CN206451240U - The device that three-dimensional tree-shaped rectangular coordinate system is built and image space is demarcated - Google Patents

Abstract

The utility model is related to a kind of simply and intuitively three-dimensional tree shape dress and put, 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, build the spatial relationship of capture apparatus and device, and the caliberating device demarcated as image space.The present apparatus is simple in construction, the global formation accuracy of manufacture is high, it is flexible using combination, present apparatus tool has been widely used and application field, operation device in being imparted knowledge to students as geometry, can also as the space coordinates of three-dimensional scanner and motion capture system based on image etc. structure and caliberating device.Specific implementer's case is based on geometry principle, with reference to the advantage of the utility model device, illustrating in detail operation and application method of the present apparatus in its concrete function.

Description

The device that three-dimensional tree-shaped rectangular coordinate system is built and image space is demarcated

Technical field

The utility model is related to the device that a kind of three-dimensional tree-shaped rectangular coordinate system is built and image space is demarcated, and the present apparatus can To be used as the device for building coordinate system and image space demarcation.Concrete function includes：Build three-dimensional cartesian rectangular coordinate system, structure Space geometrical element point, line, surface, body are built, coordinate of the space geometrical element in three-dimensional cartesian coordinate system is characterized, geometry member is judged Geometrical relationship between element, builds the spatial relationship of capture apparatus and device, and uncalibrated image space.Belong to three dimensional space coordinate The foundation of system, the coordinate of geometric element in a coordinate system is characterized, the judgement of space geometry relation, and capture apparatus and device space are closed The structure of system, and image space demarcation and the technical field 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, can also judge the geometry between them Relation, can characterize the coordinate of geometric element in the rectangular coordinate system of foundation again.

In addition, when carrying out image space two-dimensional analysis or plane motion seizure, it is necessary to camera or video camera（Hereinafter referred to as Capture apparatus or equipment）Primary optical axis keep perpendicular or parallel relation with a certain reference or plane of movement.If it cannot be guaranteed that vertical Or parallel relation, then the image shot 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, existing image space caliberating device is mostly to belong to Various plane reference plates, therefore construct two-dimentional Descartes's rectangular coordinate system, i.e.,Z=0（Or constant）Plane.Due to clapping The manufacturing process deviation of equipment, refraction error and CCD lattice position error of the 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 is easily produced, if still being demarcated using two-dimensional calibrations plate to image space, so as to add 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 use three dimensions caliberating device.

The content of the invention

The purpose of this utility model be to provide a kind of simple, image, intuitively three-dimensional tree shape dress put and embodiment, can be fast Speed, build three Cartesian coordinates exactly, build space geometrical element point, line, surface, body, determine that space geometrical element exists Coordinate in three-dimensional cartesian coordinate system is characterized, and judges the geometrical relationship between geometric element, builds the sky of capture apparatus and device Between relation, and uncalibrated image space.

The device that three-dimensional tree-shaped rectangular coordinate system described in the utility model is built and image space is demarcated is using as follows What technical scheme was realized：

The utility model device（Hereinafter referred to as device）Symmetrical mounting and asymmetric unit can be divided into.So-called symmetrical mounting, Refer to all attached spheroids（Hereinafter referred to as attached ball）Size it is identical, and to main body ball（Hereinafter referred to as cue ball）The centre of sphere away from From also equal, and respectively connect attached ball all equal with the length of connecting rod of cue ball and each attached ball and all relative cue ball centre of sphere of connecting rod are formed Central Symmetry relation.Symmetrical mounting is by a cue ball, a cylinder（Or cuboid）Base, the attached ball of six identical sizes, 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 is constituted. The size dimension that asymmetric unit refers mainly to each attached ball is differed, or the connecting rod size of connection cue ball and attached ball is unequal or attached The quantity of ball is less than six.The conventional asymmetric unit of one of which is main by a cue ball, a cylinder（Or cuboid） Base, five attached balls, respectively forecourt, rear ball, left ball, right ball, upper ball, the six roots of sensation（Five geometric parameters are identical）Connecting rod four Part is constituted.Symmetrical mounting increases an attached spheroid and a connecting rod than this asymmetric unit, and advantage is symmetrical configuration, attractive in appearance And demarcate and parse image space when more provide an index point, and for build three-dimensional cartesian rectangular coordinate system, structure Build space geometrical element point, line, surface, body and judge geometrical relationship between them, and characterize space geometrical element in three-dimensional straight Coordinate in angular coordinate system, the two devices are without this qualitative difference.The concrete structure of symmetrical and asymmetric unit see 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 metal, plastics, glass, the material such as macromolecule.Under（Or it is main）Fixed on the downside of ball 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 connect, 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 is is less than or equal to 1 meter more than or equal to 1 micron.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 outside 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 for the magnet that goes in ring is not more than cup dolly diameter or the square base length of side, and the height for 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 and other six（Or five）Root connecting rod can phase Deng can also be 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 the color consistent or inconsistent with other spheroids respectively.

