 8th beam laser is corresponding with upper and lower surface respectively to swash
Light beam forms rectangle, constructs the surface of front, rear, left and right four of cuboid, and 12 beam laser are 12 ribs of cuboid
Side.By the above method, using eight devices, 12 beam laser of auxiliary construct cuboid, with six square surfaces, eight
Summit, 12 seamed edges.The cuboid of structure can realize the diminution and amplification of rectangular parallelepiped space by the movement of device.
（Three）Characterize coordinate of the space geometrical element in three-dimensional cartesian rectangular coordinate system
1. coordinate of the point in three-dimensional cartesian rectangular coordinate system is characterized
Coordinate of the point in three-dimensional cartesian rectangular coordinate system, can make upright projection to three axles of coordinate system respectively by point,
Subpoint is the absolute value of coordinate a little to the distance of the origin of coordinates.If using coordinate as the algebraic quantity with symbol, can be with
The positive axis of reference axis is according to subpoint, then coordinate is on the occasion of conversely, being negative value.In order to determine spatial point in three-dimensional flute
The coordinate of karr rectangular coordinate system, generally requires eight devices, 12 laser line generators and two blocks of transparent plate glass.
So that point position in space is in the first octant of coordinate system as an example, specific embodiment is as follows.
Conventional method：
（1）Level fixes one flat plate glass as underlying platform, takes a device, is named asa1（Below it is similar to）It is placed on bottom
On layer platform, Descartes's rectangular coordinate system is built；
（2）Take a deviceb3, as one, the space point set up, are placed into space the first octant optional position, in its lower placement
Another block of plate glass is used as top layer platform；
（3）Launch three beams of laser with three laser line generators, by the origin of coordinate system, respectively along three of reference axis
Positive direction；
（4）Along devicea1XAxle positive direction, places a device on underlying platforma2 and laser beam is allowed along itXAxle passes through, dress
Puta1 Hea2 build straight line, used as the Descartes's rectangular coordinate system for extendingXAxle；
（5）Along devicea1YAxle positive direction, places a device on underlying platforma4 and allow laser beam to pass through along its Y-axis, fill
Put a1 and a4 and build straight line, as the Descartes's rectangular coordinate system for extendingYAxle；
（6）Along devicea1ZAxle positive direction, places a device on top layer platformb1 and allow laser beam to pass through along its Z axis, fill
Puta1 Heb1 builds straight line, used as the Descartes's rectangular coordinate system for extendingZAxle；
（7）Take a devicea3 and a laser line generator, it is placed on underlying platform, it is ensured that from deviceb3 edgesZAxle losing side
To the laser beam for passing through just from devicea3ZAxle passes through, devicea3 Hesb3 build straight line；
（8）Two laser line generators are taken, launches laser beam, and ensure devicea2XAxle anda3ZDirection of principal axis does not change
In the case of, translationa2 and rotationa3, make laser beam edgea2YAxle positive direction passes through and passes througha3YAxle, similarly, it is ensured that dress
Puta4YIn the case of direction of principal axis is immovable, translationa4, make another laser beam edgea4XAxle positive direction passes through and passes througha3X
Axle, then four devicesa1-a4 on same floor plane and formed a rectangle；
（9）Take a deviceb2 and a laser line generator, it is placed on top layer platform, it is ensured that from devicea2 edgesZAxle is square
To the laser beam for passing through just from deviceb2ZAxle passes through, devicea2 Hesb2 build straight line；
（10）Two laser line generators are taken, launches laser beam, and ensure deviceb1 Heb2ZThe immovable situation of direction of principal axis
Under, rotation regulationb1 Heb2, make laser beam edgeb1XAxle positive direction passes through and passes throughb2XAxle, similarly, rotation adjustment deviceb3, it is ensured that another laser beam edgeb2YAxle positive direction passes through and passes throughb3YAxle, then four devicesa1、a2、b1 Heb2 same
One plane（Referred to as side 1）And one rectangle of formation, a2、a3、b2 Hesb3 in one rectangle of approximately the same plane and formation（Side
Face 2）, it is known that side 1,2 is each perpendicular to orthogonal between floor plane, and two planes；
（11）Take a deviceb4 and a laser line generator, it is placed on top layer platform, it is ensured that from devicea4 edgesZAxle is square
To the laser beam for passing through just from deviceb4ZAxle passes through, devicea4 Hesb4 build straight line；
（12）Two laser line generators are taken, launches laser beam, and ensure deviceb4ZIn the case of direction of principal axis is immovable,
Rotationb4, it is ensured that laser beam edgeb1YAxle positive direction passes through and by deviceb4YAxle, similarly, adjusting meansb4, it is ensured that another
One laser beam edgeb3XAxle negative direction passes through and passes throughb4XAxle, then four devicesa3、a4、b3 Hesb4 in approximately the same plane
（Side 3）And one rectangle of formation, a1、a4、b1 Heb4 in approximately the same plane（Side 4）And form a rectangle, it is known that this side
Face 3,4 is each perpendicular to floor plane, and side 1-4 is orthogonal two-by-two, while four devicesb1-b4 is flat in same top layer
One rectangle in face and formation, and top-most-surface plane is parallel with floor plane, it is orthogonal with four additional side；
（13）By above-mentioned operating procedure, eight devicesa1-a4、b1-b4 build a cuboid just, by measurement apparatusa1 arrivesa2,a1 arrivesa4 Hesa1 arrivesb1 cue ball centre of sphere distance, it may be determined that space a bit, devicebThe 3 cue ball centre of sphere, is building
Descartes's rectangular coordinate system coordinate value.Because in aforesaid operations, spatial point is in the first octant, and distance is exactly coordinate value.
Consider residing different octants, coordinate value can be modified to the algebraic value of tape symbol, and specific method is exactly according to devicea2、a4 Hesb1 is in corresponding axis（RespectivelyX,YWithZAxle）Positive axis, then the coordinate value of spatial point is for just；Conversely, coordinate value is then
It is negative.
Specific process：Determine coordinate of the spatial point in three-dimensional cartesian rectangular coordinate system, also there is a kind of relatively easy
Method, five devices, six laser line generators and two blocks of transparent plate glass are needed in this case.Specific embodiment party
Case is as follows：
（1）Level fixes one flat plate glass as underlying platform, takes a devicea1, using the magnetic chuck below device,
It is fixed on a glass plate for surfacing, builds Descartes's rectangular coordinate system；
（2）Choose a devicea5, as one, the space point set up, are placed into the optional position of the octant of space first, under it
Another block of plate glass of horizontal positioned is used as top layer platform；
（3）Launch three beams of laser with three laser line generators, by the origin of coordinate system, respectively along three of reference axis
Positive direction；
（4）Along devicea1XAxle positive direction, places a device on underlying platforma2 and allow laser beam from itsXAxle passes through, dress
Puta1 Hea2 build straight line, used as the Descartes's rectangular coordinate system for extendingXAxle；
（5）Along devicea1YAxle positive direction, places a device on underlying platforma4 and allow laser beam from itsYAxle passes through, dress
Puta1 Hea4 build straight line, used as the Descartes's rectangular coordinate system for extendingYAxle；
（6）Take a devicea3 and a laser line generator, it is placed on underlying platform, it is ensured that from devicea3 along Z axis losing side
To the laser beam for passing through just from devicea5 Z axis pass through, devicea3 Hesa5 build straight line；
（7）Two laser line generators are taken, launches laser beam, and ensure devicea2XAxle anda3ZDirection of principal axis does not change
In the case of, translationa2 and rotationa3, make laser beam edgea2YAxle positive direction passes through and passes througha3YAxle, similarly, it is ensured that dress
Puta4YIn the case of direction of principal axis is immovable, translationa4, make another laser beam edgea4XAxle positive direction passes through and passes througha3X
Axle, then four devicesa1-a4 on same floor plane and formed a rectangle；
（8）By above-mentioned operating procedure, four devicesa1-a4 build a rectangle just, by measurement apparatusa1 arrivesa2,a1 arrivesa4 Hesa3 arrivea5 cue ball centre of sphere distance, it is possible to determine space a bit, deviceaThe 5 cue ball centre of sphere, in the flute card for building
The coordinate value of your rectangular coordinate system.In aforesaid operations, because spatial point is in the first octant, distance is exactly coordinate value.Consider institute
The different octants at place, coordinate value can be modified to the algebraic value of tape symbol, and specific method is exactly according to devicea2、a4 Hesa5 are in
Corresponding axis（RespectivelyX,YWithZAxle）Positive axis, then the coordinate value of spatial point is for just；Conversely, coordinate value is then negative.