Device described in the utility model can be applied to the method that three-dimensional tree-shaped rectangular coordinate system is built and image space is demarcated, This method adopts the following technical scheme that realization：The side that a kind of three-dimensional tree-shaped rectangular coordinate system is built and image space is demarcated Method, by the origin of coordinates, reference axis and coordinate plane build 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 and the centre of sphere of any one attached ball can determine that straight line, can set up the reference axis of coordinate system,XAxle is just Forecourt centre of sphere direction is pointed in direction 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 Upper ball centre of sphere direction is pointed to from the cue ball centre of sphere, and three axles meet right-handed helix relation, offside is respectivelyX, Y, ZThree negative half Axle；

The cue ball centre of sphere, the front/rear ball centre of sphere, the left/right ball centre of sphere not on the same line, it is determined thatXOYPlane namely level Face；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, determinationZOXPlane namely sagittal plane；No The cue ball centre of sphere, the left/right ball centre of sphere on the same 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 right angle and sat Mark 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, in addition to build 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；Each attached ball ball of one device The heart, builds a geometric point in three dimensions respectively；

（2）, one laser beam pass sequentially through the cue ball centre ofs sphere of two devices, build the straight line in three dimensions；One Each reference axis of individual device, builds the straight line in three dimensions respectively；The centre of sphere of any two ball of one device, Build the straight line in three dimensions；Cross space not on straight line a bit, build the parallel lines of this straight line；Cross not in straight line On space a bit, build point to this straight line a vertical line；

（3）, be not arranged on the same straight line the cue ball centre ofs sphere of three devices, build a plane of three dimensions；Two dresses The cue ball centre of sphere put builds the cue ball centre of sphere of the 3rd device outside straight line, with straight line, and build three dimensions one puts down Face；The straight line that two of the cue ball centre of sphere structure of three devices intersect vertically, builds a plane of three dimensions；Four devices The cue ball centre of sphere build two intersect vertically or parallel straight line, build three dimensions a plane；The master of four devices The ball centre of sphere is respectively four summits of a rectangle, builds a plane of three dimensions；Each coordinate surface of one device, A plane in three dimensions is built respectively；Three ball centre ofs sphere not on the same line of one device, build three respectively A plane in dimension space；

（4）, four devices not at grade the cue ball centre of sphere, build a tetrahedron of three dimensions；Do not exist Five and the cue ball centre of sphere of apparatus above on same plane, build a polyhedron of three dimensions；The cue ball of eight devices The centre of sphere is respectively eight summits of a cuboid, builds a cuboid of three dimensions；One device not same flat Four on face and the above ball centre of sphere, build the individual in three dimensions respectively.

Further, in addition to coordinate in three-dimensional cartesian coordinate system of point, line, surface, body geometric element is characterized, it is described The coordinate of point, line, surface, body geometric element in three-dimensional cartesian coordinate system, which is characterized, to be comprised the following steps：

（1）, coordinate characterizing method of the point in three-dimensional cartesian rectangular coordinate system：A three-dimensional cartesian right angle is built to sit Mark system, makees upright projection, the distance of subpoint to the origin of coordinates is the coordinate of point to three axles of coordinate system respectively by point Absolute 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 right angle Coordinate system, optional 2 points from straight line, according to step（1）Described method, provides this 2 points of coordinates in a coordinate system respectively, The determination method for the space line introduced in analytic geometry is recycled, seat of the straight line in three-dimensional cartesian rectangular coordinate system is provided Mark equation；

（3）, coordinate characterizing method of the plane in three-dimensional cartesian rectangular coordinate system：Build a three-dimensional cartesian right angle Coordinate system, optionally not conllinear 3 points from plane, according to step（1）Described method, provides at this 3 points in coordinate system respectively In coordinate, using the determination method for the space plane introduced in analytic geometry, provide plane in three-dimensional cartesian rectangular co-ordinate Equation in coordinates in system；

（4）, coordinate characterizing method of the body in three-dimensional cartesian rectangular coordinate system：A three-dimensional cartesian right angle is built to sit Mark system, chooses three summits, such as step respectively from each polyhedral surface successively（3）Described method, provides each table The plane equation in face, it is the area of space surrounded by the inequation group of these planes that the coordinate of body, which is characterized,.

Further, in addition to 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；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 geometric point built in three dimensions described in body space geometrical element step Method, build two points in three dimensions, whether be zero according to the distance between two points, decision space point and point it is several What relation be coincidence or from；The method characterized using coordinate of the point in three-dimensional cartesian rectangular coordinate system, provides two respectively The coordinate of individual point, according to two points coordinate it is whether identical, decision space point and point geometrical relationship be coincidence or from；

（2）, using building point, line, surface, the geometric point built in three dimensions described in body space geometrical element step Method and build three dimensions in straight line method, respectively build three dimensions in a point and straight line, The straight line in three dimensions is built, according to point whether on this straight line, the geometrical relationship of decision space point and straight line is a little It is on line or online outer；Cross and a little make vertical line to straight line, whether be zero according to point to the distance of intersection point, decision space point and straight line Geometrical relationship is that point is on line or online outer；Using coordinate characterizing method and straight line of the point in three-dimensional cartesian rectangular coordinate system The method that coordinate in three-dimensional cartesian rectangular coordinate system is characterized, provides the equation of coordinate and straight line a little respectively, according to point Coordinate whether meet the equation of straight line, the geometrical relationship of decision space point and straight line is that point is on line or online outer；

（3）It is several using one built in three dimensions described in structure point, line, surface, body space geometrical element step Whether the method for what point and a plane, builds the point and a plane in three dimensions respectively, according to point in this plane On, the geometrical relationship of decision space point and straight line is put on the whole or outside face；Cross and a little make vertical line to plane, intersection point is arrived according to point Distance whether be zero, the geometrical relationship of decision space point and plane is point on the whole or outside face；Using point in three-dimensional flute card The coordinate characterizing method of coordinate characterizing method and plane in three-dimensional cartesian rectangular coordinate system in your rectangular coordinate system, respectively Provide coordinate a little and the equation of plane, whether the coordinate according to point meets the equation of plane, decision space point and plane it is several What relation is point on the whole or outside face；

（4）, using build point, line, surface, one built in three dimensions described in body space geometrical element step it is several The method what put and built an individual of three dimensions, builds the point and an individual in three dimensions, according to structure respectively The position relationship on each surface of the regional relation that space is split on each surface of adult, decision-point and body；If point is located at structure The space that each surface of adult is surrounded, then put in vivo；If point is located on each surface for constituting body, put on body；If Point be located at constitute body each surface surround space, then body do not include point, i.e., point and body be from relation；Existed using point The coordinate sign side of coordinate characterizing method and body in three-dimensional cartesian rectangular coordinate system in three-dimensional cartesian rectangular coordinate system Method, provides the inequation group on each surface of coordinate and body a little respectively, and whether the coordinate according to point can make cuboid not Equation equation group is less than zero, equal to zero or more than zero, and decision-point is in cuboid, on cuboid or rectangular external；

（5）, using build point, line, surface, one built in three dimensions described in body space geometrical element step it is straight The method of line, builds two straight lines in three dimensions, selects three points being not arranged on the same straight line on this two straight lines, builds A plane in three dimensions, using step（3）Described method, it is known that the 4th point is sentenced on that plane or outside face The geometrical relationship for determining space line and straight line is coplanar or antarafacial；

1., two straight lines are coplanar line, and geometrical relationship is coincidence, parallel, intersecting, vertical phase between judging two straight lines Hand over, such as step（2）Described method, whether according to 2 points on straight line on another straight line, judgement two is coplanar straight Whether line overlaps；2 points on straight line are made vertical line to another straight line respectively, are one according to this 2 points and two intersection points Whether is four summits of rectangle, judges that two coplanar lines are parallel or intersecting；Two intersection points are overlapped, and judge that two coplanar lines hang down It is straight intersecting；

2., two straight lines are different surface beeline, and it is that antarafacial is vertical or general antarafacial relation to judge between two straight lines geometrical relationship： Three points being not arranged on the same straight line on this two straight lines are selected, a plane in three dimensions are built, not on that plane Straight line make upright projection to this plane, according to former straight line of the projection line in plane whether, judge the several of two former straight lines What relation is antarafacial vertical relation or general antarafacial relation；Simultaneously and the straight line that all intersects vertically of two different surface beelines is two different The common vertical line of face straight line；

（6）, coordinate characterizing method using straight line in three-dimensional cartesian rectangular coordinate system, two straight lines are provided respectively Equation, according to the equation of two straight lines, the geometrical relationship of decision space straight line and straight line is coplanar, antarafacial, coincidence, parallel, phase Hand over, intersect vertically, antarafacial is vertical or general antarafacial；Determine the common vertical line of different surface beeline；