Especially, in conventional method, ifb3 arriveXOY、YOZWithZOXThe distance of any one plane in three planes is
Zero, i.e. spatial point planar, in this case need four devices, four laser line generators.It is similar with the above method,
A rectangle is built in this plane, by measuring origin（Devicea1）The cue ball centre of sphere distance of device on to each axle, it may be determined that
DevicebCoordinate value of the 3 cue ball centre of sphere in the Descartes's rectangular coordinate system for building；Further, in conventional method, ifb3 pairsXOY、YOZWithZOXThe subpoint of any one plane in three planes existsX、Y, on any one axles of Z, three are needed in this case
Individual device, two laser line generators.It is similar with the above method, by measuring origin（Devicea1）The cue ball of device on to each axle
Centre of sphere distance, it may be determined that devicebCoordinate value of the 3 cue ball centre of sphere in the Descartes's rectangular coordinate system for building；Further move back
Change, in conventional method, ifb3 arriveX、Y, any two axles of Z distance be zero, that is, put on axle, need in this case two dress
Put, a laser line generator.It is similar with the above method, by measuring origin（Devicea1）The cue ball ball of device on to this axle
Heart distance, determining devicebThe coordinate value of the 3 cue ball centre of sphere；Finally, in conventional method, ifb3 arriveX、Y, the axles of Z tri- distance
All it is zero, i.e. deviceb3 is origin, and coordinate is（0,0,0）.The coordinate of point is characterized as the coordinate a little in coordinate system.
2. coordinate of the straight line in three-dimensional cartesian rectangular coordinate system is characterized
Specific embodiment：Similar to coordinate characterizing method of the point in three-dimensional cartesian rectangular coordinate system, determine to build respectively
Coordinate of two devices of straight line in the three-dimensional cartesian rectangular coordinate system for building is straight using the space introduced in analytic geometry
The determination method of line, provides equation in coordinates of the straight line in three-dimensional cartesian rectangular coordinate system.The coordinate of straight line is characterized as straight line
The equation that the coordinate of upper arbitrfary point is met.
3rd, coordinate of the plane in three-dimensional cartesian rectangular coordinate system is characterized
Specific embodiment：Similar to the coordinate characterizing method of point, optionally not conllinear three dresses from the device of plane is built
Put, coordinate of this three devices in the three-dimensional cartesian rectangular coordinate system for building is provided respectively, in recycling analytic geometry
Space plane determines method, provides equation in coordinates of the plane in three-dimensional cartesian rectangular coordinate system.The coordinate of plane is characterized as
The equation that the coordinate of arbitrfary point is met in plane.
4th, coordinate of the body in three-dimensional cartesian rectangular coordinate system is characterized
Specific embodiment：Similar to the coordinate characterizing method of point, arbitrarily chosen not at one from polyhedral each surface
Three devices on straight line, set up the plane equation on each surface, and polyhedron is then that the equation met by each surface is constituted
The space that inequation group is surrounded；Coordinate for cuboid is characterized, optionally not same on each surface from cuboid
Three summits of straight line, provide coordinate of this three summits in the three-dimensional cartesian rectangular coordinate system for building respectively, recycle
The determination method of the space cuboid in analytic geometry, cuboid is the inequation group that the equation met by each surface is constituted
The space for being surrounded.
（Four）The geometrical relationship of decision space geometric element
The judgement of geometrical relationship includes between space geometrical element：Point and point, Points And lines, point and face, point and body, straight line and directly
Line, straight line and face, straight line and body, face and face, face and body, body and body, and other space geometry relations judgement.
1. decision space point and point geometrical relationship
, it is necessary to a point in two devices, respectively space during geometrical relationship between decision space point and point.If two dresses
The distance between cue ball centre of sphere put is zero, then the two points are spatially to overlap, that is, be considered a point, it is only necessary to one
Individual device；If the distance of two cue ball centre ofs sphere of device is not zero, the two point be spatially it is misaligned, i.e., this
2 points is disjoint relationship；Can also be characterized according to coordinate of the point in rectangular coordinate system, according to analytic geometry cathetus equation it
Between relation, judge straight line between geometrical relationship；If the coordinate of two cue ball centre ofs sphere of device in rectangular coordinate system is identical,
Then the two points are to overlap, conversely, misaligned.
Specific embodiment：（1）Take two devices, be placed on respectively on two platforms in space, they as
Two points in space.Make one laser beam successively from two devicesXAxle,YAxle orZAxle passes through, then this laser beam constructs one
Bar straight line, the line of the stream oriented device cue ball centre of sphere is the distance between 2 points of space.Whether it is zero by distance, can be easy to really
Determine the space geometry relation between them；（2）Can also be characterized according to coordinate of the point in rectangular coordinate system, determine two devices
Coordinate of the big ball centre of sphere in rectangular coordinate system, according to the method for analytic geometry, by coordinate it is whether identical come determine a little and
Whether overlapped between point.Because apparatus of the present invention have certain physical dimension, in practical operation, two devices can not
Can overlap, therefore the relation between 2 points is only disjoint relationship.
2. the geometrical relationship of decision space point and straight line
, it is necessary to three devices build point and straight line, two of which device can build one for the geometrical relationship of decision space point and straight line
Bar straight line, another device can be used as one, space point.If the 3rd cue ball centre of sphere of device is just straight by what is had been built up
Line, then understand the point（The cue ball centre of sphere）On straight line；Conversely, then can determine that a little not on straight line, that is, put outside straight line.Now,
Intersection point a little on straight line can be found by the way that the method for making vertical line to straight line will be put, then the 3rd cue ball centre of sphere of device is to straight line
Vertical range, as point to straight line distance.
Specific embodiment：Need four devices and two laser line generators.
（1）Conventional method：Two devices are taken, is respectively placed on two platforms in space, as two of space
Point.Beam of laser passes sequentially through the cue ball centre of sphere of the two devices, constructs straight line.The 3rd device is taken as space
A bit, it is placed on another platform, if keeping the cue ball centre of sphere locus of the 3rd device constant, is filled by rotation the 3rd
Put, the first beam laser can be made by any one axle of 3rd device, then can determine that a little on straight line.If beam of laser is not
Can then be can determine that a little outside straight line by any one axle of 3rd device；Can also determine a little and straight line is in rectangular coordinate system
Coordinate, whether the equation of straight line is met according to the coordinate at analytic geometry midpoint, judge that point is on straight line with the relation of straight line
Or outside straight line.
It is determined that distance of the point to straight line, can be by following proposal：A laser line generator separately is taken, makes the beam of laser can
With by the 3rd axle of device, and produced with the straight line for building before and only produce an intersection point.The 4th device is taken,
It is placed on four platformses, keeps the cue ball centre of sphere locus of the 3rd device constant, by rotating 3rd device and adjustment
4th position of device, makes the 4th device cue ball centre of sphere be located on the intersection point of two beam laser, and two beam laser are respectively from it
Two axles pass through, then the cue ball centre of sphere of the 4th device is an intersection point of the point to straight line, and the line of third and fourth device cue ball centre of sphere is the
Three devices built the vertical line of straight line before, and wire length is distance a little to straight line.Point is not zero to the distance of straight line,
Put outside straight line.Schematic diagram is shown in accompanying drawing 8.
（2）Specific process：Two devices are positioned in identical platform.Beam of laser passes sequentially through the master of the two devices
The ball centre of sphere, constructs straight line.The 3rd device is taken as a bit, is placed on this platform, if the 3rd device of holding
Cue ball centre of sphere locus is constant, by rotating 3rd device, the first beam laser can be made to pass through 3rd deviceXOrYAxle, then
Can determine that a little on straight line.If beam of laser can not be by 3rd deviceXOrYAxle, then can determine that a little outside straight line.
If point is outside straight line, can be by following proposal, it is determined that distance of the point to straight line：It is another to take a line laser generation
Device, allows beam of laser by the 3rd deviceXOrYAxle, and produced with the straight line for building before and only produce a friendship
Point.The 4th device is taken, is placed on this platform, keep the cue ball centre of sphere locus of the 3rd device constant, by rotation the
The 4th position of device of three devices and adjustment, makes the 4th device cue ball centre of sphere be located on the intersection point of two beam laser, and two beams
Laser is respectively from itXWithYAxle passes through, then the cue ball centre of sphere of the 4th device is intersection point of the point to straight line, third and fourth device cue ball
The line of the centre of sphere is the vertical line that the 3rd device built straight line before, and wire length is distance a little to straight line.Point is to directly
The distance of line is not zero, that is, put outside straight line.
（3）Can also determine a little and coordinate of the straight line in rectangular coordinate system, according to analytic geometry midpoint to straight line away from
From whether being zero, judge that point is on straight line or outside straight line with the relation of straight line.
3. the geometrical relationship of decision space point and plane
The geometrical relationship of decision space point and plane, at least needs five devices to build point and plane, wherein four devices can be with
A plane is built, another is then as a point in space.If spatial point is zero to the vertical range of plane, this is can determine that
Point is planar；Conversely, then can determine that the point outside plane；If point outside plane, can determine a little arrive plane it is vertical away from
From；Whether plane equation can also be met according to the coordinate of point according to the method for analytic geometry, or the distance put to plane is
No is zero, and decision-point is in the plane or outside plane.
Specific embodiment：（1）Geometrical relationship between decision space point and plane is, it is necessary to seven devices and five lines swash
Optical generator.Four devices and four laser line generators are taken, according to the conventional method structure that this claims midplane builds
A plane is built, four beam laser form a rectangle, and four cue ball centre ofs sphere of device are on that plane；The 5th device is taken to place
In on another platform, as a bit in space；The six, the 7 two devices are taken, is individually placed to build on the opposite side of rectangle, made
The two beam laser for building rectangle pass through an axle of the six, the seven devices respectively, then the six, the 7 two cue ball centre ofs sphere difference of device
On two opposite side；The 5th laser line generator transmitting laser beam is taken, it is passed sequentially through the six, the seven devices two axles of residue
Any one axle, then the 5th beam laser is all vertical with the opposite side where the six, the seven devices；If keeping the 5th cue ball ball of device
Heart locus is constant, by rotating the 5th device, and parallel or vertical relation the base between five beam laser are still kept
On plinth, along each side of rectangle（And its on extended line）The position of the six, the seven devices is adjusted, the 5th beam laser can be made to pass through the 5th
Any one axle of device, then can determine that spatial point in the plane, and the vertical range of point to plane is zero.If the 5th beam laser
Cannot then can determine that spatial point outside plane by any one axle of the 5th device；
（2）If spatial point is outside plane, spatial point to the distance of plane can be determined by following proposal, at most need ten
Device and seven laser line generators：On the basis of previously described embodiment, then the eight, the 9 two devices are taken, put respectively
On another two opposite side of rectangle, make the another two beams laser of structure rectangle respectively by an axle of the eight, the nine devices, then the
8th, 9 two cue ball centre ofs sphere of device are respectively on another two opposite side；The 6th laser line generator transmitting laser beam is taken, makes it
Any one axle of the eight, the nine devices two axles of residue is passed sequentially through, then the 6th beam laser and the opposite side where the eight, the nine devices all hang down
Directly；The 7th laser line generator transmitting laser beam is taken, is passed through from an axle of the 5th device, make it flat with what is set up before
Face produces intersection point, by rotating the 5th device, and parallel or vertical relation the basis between the first six Shu Jiguang is still kept
On, along each side of rectangle（And on extended line）The the 6th to the 9th position of device is adjusted, the five, the six, seven beam laser can be made
Intersect at a bit, the tenth device is placed on point of intersection, and ensure the five, the six, seven beam laser respectively by the tenth device
Three axles pass through, then in the plane, the 7th beam laser and plane are vertical relations to the cue ball centre of sphere of the tenth device, the tenth device
The distance between upright projection point of the cue ball centre of sphere for space a little planar, the 5th and the tenth device cue ball centre of sphere are space
Distance of the point to plane.Whether whether it is zero according to the vertical range of point to plane, it is possible to determine that in the plane to put.Schematic diagram is shown in
Accompanying drawing 9, wherein, a）Upright projection point in rectangular area, b）Upright projection point is outside rectangular area；
（3）Can also determine a little and coordinate of the plane in rectangular coordinate system, whether the coordinate according to point meets plane equation, sentences
Fixed point is in the plane or outside plane；Or whether can also be zero according to the distance at analytic geometry midpoint to plane, judge a little
It is on straight line or outside straight line with the relation of straight line.
4. the geometrical relationship between decision space point and body
The geometrical relationship of decision space point and body, refers mainly to spatial point and polyhedral relation, for spatial point and complicated body
Relation, can be using similar method treatment.According to each surface regional relation that space split for constituting body, decision-point and
The position relationship on each surface of body, if point is located at constitutes the space that each surface of body surrounds, puts in vivo；If point is located at
Constitute on each surface of body, then put on body；If point is not located at constitutes the space that each surface of body surrounds, body does not include
Point, i.e., point with body be from relation；Can also decision-point and polyhedral each surface, each bar seamed edge and each summit it
Between geometrical relationship；If the vertical range put to some surface of polyhedron is zero, this can be determined on the surface of the body
On；If the vertical range of point to a certain seamed edge of polyhedron is zero, can determine the point on seamed edge；If point is a certain to polyhedron
The distance on summit is zero, then can determine that the point overlaps with summit；Can also determine a little and polyhedron is in rectangular coordinate system
Whether coordinate is characterized, according to the coordinate of point polyhedral inequation group can be made less than zero, equal to zero or more than zero, is judged
Point is in polyhedron, on polyhedron or external in multiaspect；The judgement with cuboid geometrical relationship is put similar to above-mentioned point
With the judgement of polyhedron relation.
Specific embodiment：By taking cuboid as an example, using nine devices and 12 beam laser, wherein eight devices and 12
Shu Jiguang constructs, another device build space in a bit.After the locus of point and body determines, it is possible to determine that point
The position relationship on each surface of space is split regional relation with each surface for constituting cuboid, decision-point and body, from
And decision-point is in the outside of cuboid, on surface or positioned at the inside of cuboid；Point and cuboid can also be based on straight
Coordinate in angular coordinate system is characterized, according to the coordinate of point whether the inequation group of cuboid can be made less than zero, equal to zero or
Person is more than zero, and decision-point is in cuboid, on cuboid or rectangular external.
5. the geometrical relationship of straight line and straight line is judged
Judge the geometrical relationship between straight line and straight line, it is necessary to four devices, build two straight lines respectively.Being gained knowledge by geometry can
Know, three for being arbitrarily not arranged on the same straight line point can determine a plane.From four devices, optionally not in straight line
On three devices, build a plane.Another device carries out upright projection to the plane that first three device builds, according to point
To the distance of plane, it may be determined that the geometrical relationship between this two straight lines, if vertical range is zero, this device is also in plane
Interior, i.e., this two straight lines are coplanar line；Conversely, if vertical range is not zero, this device not planar, this two straight lines
It is different surface beeline.
If two geometrical relationships of straight line are coplanar line, two devices on wherein any straight line can be distinguished
Upright projection is carried out to another straight line, according to the difference for obtaining intersection point, is divided into following three kinds of situations：1）Intersection point be all device from
If body, then can be determined that this two straight lines are coincidence relation；2）If obtaining two intersection points, and projected with two intersection points and two
The cue ball centre of sphere of device is that four summits form a rectangle, then can determine that two former straight lines are the parallel relation in plane；
3）If obtaining two intersection points, but rectangle cannot be formed；Or two intersection points overlap；Can then judge two straight lines as in plane
Overlapping relation；Wherein, if two intersection points overlap, can be determined that two straight lines is the relation that intersects vertically.Schematic diagram is shown in accompanying drawing 10.
If the vertical range that two straight lines are different surface beeline, i.e. another device builds plane to first three device is not zero.
Out-of-plane straight line is being built to upright projection is done in plane, if former straight line of the projection line in plane, two former straight lines
Geometrical relationship be antarafacial vertical relation；If projection line is not orthogonal to the former straight line in plane, two former straight lines are different surface beeline
The universal relation in space.Gained knowledge from geometry, and the straight line that all intersects vertically of two different surface beelines to be called two antarafacials straight
The common vertical line of line.
Can also be characterized according to coordinate of the straight line in rectangular coordinate system, according to the pass between analytic geometry cathetus equation
System, judge the antarafacial between straight line, it is coplanar, parallel, the relation such as intersect, intersect vertically
Specific embodiment：Four devices are taken, first and second device builds straight line, and it is straight that third and fourth device builds Article 2
Line, and any three devices are not point-blank.Appoint and take three devices one planes of structure, according in this claims
Whether planar the embodiment of " relation between decision-point and plane ", judge the 4th device, if device is in plane
Interior, then two former straight lines are coplanar line, if being different surface beeline not planar.
If coplanar line, make two devices on wherein straight line（By taking third and fourth device as an example）Respectively to another
Bar straight line makees vertical line, according to the embodiment of " relation between decision-point and straight line " in this claims, finds third and fourth
Intersection point of the device on straight line.According to the difference for obtaining intersection point, then two geometrical relationships of straight line are can be determined that.
If different surface beeline, according to the embodiment of " relation between decision-point and plane " in this specification, the 4th is crossed
Individual device does upright projection to the plane that first three device builds, and finds the upright projection point in plane, takes the 5th device and puts
At subpoint, then the three, the five devices construct Article 3 straight line, are Article 2 straight line projection lines planar, then first,
Three straight lines are coplanar line, and two straight lines are misaligned, according to the embodiment of above-described coplanar line, if Article 3 is straight
Line is antarafacial vertical relation perpendicular to straight line, then first and second straight line；If Article 3 straight line is not orthogonal to first directly
Line, then first and second straight line is the universal relation of different surface beeline.The six, the seven devices are taken, is individually placed on two platforms, make
First, two beam laser separately take a laser line generator respectively by the six, the seven any one axles of device, produce the 7th beam
Laser, passes through from the axle in the 6th remaining two axle of device, the 7th device of directive, it is ensured that the cue ball of the six, the seven devices
The centre of sphere is respectively on the basis of first and second straight line, while position and the anglec of rotation of the six, the seven devices are adjusted, until the 7th
Shu Jiguang can also pass through from the axle in the 7th remaining two axle of device, because the axle of apparatus of the present invention three is vertical two-by-two, then the
Seven beam laser are vertical with first and second straight line, and the laser beam between the six, the seven devices is two articles of common vertical lines of different surface beeline.
Can also be characterized according to coordinate of the straight line in rectangular coordinate system, according to the pass between analytic geometry cathetus equation
System, judge the antarafacial between straight line, it is coplanar, parallel, the relation such as intersect, intersect vertically.