（7）, using build point, line, surface, one built in three dimensions described in body space geometrical element step it is straight The method of line and a plane, builds the straight line and a plane in three dimensions respectively, and straight line makees vertical to this plane Projection, space line and projection line are overlapped, the geometrical relationship of decision space straight line and plane be straight line planar；Space line Intersecting with projection line, the geometrical relationship of decision space straight line and plane is that straight line and plane are intersecting；Projection line is degenerated to a throwing The geometrical relationship of shadow point, decision space straight line and plane is that straight line and plane intersect vertically；Space line is parallel with projection line, sentences It is that straight line is parallel with plane to determine space line with the geometrical relationship of plane, and the distance between straight line and projection straight line are straight line peace The distance in face；Using coordinate characterizing method of the straight line in three-dimensional cartesian rectangular coordinate system and plane at three-dimensional cartesian right angle Coordinate characterizing method in coordinate system, provides straight line and the equation of plane respectively, according to straight line and the equation of plane, decision space The geometrical relationship of straight line and plane be straight line in face, straight line and plane intersect, intersected vertically, and straight line is parallel with plane；

（8）, using build point, line, surface, one built in three dimensions described in body space geometrical element step it is straight The method of line and an individual, builds the straight line and an individual in three dimensions, such as step respectively（7）Described method, according to Whether intersect with polyhedron arbitrary surfaces according to straight line, 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 are overlapped or straight line is on polyhedral surface, decision space straight line and The geometrical relationship of body is space line on body；Using coordinate characterizing method of the straight line in three-dimensional cartesian rectangular coordinate system and Coordinate characterizing method of the body in three-dimensional cartesian rectangular coordinate system, provides the equation of straight line and each surface of body respectively Formula equation group, according to linear equation and the relation of the inequation group on each surface of body, the geometry of decision space straight line and body Relation be straight line and the cross, straight line of body phase on the border of body or with body phase from；

（9）, using a plane for building point, line, surface, structure three dimensions described in body space geometrical element step Method, build two planes in three dimensions, four points in a plane do upright projection, four to another plane respectively Individual point is all zero to distance between intersection point, and the geometrical relationship of decision space plane and plane is to overlap；Four points are between intersection point Distance it is all equal and be all not equal to the homonymy that zero, and four points are located at another plane, the geometry of decision space plane and plane Relation is parallel；The geometrical relationship of straight line in four another planes of intersection points composition, decision space plane and plane is vertical It is straight intersecting；Four points are unequal to the distance between intersection point, although or apart from all equal, four points are located at another plane The geometrical relationship of both sides, decision space plane and plane is intersecting；

（10）, using build point, line, surface, one of structure three dimensions described in body space geometrical element step put down The method in face, build three dimensions in two planes, will in a plane intersect two straight lines on three points respectively to Another plane makees vertical line, and for two former straight lines in itself, the geometrical relationship of decision space plane and plane is weight to two projection lines Close；Intersection point can only build straight line, and the geometrical relationship of decision space plane and plane is to intersect vertically；Intersection point builds two phases The straight line of friendship, and this two intersecting projection lines respectively with original three points build two straight line parallels, decision space plane and The geometrical relationship of plane is parallel；Intersection point build two intersecting straight lines, and this two intersecting projection lines respectively with original three At least a pair are not parallel in two straight lines that point is 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, two planes are provided respectively Equation, according to plane equation, the geometrical relationship of decision space plane is that plane and plane are overlapped, and intersects, intersects vertically, parallel；

（12）, using build point, line, surface, one of structure three dimensions described in body space geometrical element step put down Face and the method for an individual, build the plane and an individual in three dimensions, such as step respectively（7）、（8）、（9）Described Any one surface of method, plane and cuboid is intersected, and the geometrical relationship of decision space plane and body is intersecting；Plane and length The geometrical relationship of any one surface coincidence of cube, decision space plane and body is plane on body；Plane not with cuboid Any one surface it is intersecting or overlap, the geometrical relationship of decision space plane and body be from；Using plane in three-dimensional flute card The coordinate characterizing method of coordinate characterizing method and body in three-dimensional cartesian rectangular coordinate system in your rectangular coordinate system, gives respectively Go out the inequation group on the equation of plane and each surface of body, according to plane equation and the inequation group on each surface of body Relation, the geometrical relationship of decision space plane and body is plane and body phase is handed over, plane on the border of body or with body phase from；

（13）, using build point, line, surface, one built in three dimensions described in body space geometrical element step The method of body, builds two individuals in three dimensions, using step（4）Described method, each summit of a cuboid is all Inside another cuboid, the geometrical relationship of decision space body and body is to include；Using step（7）、（8）、（9）Described Method, each surface of an individual can be overlapped with an another individual surface, and the geometrical relationship of decision space body and body is Body and body weight are closed；Using step（12）Described method a, cuboid intersects with any one surface of another cuboid Whether, the geometrical relationship of decision space body and body be it is intersecting or from；Using seat of the body in three-dimensional cartesian rectangular coordinate system Characterizing method is marked, the inequation group on each surface of two individuals, the inequation group according to each surface of body are provided respectively Relation, the geometrical relationship of decision space body and body be include, overlap, intersecting or from.

Further, the demarcation of capture apparatus and the structure and image space of device spatial relationship is included, 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 observing that one is attached in capture apparatus Ball and cue ball formation concentric circles, i.e., above and below, equal, the master of capture apparatus of distance difference of the attached ball of right position to cue ball Optical axis is on this attached ball, cue ball, the line of the attached ball of offside, and the primary optical axis of capture apparatus is perpendicular to positioned at left, upper, right position The coordinate plane that attached ball is built；

2., two capture apparatus primary optical axis are mutually perpendicular to：Using step 1. described method, the primary optical axis point of two capture apparatus Vertical not with two mutually perpendicular coordinate planes of a device, the primary optical axis of two capture apparatus is orthogonal；

3., capture apparatus primary optical axis is parallel with the coordinate plane of device：Side of the beam of laser successively from two devices is attached Ball enters, and by the cue ball centre of sphere, is passed from the attached ball of offside, and at least a pair of the coordinate plane that builds of two devices is parallel to each other , using step 1. described method, the primary optical axis of capture apparatus is not parallel with another device in a device Coordinate 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 The a pair of parallel coordinate plane of two devices, 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, it can be demarcated using one, two or multiple devices；The conventional group of multiple devices Close the Spatial Coupling of the plane combination and eight devices that there are four devices；

3., image space demarcation conventional method：According to the conversion dimension of image space to real space, using image space Demarcating steps 1. and 2. described method, select appropriate number of caliberating device and capture apparatus；On a caliberating device Set up two dimension or three-dimensional cartesian rectangular coordinate system；Laser beam is projected, using step（1）Described method, builds capture apparatus With the spatial relationship of caliberating device；The image shot is obtained, by image procossing circle and the algorithm of center identification, device is found Cue ball and each the two-dimensional pixel coordinate of attached ball centre of sphere on image；By the design size and the feelings of Spatial Coupling of each device Condition, determines the coordinate of the rectangular coordinate system of the real space of each cue ball and each attached ball in structure；Pass through linearly or nonlinearly equation The transformation relation between them is found in establishment；According to the method for solving of linearly or nonlinearly equation group, set up that coordinate is linear or non-thread Property conversion coefficient, demarcated the transformation matrix of image space；According to different capture apparatus imaging models, equipment is derived Inside and outside parameter matrix, demarcates the parameters of capture apparatus；

4., the transformation matrix of coordinates of uncalibrated image space and two-dimensional space, it is 3. described using the demarcating steps of image space Method, determine the transformation parameter needed in scaling method, set up coordinate conversion relation, the transformation matrix in uncalibrated image space； According to different capture apparatus imaging models, the inside and outside parameter matrix of capture apparatus can be also derived, demarcation shooting is set Standby parameters；

5., the transformation matrix of coordinates of uncalibrated image space and three dimensions, it is 3. described using the demarcating steps of image space Method, determine the transformation parameter needed in scaling method, set up transformation relation, the transformation matrix in uncalibrated image space；Foundation Different capture apparatus imaging models, can derive the inside and outside parameter matrix of equipment, each ginseng of demarcation capture apparatus Number.

The beneficial effects of the utility model：

The utility model has obvious advance compared with background technology, and there is provided a kind of simply and intuitively three-dimensional tree-like Device and embodiment, can quickly and accurately build three-dimensional cartesian rectangular coordinate system, build space geometrical element point, line, Face, body and judge geometrical relationship between them, determine that coordinate of the space geometrical element in three-dimensional cartesian coordinate system is characterized, And image space is demarcated and parsed using the utility model device.Specific implementer's case is based on geometry principle, With reference to the advantage of the utility model device, the utility model device illustrating in detail several in the structure of three-dimensional system of coordinate, space The structure of what element and the judgement of geometrical relationship, characterize space geometrical element coordinate in a coordinate system and its relation and adopt Image space is demarcated with multiple devices and Duo Tai capture apparatus.

Brief description of the drawings

Fig. 1, symmetrical mounting provided with cylinder base top view.

Fig. 2, symmetrical mounting front view.

Fig. 3, asymmetric unit front view.

Fig. 4, symmetrical mounting provided with cuboid base top view.

Fig. 5, cylinder base upward view.

Fig. 6, cuboid base upward view.