6. the geometrical relationship of decision space straight line and plane
The geometrical relationship of decision space straight line and plane is, it is necessary to six devices structure straight line and planes, four devices therein can
To build a plane, two other builds the straight line in space.Gained knowledge from geometry, in straight line parallel plane
Straight line, then this straight line is parallel with plane.During the geometrical relationship of judgement straight line and plane, by two devices on straight line
Upright projection is carried out to plane respectively, then two subpoints can planar set up straight line.If space line and projection
Straight line overlaps, and decision space straight line is planar；If straight line subpoint in the plane is to overlap, space line and plane
It is the relation for intersecting vertically；It is overlapping relation if space line and projection straight line are intersecting；If space line and projection straight line are flat
OK, can determine that be parallel relation, then straight line and plane distance be the distance between space line and projection straight line.If space is straight
Line and plane are intersecting, then the angle of straight line and plane is the angle between space line and projection straight line；
Can also be characterized according to the coordinate of straight line and plane in rectangular coordinate system, according to analytic geometry cathetus and plane equation
Between relation, judge the straight line between straight line and plane in face, straight line intersects with plane, intersects vertically, straight line and plane
The relation such as parallel.
Specific embodiment is：The method that plane and straight line are built according to this specification, uses six devices and five lines
Laser generator builds a plane and straight line respectively；Two devices on space line are carried out to the plane for building respectively
Upright projection, according to the embodiment of " geometrical relationship of decision-point and plane " in this specification, can respectively obtain on straight line
Two devices upright projection point in the plane, can be built between two subpoints straight line or coincidence, i.e. projection line or
The subpoint of coincidence, according to the geometrical relationship between space line and projection straight line, it is possible to determine that space line and plane it is several
What relation；Characterized according to coordinate in rectangular coordinate system of straight line and plane, according to analytic geometry cathetus and plane equation it
Between relation, judge the straight line between straight line and plane in face, straight line intersects with plane, intersects vertically, and straight line is flat with plane
The relations such as row.
7. the geometrical relationship of decision space straight line and body
Geometrical relationship between decision space straight line and body, refers mainly to straight line and polyhedral relation, for straight line and complicated body
Spatial relationship, can be using similar method.According to the regional relation that space is split on each surface for constituting body, judge straight
The geometrical relationship on each surface of line and body, if the point on straight line has the space surrounded positioned at each surface for constituting body, directly
Line and body phase are handed over；If straight line is located on each surface for constituting body or is overlapped with seamed edge, straight line is on body；If the point on straight line
Be not located at and constitute the space that each surface of body surrounds, then straight line and body be from relation；Can also decision-point and multiaspect
Geometrical relationship between each surface of body, each bar seamed edge and each summit；According to straight line and body in rectangular coordinate system
Coordinate is characterized, and according to the relation between analytic geometry cathetus equation and the inequation group of body, is judged between straight line and body
On the face of body, it is intersecting or from etc. relation.The judgement of straight line and cuboid geometrical relationship similar to above-mentioned straight line with it is many
The judgement of face body geometrical relationship.
Specific embodiment：By taking cuboid as an example, the method that straight line and cuboid are built according to this specification uses ten
Device and 13 laser line generators build straight line and body, and eight devices therein build a cuboid, another two device
Build straight line.After the locus of straight line and body determines, can be by the space on each surface of straight line and cuboid
Geometrical relationship, so as to finally judge the geometrical relationship of straight line and cuboid；Can be determined that each surface of straight line and cuboid, each
Geometrical relationship between bar seamed edge and each summit, using point and straight line, straight line and straight line and straight line and plane geometry pass
The decision method of system, judges the geometrical relationship on summit and straight line, straight line and each seamed edge and straight line and each surface；According to straight line and
Coordinate of the cuboid in rectangular coordinate system is characterized, the inequation group according to analytic geometry cathetus equation and cuboid it
Between relation, judge the straight line between straight line and cuboid on the face of body, straight line and the cross, straight line of body phase and body phase are from waiting pass
System.
8. the geometrical relationship of decision space plane and plane
The geometrical relationship of judgement plane and plane is, it is necessary to 8 devices build two planes respectively.
（1）Four devices in one plane carry out upright projection to another plane respectively, are filled to projection according to four devices
Put the geometrical relationship that can the distance between a little determine between plane.If the cue ball centre of sphere of the four of plane devices is to another
The distance of individual plane is equal to zero, then can determine that the two planes overlap；Conversely, then can determine that the two planes are misaligned；If
One cue ball centre of sphere of the four of plane devices is all equal to the distance of another plane and is all not equal to zero, and four cue balls
The centre of sphere is located at the homonymy of another plane, then can determine that the two planes are parallel；If four upright projection point compositions are another after projection
Straight line in plane, then the two planes intersect vertically；If the cue ball centre of sphere of the four of plane devices is to another
The distance of individual plane is all unequal, although or distance it is all equal, build plane four device cue ball centre ofs sphere be located at it is another
The both sides of plane, then can determine that the two planes intersect.After the intersection of two planes is found, the angle between two planes,
I.e. dihedral angle, is the straight line and its angle between the upright projection straight line of another plane perpendicular to intersection in one side；
（2）Gained knowledge from geometry, two intersecting straight lines are respectively parallel to two phases in another plane in a plane
Straight line is handed over, then the two planes are parallel.Therefore, by three devices adjacent in a plane respectively to another plane projection,
If the subpoint obtained in another plane can only build straight line, two planes intersect vertically；If subpoint can be built
Two intersecting straight lines, and two straight line parallels that two intersecting straight lines for creating build with original three devices respectively are found, then
Two planes are parallel；If in two straight lines that two intersecting straight lines for creating build with original three devices respectively at least
A pair is not parallel, then two planes intersect.After finding two intersections of plane, the angle between two planes, i.e. two faces
Angle, is the straight line and its angle between the upright projection straight line of another plane perpendicular to intersection in one side；
（3）Coordinate according to plane in rectangular coordinate system is characterized, according to the pass between analytic geometry midplane and plane equation
System, judge the coincidence between plane and plane, intersect, parallel, the relation such as intersect vertically.
Specific embodiment：The method that plane is built according to this specification, is occurred using eight devices and eight line lasers
Device builds two planes, and four devices in a plane do upright projection to another plane, according to " decision-point and plane
The embodiment of geometrical relationship ", obtains upright projection point of four devices in another plane.Can use（1）Decision method,
The geometrical relationship between plane and plane is judged according to the distance between original device to subpoint；Can also use（2）Judge
Method, optional three from four subpoints, builds projection line, according to whether being parallel relation between former straight line and projection line,
Judge the geometrical relationship between plane and plane；Coordinate according to plane in rectangular coordinate system is characterized, according in analytic geometry
Relation between plane equation and plane equation, judges that the plane between plane and plane overlaps with plane, plane and plane phase
Hand over, the relation such as plane intersects vertically with plane, plane is parallel with plane.
9. the geometrical relationship of decision space plane and body
The geometrical relationship of decision space plane and body, refers mainly to space plane and polyhedral relation, for space plane and again
The geometrical relationship of miscellaneous body, can be using similar method treatment.According to the region pass that space is split on each surface for constituting body
System, judges the geometrical relationship of plane and each surface of body, if plane intersects with any one surface of body, plane and body are
Intersecting；If plane overlaps with polyhedral any one surface, plane is on body；If plane is not any one with polyhedral
Individual surface is intersecting or overlaps, then plane and body are non-intersect, i.e., plane and body be from relation.If plane to polyhedron some
The vertical range on surface is zero, it is also possible to determine the plane on the surface of body；Can also judge plane with it is polyhedral each
Geometrical relationship between surface, each bar seamed edge and each summit；Coordinate according to plane and body in rectangular coordinate system is characterized,
According to the relation between analytic geometry midplane equation and the inequation group of body, judge the plane between plane and body in body
Face on and body phase hand over or with body phase from etc. relation.The judgement of plane and cuboid geometrical relationship similar to above-mentioned plane with
The judgement of polyhedron relation.
Specific embodiment：By taking cuboid as an example, the method that plane and cuboid are built according to patent specification is used
12 devices and 16 laser line generators build plane and cuboid, and eight devices therein build a cuboid,
Four additional device builds a plane.After the locus of plane and body determines, can be by each of plane and cuboid
The space geometry relation on individual surface, so as to finally judge the geometrical relationship of plane and cuboid；Can also judge plane with it is rectangular
Geometrical relationship between each surface of body, each bar seamed edge and each summit；Summit and plane, seamed edge and plane can be used
And the decision method of plane and plane geometrical relationship, from summit to each bar seamed edge of plane or cuboid to plane or flat
Upright projection is made on each surface towards cuboid, then judges summit and plane, each seamed edge and plane and each surface and puts down
The geometrical relationship in face；Coordinate according to plane and cuboid in rectangular coordinate system is characterized, according to analytic geometry midplane equation
And the relation between the inequation group of cuboid, judges the plane between plane and cuboid on the face of body, plane and
Body phase is handed over, plane and body phase from etc. relation.
10. the geometrical relationship of decision space body and body
The geometrical relationship of decision space body and body, refers mainly to polyhedron and polyhedral relation, for the space between complicated body
Relation, can be using similar processing method.According to the regional relation that space is split on each surface for constituting body, one is judged
Polyhedral each surface and the space geometry relation on another each surface of polyhedron, or according to " judgement plane and body
The method of geometrical relationship ", judges the space geometry relation of an individuality and another each surface of individuality, if two individualities have the table of coincidence
Other surfaces of face and an individuality are still located at the space that another polyhedron is surrounded, then a polyhedron includes another multiaspect
Body；If a polyhedron intersects with another polyhedral any one surface, two polyhedrons intersect；If two polyhedrons
Both it is non-intersect, do not include, then yet it is disjoint relationship；Polyhedral each surface, each bar seamed edge and each can also be judged
Individual summit and another polyhedral each surface, the geometrical relationship between each bar seamed edge and each summit；According to body straight
Coordinate in angular coordinate system is characterized, and the relation between inequation group according to two individualities in analytic geometry judges body and body
Between body in vivo and body phase hand over or with body phase from etc. relation.The judgement of cuboid and cuboid geometrical relationship is similar to upper
The judgement of the polyhedron and polyhedron relation stated.