The inventory of reference is as follows shown in each figures of Fig. 1 ~ Fig. 6：

1. cue ball, 2. forecourts, ball after 3., 4. left balls, 5. right balls, ball, 7. times balls, 8. front rods, 9. on 6. Back link, 10. left connecting rods, 11. right connecting rods, 12. upper connecting rods, 13. lower links, 14. base connecting rods, 15. bases, 16. Annular 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 is built 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）.

Scheme a：Subpoint（That is round dot 10）In rectangle inside region；Scheme 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：Geometry is built to close

The device of system；Round dot 10：The subpoint of point 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）.

Scheme a：General different surface beeline；Scheme 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 dress of geometrical relationship Put；Round dot 5：The subpoint of point planar（4,5 overlap on top view）Round dot 5-11：Servicing unit；Solid line：Build geometry The laser beam of relation；Dotted line：Secondary laser beams.

Embodiment

Operation principle of the present utility model 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 be to build sky Between geometric element point, line, surface, body；Three be the coordinate for characterizing space geometrical element in three-dimensional cartesian coordinate system, i.e., in a structure Determine that the three-dimensional coordinate of space point, line, surface and body is characterized in the three-dimensional cartesian coordinate system built, setting up geometric element space coordinate expires The equation and relation of foot；Four be the geometrical relationship between decision space geometric element；Five be uncalibrated image space；Using this practicality New described device, by carrying out the conversion of image space and real space, determines that transformation matrix of coordinates comes uncalibrated image space. Three-dimensional coordinate of any pixel in real space on image can be obtained by analysis diagram picture, it is possible to achieve the reality of subject Angle quantifies between border geometric properties measurement, such as length and space line between the size and profile, spatial point of object Quantitative coordinate sign of measurement and complex space geometrical relationship etc..

（One）Build three-dimensional cartesian rectangular coordinate system

1. build the origin of coordinates

The present apparatus can build a three-dimensional cartesian rectangular coordinate system, wherein the centre of sphere of cue ball can as coordinate system coordinate Origin, is referred to asOPoint.

2. build reference axis

The origin of coordinates and the centre of sphere of any one attached ball can determine that straight line, so that the reference axis of coordinate system is set up, IncludingX, Y, ZThe positive and negative semiaxis in three directions, can be referred to as positive and negativeOX, OY, OZAxle, whereinXAxle positive direction is from cue ball ball The heart points 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 from cue ball ball The heart points to upper ball centre of sphere direction, and three axles meet right-handed helix relation.

3. build coordinate plane

Any centre of sphere for choosing three spheroids not on the same line a, it may be determined that coordinate plane.Selection does not exist The cue ball centre of sphere, the front/rear ball centre of sphere, the left/right ball centre of sphere on same straight line, it may be determined that a plane, are referred to asXOYPlane, or Horizontal plane；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, claim BeZOXPlane, or sagittal plane；The cue ball centre of sphere, the left/right ball centre of sphere not on the same line is chosen, the up/down ball centre of sphere can A plane is determined, is referred to asYOZPlane, or coronal-plane.Plane is determined according to the coplanar attached ball centre of sphere of four and the above, The accuracy of demarcation and parsing image space plane can then be improved.

4. build three-dimensional cartesian rectangular coordinate system

Based on the origin of coordinates, three reference axis and three coordinate planes build a three-dimensional cartesian rectangular coordinate system.Base In the origin of coordinates, the orthogonal reference axis of any two and the coordinate plane determined by two orthogonal reference axis build one two Tie up Descartes's rectangular coordinate system；Based on the origin of coordinates and any one reference axis, an one-dimensional cartesian coordinate system is built, that is, is counted Axle；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 being aided with laser line generator and use, can build space point, line, surface, Body and judge geometrical relationship between them.By laser beam, can also extend the reference axis for building space, coordinate plane with And the yardstick in space.

1. build one, space point

The cue ball centre of sphere or the attached ball centre of sphere of one device, can be used as a geometric point in three dimensions.Not special In the case of explanation, a point refers mainly to the cue ball centre of sphere of device, similar below.

2. build space straight line

Gained knowledge according to geometry, 2 points can determine the line of straight line, i.e. any two device cue ball centre of sphere, can structure The straight line built in three dimensions, 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）, it is used as two points in space.Pass through 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 are built, and the cue ball centre of sphere of two devices is on this straight line；（2） Specific process：Two devices are positioned in identical platform, pass through rotationZAxle adjusts two devices, makes laser beam successively from it XAxle orYAxle passes through.Now laser beam is the straight line that two devices are built, and the cue ball centre of sphere of two devices is at this On bar straight line；（3）Any one reference axis of a device is taken, straight line can be built；（4）Take any the two of a device The centre of sphere of individual ball, can build straight line；（5）If point is outside straight line, it can cross outside straight line and a little build directly by following proposal The vertical line of line：Two devices are taken, are respectively placed on two platforms in space, two points in space are used as.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 The 3rd device can be passed throughXOrYAxle, and produced with the straight line that builds 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 The position of four devices, 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 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 is built Straight line intersected vertically with the straight line that builds before；（6）If point is outside straight line, it can be crossed by following proposal outside straight line a bit Build the parallel lines of straight line：Two devices are taken, are respectively placed on two platforms in space, the first of space and is used as 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 one Point builds the vertical line method of straight line, and the 3rd device is done into vertical line to the straight line 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. build a plane in space