Specific embodiment：By taking cuboid as an example, according to the method for patent specification construct, 16 devices are used
Two cuboids are built with 24 laser line generators.It is long according to one after two locus of cuboid determine
Coincidence between each surface of cube and another cuboid surface, intersect, intersect vertically, the geometrical relationship such as parallel, or
According to an individuality with it is another individuality each surface space geometry relation, the geometrical relationship between the individuality of synthetic determination two；Also may be used
To judge each surface of cuboid, each bar seamed edge and each surface, each bar of each summit and another cuboid
Geometrical relationship between seamed edge and each summit；Coordinate according to cuboid in rectangular coordinate system is characterized, several according to parsing
Relation in what between two inequation groups of cuboid, judges that the body between a cuboid and another cuboid exists
The inside of body, body and body phase are handed over, body and body phase from etc. relation.
11. judge other geometrical relationships
For other complicated objects and spatial relationship between point, line, surface, body, can be gained knowledge based on geometry, analytic geometry
Knowledge and above-mentioned basic geometric relationship are built and are judged.
（Five）The demarcation of image space
Apparatus of the present invention are shot by camera or video camera, can obtain its projected image in camera plane.In handle
, it is necessary to be demarcated by image space and image space solution when image space after shooting is converted to the real space of two-dimentional or three-dimensional
Two steps of analysis.Image space is demarcated：Determine that the device cue ball and attached ball of known real space coordinate in real space are shooting
The respective coordinates represented with pixel on image, so as to set up their transformation relation according to different scaling methods.Image is empty
Between parse：The two-dimensional coordinate that any one is represented with pixel on image, using the inverse transformation method in uncalibrated image space, conversion
It is the two dimension or three-dimensional coordinate of real space.The particular content that above-mentioned steps are related to has：Capture apparatus and device spatial relationship
Structure, and image space demarcation.
1. the structure of capture apparatus and device spatial relationship
Specific embodiment is as follows：
Method A：Capture apparatus primary optical axis vertical coordinate plane
By taking the coronal coordinates plane of the vertical apparatus of the present invention of capture apparatus primary optical axis as an example, a device is taken, below device
Magnetic chuck, fixing device is on a flat board for surfacing（Metallic plate, glass plate etc., it is same as below）, build one
Three-dimensional cartesian rectangular coordinate system, a capture apparatus are placed on tripod, adjustment tripod, capture apparatus and device position
Put, the cue ball of device is located at the center of device screen, and ensure in capture apparatus it can be seen that forecourt is in cue ball
It can be seen that forecourt and cue ball form concentric circles on heart position, i.e. image, and left and right two ball is equal to the distance of cue ball, shoots
The primary optical axis of equipment is located on forecourt, cue ball, the line of rear ball center（Sagittal axis）.Now, the primary optical axis of capture apparatus is vertical
Yu Zuoqiu, upper ball, the coordinate plane of right ball composition（Coronal-plane）, the camera plane of capture apparatus is parallel with this coordinate plane.It is right
In other coordinate planes, such as perpendicular to sagittal plane, horizontal plane etc., by that analogy.
Method B：Two capture apparatus primary optical axis are mutually perpendicular to
Using method mentioned above A, first a primary optical axis for capture apparatus is put down with a certain coordinate constructed by a device
Face is vertical；Another capture apparatus are placed on tripod again, are placed on the left/right side or up/down side of First equipment, mesh
Its primary optical axis is surveyed with the primary optical axis of First equipment in substantially vertical position, the position of adjustment tripod, capture apparatus and device
Put, also with method mentioned above A, by another coordinate plane constructed by second primary optical axis of capture apparatus and device
Vertically, and this coordinate plane is perpendicular to previous coordinate plane, even the primary optical axis of First capture apparatus before device, advocate peace
Afterwards on the line of the ball centre of sphere（Sagittal axis）, then ensure second primary optical axis of capture apparatus in the left of device, the right ball centre of sphere of advocating peace
Line on（Trunnion axis）, on Huo Zheshang, the line of the cue ball centre of sphere（Vertical axis）.Now, the primary optical axis of two capture apparatus is
Vertical relation.
Method C：Capture apparatus primary optical axis parallel coordinates plane
Two devices are separately fixed on two flat boards of surfacing, flat position is adjusted, make stream oriented device approximate horizontal.Make
Beam of laser, and horizontal sheaf apparatus of the present invention are produced with laser line generator, two setting positions are adjusted, enables light successively
Enter device from the same side ball of two devices, without stop ground by cue ball, and passed from another ball outside, you can to ensure
Two devices can build space straight line.According to method mentioned above A, one of device is selected to build Descartes right angle
Coordinate system, the then primary optical axis of capture apparatus is vertical with the coronal plane constructed by one of device, the master of this capture apparatus
Optical axis is parallel with the sagittal plane of second device.For other coordinate planes, by that analogy.
Method D：Two equipment primary optical axis are parallel to each other
Two devices are separately fixed on two flat boards of surfacing, flat position is adjusted, make stream oriented device approximate horizontal.Make
Beam of laser, and horizontal sheaf apparatus of the present invention are produced with laser line generator, two setting positions are adjusted, enables light successively
Enter device from the same side ball of two devices, without stop by cue ball, and passed from another ball outside, you can to ensure
Two devices can build space straight line.Two capture apparatus are distinguished one device of each autoregistration and are placed, according to carrying above
The method A for arriving, optionally one of device builds Descartes's rectangular coordinate system, ensures that every equipment primary optical axis is filled in correspondence respectively
Before putting, on main body, the line of the rear ball centre of sphere（Sagittal axis）.Now, you can ensure that the primary optical axis of two equipment is parallel.
2. the demarcation of image space
The demarcation of image space is exactly by determining the device cue ball and attached ball of known spatial coordinate in real space in shooting figure
As the respective coordinates of upper use pixel denotation coordination value, so that their transformation relation is set up according to different scaling methods, and
Parsing is usually the coordinate in two-dimentional or three-dimensional real space for obtaining any pixel on image.
Specific embodiment is as follows：
（1）The selection of capture apparatus, its Choice is as follows：The difference of purpose and real space dimension according to graphical analysis,
Will consider the number of capture apparatus used, how place apparatus, and determining device and device therefor spatial relation；
If it is sufficient that obtaining the two-dimensional space coordinate of small range, single device, and if large-scale three dimensional space coordinate,
Then need two or more equipment sync pulse jammings；Digital camera single image can have resolution ratio higher, but continuous bat
Take the photograph picture frequency not high, digital camera camera function can be with continuously shot images, but the resolution ratio of image is general, and frequency acquisition is
25 or 30 frames/second；High-speed camera then not only with continuously shot images, and can have resolution ratio very high and collection frequency
Rate, but it is expensive；The image space that camera shoots demarcate be a width demarcated, video camera is then continuous shooting
Image, need to be after frame be extracted and is converted to image sequence, a width ground（Or ensemble average）Uncalibrated image space.
（2）The selection of caliberating device, its Choice is as follows：Spatial dimension, real space according to IMAQ are not
With the complexity of dimension and image space scaling method it is necessary to consider the number of caliberating device used, how apparatus for placing,
And the spatial relation of determining device and device therefor；Demarcation of the image calibration precision of multiple devices higher than single assembly
Precision；If the spatial dimension of IMAQ is smaller, separate unit capture apparatus, and obtain the two-dimensional coordinate of real space, then may be used
With using the caliberating device of or less than three；If the spatial dimension of IMAQ is than larger, the shooting of more than two
Equipment, and obtain the three-dimensional coordinate of real space, then can be using the caliberating device of more than three；According to multi-parameter description
Capture apparatus imaging model, then need multiple index points, is also accomplished by being applied in combination multiple caliberating devices.
（3）Many devices are applied in combination, and it is as follows that it is applied in combination scheme：Due to the mark points that single caliberating device is provided
Amount is limited, and symmetrical mounting can at most provide 7 index points, and asymmetric unit can at most provide six index points.If clapping
Run into when taking the photograph and blocked, then the quantity of index point is also possible to reduce, therefore, it is necessary to more index point when actually used, can be with
Using the combination of multiple devices come uncalibrated image.Conventional combination has the plane combination and eight spatial groups of device of four devices
Close.Similar to the construction method of rectangle plane, a device sets up three-dimensional cartesian coordinate system, four to four plane combinations of device
Device builds a rectangle in plane, and the attached ball of all devices can serve as index point to make in the case of visible
With symmetrical mounting and asymmetric unit can at most provide 28 and 24 index points respectively.Eight Spatial Couplings of device similar to
The construction method of space cuboid a, device sets up three-dimensional cartesian coordinate system, and eight devices build a cuboid in space,
The attached ball of all devices can serve as index point to use in the case of visible, and symmetrical mounting and asymmetric unit are distinguished
56 and 48 index points can be at most provided.