Gained knowledge according to geometry, any three points on the same line can not determine a plane, or two it is intersecting 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, are 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 the axle of remaining in device two passes through, and takes the 3rd device, is positioned on the 3rd platform, adjusts the position of the 3rd platform Put, the second beam laser is passed through any one axle of the 3rd 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 existed, the cue ball centre of sphere of three devices is on that plane.To make this plane more directly perceived, the 3rd can be taken respectively 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, second, four straight lines be parallel to each other, and opposite side distance two-by-two Equal, four laser beams construct a rectangle.This laser-formed rectangle of four beams is in the plane of structure, the master of four devices 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 devices position, make two beam laser beams according toXAxle,YAxle（OrYAxle,XAxle）Order pass through successively from neighboring devices two-by-two, then build two of two laser beams intersect vertically straight Line constructs a plane uniquely existed, and the cue ball centre of sphere of three devices is on that plane., can to make this plane more directly perceived 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, is adjusted the position of the 4th device, is made its cue ball centre of sphere On intersection point, andXAxle,YAxle passes through third and fourth laser beam simultaneously.Understand, then four laser beam one rectangles of formation, four Device is located at four summits of rectangle, and this rectangle is in the plane of structure, and the cue ball centre of sphere of four devices is on that plane.（3） Each coordinate surface of one 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. build the individual of space one

Gained knowledge by geometry, four points at grade are not assured that the body in a space.In three dimensions In, most common body is exactly cuboid, if the length of side of cuboid is all equal, then it is exactly square.Body in this specification Polyhedron is referred mainly to, i.e., the body for forming and occupying certain space is surrounded by multiple polygon planes.The main pin of specific embodiment To polyhedron, by taking cuboid as an example, for the body of spatial complex, similar construction method can be used.

Specific embodiment：Need eight devices and 12 laser line generators；

（1）Conventional method：The specific of lower surface sets up process with above-described using four devices structure rectangles, it is determined that Conventional method 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, the cue ball centre of sphere of four devices is 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 Put in a remaining axle and pass through, then four beam laser are each perpendicular to lower surface；The the 5th to the 8th device separately is taken, four have been reused Laser line generator, produces the 9th to the 12nd beam laser respectively, and rectangle, and the 5th are built using with lower surface identical method A remaining axle to the 8th device is passed through respectively by the 5th to the 8th beam laser, then the 9th to the 12nd beam laser constructs square Shape, the cue ball centre of sphere of the 5th to the 8th device is four summits of rectangular top surface.Because this device hasX、Y、ZThree axles two Two it is vertical the characteristics of, therefore the 5th to the 8th beam laser must be perpendicular to upper surface, and laser beam corresponding with upper and lower surface is formed respectively Rectangle, constructs the surface of front, rear, left and right four of cuboid, and 12 beam laser are 12 seamed edges of cuboid.By upper Method is stated, using eight devices, 12 beam laser of auxiliary construct cuboid, with six square surfaces, eight summits, 12 Bar seamed edge.See Fig. 7.

（2）Specific process：The specific of lower surface sets up process with above-described using four devices structure rectangles, 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, the cue ball centre of sphere of four devices is 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 formation 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. the coordinate point in three-dimensional cartesian rectangular coordinate system is characterized

Coordinate of the point in three-dimensional cartesian rectangular coordinate system, can will put and make vertical throw to three axles of coordinate system respectively Shadow, the distance of subpoint to the origin of coordinates is the absolute value of the coordinate of point.If, can using coordinate as the algebraic quantity with symbol To be in the positive axis of reference axis according to subpoint, then coordinate is on the occasion of conversely, being negative value.In order to determine spatial point in three-dimensional The coordinate of Descartes's rectangular coordinate system, generally requires eight devices, 12 laser line generators and two pieces of transparent flat board glass 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（It is similar below）Place On underlying 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, under it Place another block of plate glass and be used as top layer platform；

（3）Launch three beams of laser with three laser line generators, by the origin of coordinate system, respectively along reference axis Three positive directions；

（4）Along devicea1XAxle positive direction, places a device on underlying platforma2 and allow laser beam along itsXAxle leads to Cross, devicea1 Hea2 build straight line, are used as Descartes's rectangular coordinate system of extensionXAxle；