（4）Image space demarcates conventional method, and its specific scaling method is as follows：According to the change of image space to real space
Change dimension, foundation（1）With（2）Described method, selects appropriate number of caliberating device and capture apparatus；In a caliberating device
It is upper to set up two dimension or three-dimensional cartesian rectangular coordinate system；Projection laser beam, according to capture apparatus and the structure of device spatial relationship
Method, build the spatial relationship of capture apparatus and caliberating device；The image for shooting is obtained, by image procossing circle and the center of circle
The algorithm of identification, finds the cue ball and each the two-dimensional pixel coordinate of attached ball centre of sphere on image of device；By the design of each device
The situation of size and Spatial Coupling, determines the coordinate of each cue ball and each attached ball in the rectangular coordinate system of the real space for building；It is logical
Cross the transformation relation that linearly or nonlinearly equation group is set up between them；According to the method for solving of linearly or nonlinearly equation group,
Set up that coordinate is linear or coefficient of nonlinear transformation, demarcated the transformation matrix of image space；According to different capture apparatus into
As model, the inside and outside parameter matrix of equipment is derived, demarcate the parameters of capture apparatus.
（5）Uncalibrated image space and the transformation matrix of coordinates of two-dimensional space, its scaling scheme are as follows：Using（4）Described
Image space demarcates conventional method, according to the linear transformation method that common coordinate is represented, then need to obtain two of device or
The space coordinates of the above centre of sphere, finds their corresponding pixel coordinate values respectively on image, is set up by four linear equations
Found the transformation relation between them；According to the method for solving of system of linear equations, the coefficient of coordinate linear transformation is determined, demarcated figure
Image space and the transformation matrix of coordinates of two-dimensional space；According to the linear transformation method that homogeneous coordinates are represented, then need to be filled
Five or more the space coordinates of the centre of sphere put, find their corresponding pixel coordinate values respectively on image, by nine lines
The transformation relation that property equation group is set up between them；According to the method for solving of system of linear equations, the nine of coordinate linear transformation are determined
Individual coefficient, so that the transformation matrix in uncalibrated image space；According to conventional DLT methods（Direct Linear
Transformation, Method of Direct Liner Transformation）, then need to obtain four or more the space coordinates of the centre of sphere of device, in figure
Their corresponding pixel coordinate values are found respectively as upper, 8 transformation parameters needed in DLT methods are determined, set up coordinate transform
Relation, the transformation matrix in uncalibrated image space.
（6）Uncalibrated image space and the transformation matrix of coordinates of three dimensions, its scaling scheme are as follows：Using（4）The figure
The conventional method that image space is demarcated, according to the linear transformation method that common coordinate is represented, then need to obtain three of device or
The space coordinates of the above centre of sphere, finds their corresponding pixel coordinate values respectively on image, is set up by six linear equations
Found the transformation relation between them.According to the method for solving of system of linear equations, six coefficients of coordinate linear transformation are determined, demarcate
The transformation matrix of coordinates of image space and three dimensions；According to the linear transformation method that homogeneous coordinates are represented, then need
To six or more the space coordinates of the centre of sphere of device, their corresponding pixel coordinate values are found respectively on image, by ten
The transformation relation that two systems of linear equations are set up between them.According to the method for solving of system of linear equations, determine that coordinate linearly becomes
12 coefficients for changing, so that the transformation matrix in uncalibrated image space；According to conventional DLT methods, then need to obtain device
Six or more the space coordinates of the centre of sphere, their corresponding pixel coordinate values are found respectively on image, in determining DLT methods
11 transformation parameters for needing, set up coordinate conversion relation, the transformation matrix in uncalibrated image space.
Claims (10)
1. the device that a kind of three-dimensional tree-shaped rectangular coordinate system is built and image space is demarcated, it is characterised in that including a cue ball,
Five attached balls, attached ball is respectively forecourt, rear ball, left ball, right ball, upper ball, and the six roots of sensation hollow connecting rod and base, attached ball pass through five
Individual hollow connecting rod is separately fixed at the front, rear, left and right and upside of cue ball；Cue ball downside is consolidated by the 6th connecting rod with base
Fixed, cue ball has through hole in three mutually perpendicular directions being connected with connecting rod, and attached ball has logical on the direction being connected with connecting rod
Hole, base is also provided with through hole on the direction being connected with connecting rod, and all clear size of opening are identical；Five attached balls, connecting rod, base and
One cue ball constitutes an asymmetric unit.
2. the device that three-dimensional tree-shaped rectangular coordinate system as claimed in claim 1 is built and image space is demarcated, it is characterised in that
Five sizes of attached ball can be with identical or differ, and connection cue ball can be with identical with five connecting rod physical dimensions of attached ball
Or differ, connection cue ball can be with equal with five connecting rods of physical dimension and other of the six roots of sensation connecting rod of base, it is also possible to
It is unequal；
Asymmetric unit global formation, it is ensured that the line of centres of forecourt, cue ball and rear ball is on link centerline, it is ensured that left ball,
The line of centres of cue ball and right ball is on link centerline, it is ensured that upper ball, cue ball and the base line of centres on link centerline,
And ensure front-rear linkage, left linkages, upper and lower strut center line it is orthogonal.
3. the device that three-dimensional tree-shaped rectangular coordinate system as claimed in claim 1 is built and image space is demarcated, it is characterised in that
Also include the 6th attached ball and the 7th hollow connecting rod；The 6th attached ball is connected to cue ball by six roots of sensation connecting rod
Lower section, constitutes lower ball；6th attached ball have on the direction being connected with connecting rod with other attached ball clear size of opening identical through holes, under
The lower section of ball is connected by the 7th connecting rod with base, constitutes symmetrical mounting.
4. the device that three-dimensional tree-shaped rectangular coordinate system as claimed in claim 3 is built and image space is demarcated, it is characterised in that
The size of six attached balls is identical, and connection cue ball is identical with the six roots of sensation connecting rod physical dimension of attached ball, the geometric parameter of the 7th
Can be with equal with other six roots of sensation connecting rods, it is also possible to unequal；
Device global formation, it is ensured that the line of centres of forecourt, cue ball and rear ball is on link centerline, it is ensured that left ball, cue ball with
The line of centres of right ball is on link centerline, it is ensured that upper ball, cue ball with lower ball and the base line of centres on link centerline,
And ensure front-rear linkage, left linkages, upper and lower strut center line it is orthogonal.
5. the device that the three-dimensional tree-shaped rectangular coordinate system as described in any one of claim 1 ~ 4 is built and image space is demarcated, its
It is characterised by, the size of through-hole diameter is more than or equal to 1 micron or less than or equal to 1 meter；
Attached bulb diameter is more than 1.1 times of through-hole diameter, cue ball diameter be 1 times of attached bulb diameter and more than, connecting rod overall diameter is
1.1 times of through-hole diameter and more than, the length and overall diameter of the connecting rod of connect base be respectively 1 times of attached bulb diameter and the above and
1.1 times and more than；
Base is circular or square, and round diameter or the square length of side are more than 4 times of cue ball diameter, and substructure height is through hole
6 times of diameter and more than, the diameter of the magnet that goes in ring be not less than 8 times of through-hole diameter and more than, the diameter of the magnet that goes in ring is not more than
Cup dolly diameter or the square base length of side；
Forecourt, left ball, on outer surface of ball brush color consistent with other spheroids or inconsistent respectively；
Base bottom is embedded in annular magnet, and the height of the magnet that goes in ring is not higher than substructure height；
Cue ball, base, attached ball, connecting rod can use metal, plastics, glass, timber, macromolecular material to be made.
6. a kind of method that three-dimensional tree-shaped rectangular coordinate system is built and image space is demarcated, using dress as claimed in claim 3
Put, by the origin of coordinates, reference axis and coordinate plane build three-dimensional cartesian rectangular coordinate system, it is characterised in that：
The described device cue ball centre of sphere is the origin of coordinates of coordinate system；
The origin of coordinates can determine that straight line with the centre of sphere of any one attached ball, can set up the reference axis of coordinate system,XAxle positive direction
Forecourt centre of sphere direction is pointed to from the cue ball centre of sphere,YAxle positive direction points to left ball centre of sphere direction from the cue ball centre of sphere,ZAxle positive direction is from master
The ball centre of sphere points to upper ball centre of sphere direction, and three axles meet right-handed helix relation, and offside is respectivelyX, Y, ZThree negative semiaxis；
The cue ball centre of sphere not on the same line, the front/rear ball centre of sphere, the left/right ball centre of sphere, it is determined thatXOYPlane namely horizontal plane；No
The cue ball centre of sphere on the same line, the front/rear ball centre of sphere, the up/down ball centre of sphere, determinationZOXPlane namely sagittal plane；Not same
The cue ball centre of sphere, the left/right ball centre of sphere on straight line, the up/down ball centre of sphere, it is determined thatYOZPlane namely coronal-plane；
Based on the origin of coordinates, three reference axis and three coordinate planes build three-dimensional cartesian rectangular coordinate system；
Based on the origin of coordinates, any two reference axis and the coordinate plane determined by its build two-dimentional Descartes's rectangular coordinate system；
Based on the origin of coordinates and any one reference axis, one-dimensional cartesian coordinate system, i.e. number axis are built；
Based on the origin of coordinates, zero dimension cartesian coordinate system, i.e. point are built.
7. the method that three-dimensional tree-shaped rectangular coordinate system as claimed in claim 6 is built and image space is demarcated, it is characterised in that：
Also include building point, line, surface, body space geometrical element, the structure point, line, surface, body space geometrical element include following step
Suddenly：
（1）, device the cue ball centre of sphere, build a geometric point in three dimensions；One each attached ball centre of sphere of device, point
Geometric point that Gou Jian be in three dimensions；
（2）, one laser beam pass sequentially through two cue ball centre ofs sphere of device, build the straight line in three dimensions；One dress
Each reference axis put, builds the straight line in three dimensions respectively；One centre of sphere of any two ball of device, builds
Straight line in three dimensions；Cross space not on straight line a bit, build the parallel lines of this straight line；Cross not on straight line
Space a bit, builds point to the vertical line of this straight line；
（3）, be not arranged on the same straight line three cue ball centre ofs sphere of device, build a plane of three dimensions；Two devices
The cue ball centre of sphere builds the 3rd cue ball centre of sphere of device outside straight line, with straight line, builds a plane of three dimensions；Three
Two straight lines for intersecting vertically that the cue ball centre of sphere of individual device builds, build a plane of three dimensions；Four masters of device
Two of ball centre of sphere structure intersect vertically or parallel straight line, build a plane of three dimensions；Four cue ball balls of device
The heart is respectively the four of rectangle summits, builds a plane of three dimensions；One each coordinate surface of device, respectively
Build a plane in three dimensions；One three ball centre of sphere not on the same line of device, builds three-dimensional space respectively
Between in a plane；
（4）, four devices not at grade the cue ball centre of sphere, build a tetrahedron of three dimensions；Not same
Five and the cue ball centre of sphere of apparatus above in plane, build a polyhedron of three dimensions；Eight cue ball centre ofs sphere of device
Respectively one the eight of cuboid summits, build a cuboid of three dimensions；One device not at grade
Four and the above ball centre of sphere, build respectively one individual in three dimensions.
8. the method that three-dimensional tree-shaped rectangular coordinate system as claimed in claim 7 is built and image space is demarcated, it is characterised in that：
Also include that the coordinate of point, line, surface, body geometric element in three-dimensional cartesian coordinate system is characterized, the point, line, surface, body geometric element
Coordinate in three-dimensional cartesian coordinate system is characterized and comprised the following steps：
（1）, coordinate characterizing method of the point in three-dimensional cartesian rectangular coordinate system：Build a three-dimensional cartesian rectangular co-ordinate
System, upright projection is made by point to three axles of coordinate system respectively, and the distance of subpoint to the origin of coordinates is the exhausted of coordinate a little
To value, the positive and negative semiaxis of reference axis is respectively at according to subpoint, coordinate is respectively positive and negative value；
（2）, coordinate characterizing method of the straight line in three-dimensional cartesian rectangular coordinate system：Build a three-dimensional cartesian rectangular co-ordinate
System, optional 2 points from straight line, according to step（1）Described method, provides this 2 points of coordinates in a coordinate system, then profit respectively
With the determination method of the space line introduced in analytic geometry, coordinate side of the straight line in three-dimensional cartesian rectangular coordinate system is given
Journey；
（3）, coordinate characterizing method of the plane in three-dimensional cartesian rectangular coordinate system：Build a three-dimensional cartesian rectangular co-ordinate
System, optionally not conllinear 3 points from plane, according to step（1）Described method, provides this 3 points in a coordinate system respectively
Coordinate, using the determination method of the space plane introduced in analytic geometry, provides plane in three-dimensional cartesian rectangular coordinate system
Equation in coordinates；
（4）, coordinate characterizing method of the body in three-dimensional cartesian rectangular coordinate system：Build a three-dimensional cartesian rectangular co-ordinate
System, chooses three summits, such as step respectively from polyhedral each surface successively（3）Described method, provides each surface
Plane equation, it is the area of space surrounded by the inequation group of these planes that the coordinate of body is characterized.
9. three-dimensional tree-shaped rectangular coordinate system as claimed in claim 8 builds and image space demarcation, it is characterised in that：Including
Point and point, Points And lines, point and face, point and body, straight line and straight line, straight line and face, straight line and body, face and face, face and body, body and body
The judgement of space geometry relation；Described point and point, Points And lines, point and face, point and body, straight line and straight line, straight line and face, straight line
And body, face and face, face and body, the judgement of body and body space geometry relation is as follows：
（1）, using building point, line, surface, the side for building the geometric point in three dimensions described in body space geometrical element step
Whether method, builds two points in three dimensions, be zero according to the distance between two points, and the geometry of decision space point and point is closed
System be overlap or from；The method characterized using coordinate of the point in three-dimensional cartesian rectangular coordinate system, provides two points respectively
Coordinate, according to two points coordinate it is whether identical, decision space point and point geometrical relationship be overlap or from；
（2）, using building point, line, surface, the side for building the geometric point in three dimensions described in body space geometrical element step
The method of the straight line in method and structure three dimensions, builds the point and straight line in three dimensions respectively, builds
Straight line in three dimensions, whether according to point on this straight line, the geometrical relationship of decision space point and straight line is that point is online
It is upper or online outer；Cross and a little make vertical line to straight line, whether the distance of foundation point to intersection point is zero, the geometry of decision space point and straight line
Relation is on line or online outer point；Coordinate characterizing method and straight line using point in three-dimensional cartesian rectangular coordinate system is three
The method that coordinate in dimension Descartes's rectangular coordinate system is characterized, provides the equation of coordinate and straight line a little respectively, according to the seat of point
Whether mark meets the equation of straight line, and the geometrical relationship of decision space point and straight line is on line or online outer point；
（3）Using the geometric point built in three dimensions built described in point, line, surface, body space geometrical element step
Whether with a method for plane, the point and a plane in three dimensions are built respectively, sentence according to point on that plane
The geometrical relationship for determining spatial point and straight line is put on the whole or outside face；Cross and a little make vertical line to plane, according to point to intersection point away from
Whether from being zero, the geometrical relationship of decision space point and plane is put on the whole or outside face；It is straight in three-dimensional cartesian using putting
The coordinate characterizing method of coordinate characterizing method and plane in angular coordinate system in three-dimensional cartesian rectangular coordinate system, is given respectively
Whether the coordinate of point and the equation of plane, the geometry pass of the equation of plane, decision space point and plane is met according to the coordinate of point
System is point on the whole or outside face；
（4）, using building point, line, surface, the geometric point built in three dimensions described in body space geometrical element step
And the method for building an individuality of three dimensions, the point and individual, a foundation composition body in three dimensions are built respectively
Each surface regional relation that space is split, the position relationship on each surface of decision-point and body；If point is located at constitutes body
Each surface surround space, then put in vivo；If point is located on each surface for constituting body, put on body；If point is not
Positioned at constitute body each surface surround space, then body do not include point, i.e., point and body be from relation；Using point in three-dimensional
The coordinate characterizing method of coordinate characterizing method and body in Descartes's rectangular coordinate system in three-dimensional cartesian rectangular coordinate system, point
The inequation group on each surface of coordinate and body a little is not given, and whether the coordinate according to point can make the inequality side of cuboid
, less than zero, equal to zero or more than zero, decision-point is in cuboid, on cuboid or rectangular external for journey group；
（5）, using building point, line, surface, the straight line built in three dimensions described in body space geometrical element step
Method, builds two straight lines in three dimensions, selects three points being not arranged on the same straight line on this two straight lines, builds three-dimensional
A plane in space, using step（3）Described method, it is known that the 4th point on that plane or outside face, decision space
The geometrical relationship of straight line and straight line is coplanar or antarafacial；
1., two straight lines are coplanar line, judge between two straight lines geometrical relationship be overlap, it is parallel, intersect, intersect vertically, such as
Step（2）Whether whether described method, according to 2 points on straight line on another straight line, judge two coplanar lines
Overlap；2 points on straight line are made vertical line to another straight line respectively, are a rectangle with two intersection points according to this 2 points
Whether is four summits, judges that two coplanar lines are parallel or intersecting；Two intersection points overlap, and judge two vertical phases of coplanar line
Hand over；
2., two straight lines are different surface beeline, judge between two straight lines that geometrical relationship is that antarafacial is vertical or general antarafacial relation：Select this
Three points being not arranged on the same straight line on two straight lines, build a plane in three dimensions, not on that plane straight
Line makees upright projection to this plane, and whether is the former straight line according to projection line in plane, judges that the geometry of two former straight lines is closed
It is antarafacial vertical relation or general antarafacial relation to be；Simultaneously and the straight line that all intersects vertically of two different surface beelines is that two antarafacials are straight
The common vertical line of line；
（6）, coordinate characterizing method using straight line in three-dimensional cartesian rectangular coordinate system, two sides of straight line are given respectively
Journey, according to the equations of two straight lines, the geometrical relationship of decision space straight line and straight line is coplanar, antarafacial, overlap, it is parallel, intersecting,
Intersect vertically, antarafacial is vertical or general antarafacial；Determine the common vertical line of different surface beeline；
（7）, using build point, line, surface, the straight line built in three dimensions described in body space geometrical element step and
One method of plane, builds the straight line and a plane in three dimensions respectively, and straight line makees upright projection to this plane,
Space line and projection line overlap, the geometrical relationship of decision space straight line and plane be straight line planar；Space line and throwing
Hachure intersects, and the geometrical relationship of decision space straight line and plane is that straight line and plane are intersecting；Projection line is degenerated to a subpoint,
The geometrical relationship of decision space straight line and plane is that straight line and plane intersect vertically；Space line is parallel with projection line, judges empty
Between straight line be straight line parallel with plane with the geometrical relationship of plane, the distance between straight line and projection straight line are straight line and plane
Distance；Coordinate characterizing method and plane using straight line in three-dimensional cartesian rectangular coordinate system is in three-dimensional cartesian rectangular co-ordinate
Coordinate characterizing method in system, provides the equation of straight line and plane respectively, according to straight line and the equation of plane, decision space straight line
With the geometrical relationship of plane be straight line in face, straight line and plane intersect, intersect vertically, and straight line is parallel with plane；
（8）, using build point, line, surface, the straight line built in three dimensions described in body space geometrical element step and
The method of one individuality, builds the straight line and an individuality in three dimensions, such as step respectively（7）Described method, according to straight
Whether line intersects with polyhedron arbitrary surfaces, the geometrical relationship of decision space straight line and body be it is intersecting or from；Such as step（5）Or
（6）Described method, straight line and polyhedral seamed edge overlap or straight line is on polyhedral surface, decision space straight line and body it is several
What relation is space line on body；Coordinate characterizing method and body using straight line in three-dimensional cartesian rectangular coordinate system is three
Coordinate characterizing method in dimension Descartes's rectangular coordinate system, provides the inequation on the equation of straight line and each surface of body respectively
Group, according to linear equation and the relation of the inequation group on each surface of body, the geometrical relationship of decision space straight line and body is
Straight line and the cross, straight line of body phase on the border of body or with body phase from；
（9）, using a side for plane for building point, line, surface, structure three dimensions described in body space geometrical element step
Method, builds two planes in three dimensions, and four points in a plane do upright projection, four points to another plane respectively
All it is zero to distance between intersection point, the geometrical relationship of decision space plane and plane is to overlap；Four points between intersection point away from
From all equal and be all not equal to homonymy of zero, and four points positioned at another plane, the geometrical relationship of decision space plane and plane
It is parallel；The geometrical relationship of the straight line in four intersection point another planes of composition, decision space plane and plane is vertical phase
Hand over；Four points are unequal to the distance between intersection point, although or distance it is all equal, four points are located at the two of another plane
The geometrical relationship of side, decision space plane and plane is intersecting；
（10）, using building point, line, surface, a plane of structure three dimensions described in body space geometrical element step
Method, builds two planes in three dimensions, and three points on two straight lines that will intersect in a plane are respectively to another
Individual plane makees vertical line, and for two former straight lines in itself, the geometrical relationship of decision space plane and plane is to overlap to two projection lines；Hang down
Foot can only build straight line, and the geometrical relationship of decision space plane and plane is to intersect vertically；Intersection point build two it is intersecting
Straight line, and two straight line parallels that this two intersecting projection lines build with original three points respectively, decision space plane and plane
Geometrical relationship be parallel；Intersection point build two intersecting straight lines, and this two intersecting projection lines respectively with original three structures
At least a pair is not parallel in two straight lines built, and the geometrical relationship of decision space plane and plane is intersecting；
（11）, coordinate characterizing method using plane in three-dimensional cartesian rectangular coordinate system, the equation of two planes is given respectively,
According to plane equation, the geometrical relationship of decision space plane is that plane and plane overlap, and intersects, intersects vertically, parallel；
（12）, using build point, line, surface, a plane of structure three dimensions described in body space geometrical element step and
The method of one individuality, builds the plane and an individuality in three dimensions, such as step respectively（7）、（8）、（9）Described side
Any one surface of method, plane and cuboid is intersected, and the geometrical relationship of decision space plane and body is intersecting；Plane and rectangular
The geometrical relationship of any one surface coincidence of body, decision space plane and body is plane on body；Plane not with cuboid
Any one surface is intersecting or overlaps, the geometrical relationship of decision space plane and body be from；Using plane in three-dimensional cartesian
The coordinate characterizing method of coordinate characterizing method and body in rectangular coordinate system in three-dimensional cartesian rectangular coordinate system, is given respectively
The inequation group on each surface of the equation of plane and the inequation group on each surface of body, foundation plane equation and body
The geometrical relationship of relation, decision space plane and body be plane and body phase hand over, plane on the border of body or with body phase from；
（13）, using building point, line, surface, the individuality built in three dimensions described in body space geometrical element step
Method, builds two individualities in three dimensions, using step（4）Described method, each summit of a cuboid is all located at
Inside another cuboid, the geometrical relationship of decision space body and body is to include；Using step（7）、（8）、（9）Described side
Method, each surface of an individuality can overlap with an another individual surface, and the geometrical relationship of decision space body and body is body
Closed with body weight；Using step（12）Described method a, cuboid is mutually given with any one surface of another cuboid
It is no, the geometrical relationship of decision space body and body be it is intersecting or from；Using coordinate of the body in three-dimensional cartesian rectangular coordinate system
Characterizing method, provides the inequation group on each surface of two individualities respectively, the inequation group on each surface of foundation body
The geometrical relationship of relation, decision space body and body be include, overlap, intersecting or from.
10. the method that three-dimensional tree-shaped rectangular coordinate system as claimed in claim 9 is built and image space is demarcated, its feature exists
In：Also include the demarcation of the structure and image space of capture apparatus and device spatial relationship, it comprises the following steps：
（1）, capture apparatus and device spatial relationship structure：
1., capture apparatus primary optical axis is vertical with any coordinate plane of device, by capture apparatus observe an attached ball with
Cue ball forms concentric circles, the i.e. distance positioned at upper and lower, right position attached ball to cue ball and distinguishes equal, the primary optical axis of capture apparatus
On this attached ball, cue ball, the line of the attached ball of offside, the primary optical axis of capture apparatus is perpendicular to the attached ball positioned at left upper, right position
The coordinate plane of structure；
2., two capture apparatus primary optical axis are mutually perpendicular to：Using the 1. described method of step, the primary optical axis of two capture apparatus respectively with
One the two of device mutually perpendicular coordinate plane is vertical, and the primary optical axis of two capture apparatus is orthogonal；
3., capture apparatus primary optical axis is parallel with the coordinate plane of device：Beam of laser is entered from the attached ball in side of two devices successively
Enter, by the cue ball centre of sphere, passed from the attached ball of offside, the coordinate plane that two devices build be at least a pair it is parallel to each other,
Using the 1. described method of step, the primary optical axis of the capture apparatus not coordinate parallel with another device in a device
Plane, equipment primary optical axis is parallel to coordinate plane parallel with first device in another device；
4., two capture apparatus primary optical axis are mutually perpendicular to：Step 3. as described in method, two equipment primary optical axis are respectively parallel to two
The a pair of parallel coordinate plane of device, the primary optical axis of two capture apparatus is parallel to each other；
（2）The demarcation of image space：
1., capture apparatus can be one, two or many, the optional digital camera of equipment or video camera；
2., at uncalibrated image space, can be using one, two or multiple device is demarcated；The conventional combination of multiple devices has
Four plane combinations and eight Spatial Couplings of device of device；
3., image space demarcates conventional method：According to the conversion dimension of image space to real space, using the mark of image space
The method that to determine step 1. and 2. described, selects appropriate number of caliberating device and capture apparatus；Set up on a caliberating device
Two dimension or three-dimensional cartesian rectangular coordinate system；Projection laser beam, using step（1）Described method, builds capture apparatus and mark
Determine the spatial relationship of device；The image for shooting is obtained, the algorithm of and center identification circular by image procossing finds the master of device
Ball and each the two-dimensional pixel coordinate of attached ball centre of sphere on image；By the design size and the situation of Spatial Coupling of each device, really
Determine the coordinate of each cue ball and each attached ball in the rectangular coordinate system of the real space for building；Set up by linearly or nonlinearly equation group
Transformation relation between them；According to the method for solving of linearly or nonlinearly equation group, coordinate is set up linearly or nonlinear transformation
Coefficient, demarcated the transformation matrix of image space；According to different capture apparatus imaging models, derive equipment inside and
External parameter matrix, demarcates the parameters of capture apparatus；
4., the transformation matrix of coordinates of uncalibrated image space and two-dimensional space, using the 3. described side of the demarcating steps of image space
Method, determines the transformation parameter needed in scaling method, sets up coordinate conversion relation, the transformation matrix in uncalibrated image space；Foundation
Different capture apparatus imaging models, can also derive the inside and outside parameter matrix of capture apparatus, demarcate capture apparatus
Parameters；
5., the transformation matrix of coordinates of uncalibrated image space and three dimensions, using the 3. described side of the demarcating steps of image space
Method, determines the transformation parameter needed in scaling method, sets up transformation relation, the transformation matrix in uncalibrated image space；According to different
Capture apparatus imaging model, can derive the inside and outside parameter matrix of equipment, demarcate the parameters of capture apparatus.
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