（5）Along devicea1YAxle positive direction, places a device on underlying platforma4 and make laser beam logical along its Y-axis Cross, device a1 and a4 build straight line, are used as Descartes's rectangular coordinate system of extensionYAxle；

（6）Along devicea1ZAxle positive direction, places a device on top layer platformb1 and make laser beam logical along its Z axis Cross, devicea1 Heb1 builds straight line, is used as Descartes's rectangular coordinate system of extensionZAxle；

（7）Take a devicea3 and a laser line generator, it is placed on underlying platform, it is ensured that from deviceb3 edgesZAxle The laser beam that negative direction passes through is just from devicea3ZAxle passes through, devicea3 Hesb3 build straight line；

（8）Two laser line generators are taken, launch laser beam, and ensure devicea2XAxle anda3ZDirection of principal axis is not In the case of change, translationa2 and rotationa3, make laser beam edgea2YAxle positive direction by and pass througha3YAxle, similarly, is protected Card devicea4YIn the case of direction of principal axis is immovable, translationa4, make another laser beam edgea4XAxle positive direction by and pass througha3XAxle, 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 The laser beam that positive direction passes through is just from deviceb2ZAxle passes through, devicea2 Hesb2 build straight line；

（10）Two laser line generators are taken, launch laser beam, and ensure deviceb1 Heb2ZDirection of principal axis is immovable In the case of, rotation regulationb1 Heb2, make laser beam edgeb1XAxle positive direction by and pass throughb2XAxle, similarly, rotation regulation Deviceb3, it is ensured that another laser beam edgeb2YAxle positive direction by and pass throughb3YAxle, then four devicesa1、a2、b1 Heb2 In approximately the same 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 （Sideways 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 The laser beam that positive direction passes through is just from deviceb4ZAxle passes through, devicea4 Hesb4 build straight line；

（12）Two laser line generators are taken, launch laser beam, and ensure deviceb4ZThe immovable situation of direction of principal axis Under, rotationb4, it is ensured that laser beam edgeb1YAxle positive direction by and pass through deviceb4YAxle, similarly, adjusting meansb4, it is ensured that Another laser beam edgeb3XAxle negative direction by and pass throughb4XAxle, then four devicesa3、a4、b3 Hesb4 in approximately the same plane （Sideways 3）And one rectangle of formation, a1、a4、b1 Heb4 in approximately the same plane（Sideways 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, pass through measurement Devicea1 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, The coordinate value of Descartes's rectangular coordinate system of structure.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 just；Conversely, coordinate value It is then negative.

Specific process：Coordinate of the spatial point in three-dimensional cartesian rectangular coordinate system is determined, 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, inhaled using the magnetic below device On disk, the glass plate for being fixed on a surfacing, Descartes's rectangular coordinate system is built；

（2）Choose a devicea5, as one, the space point set up, are placed into the optional position of the octant of space first, Its lower 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 reference axis Three positive directions；

（4）Along devicea1XAxle positive direction, places a device on underlying platforma2 and allow laser beam from itsXAxle leads to Cross, devicea1 Hea2 build straight line, are used as Descartes's rectangular coordinate system of extensionXAxle；

（5）Along devicea1YAxle positive direction, places a device on underlying platforma4 and allow laser beam from itsYAxle leads to Cross, devicea1 Hea4 build straight line, are used as Descartes's rectangular coordinate system of extensionYAxle；

（6）Take a devicea3 and a laser line generator, it is placed on underlying platform, it is ensured that from devicea3 along Z axis The laser beam that negative direction passes through is just from devicea5 Z axis passes through, devicea3 Hesa5 build straight line；

（7）Two laser line generators are taken, launch laser beam, and ensure devicea2XAxle anda3ZDirection of principal axis is not In the case of change, translationa2 and rotationa3, make laser beam edgea2YAxle positive direction by and pass througha3YAxle, similarly, is protected Card devicea4YIn the case of direction of principal axis is immovable, translationa4, make another laser beam edgea4XAxle positive direction by and pass througha3XAxle, 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, pass through measurement apparatusa1 Arrivea2,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, is building Descartes's rectangular coordinate system coordinate value.In aforesaid operations, because spatial point is in the first octant, 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 Hesa5 are in corresponding axis（RespectivelyX,YWithZAxle）Positive axis, then the coordinate value of spatial point is just；Conversely, coordinate value is then It is 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 Descartes's rectangular coordinate system of structure；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 Descartes's rectangular coordinate system of structure；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 be 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 respectively Coordinate of two devices of straight line in the three-dimensional cartesian rectangular coordinate system of structure is built, the sky introduced in analytic geometry is utilized Between straight line determination method, provide equation in coordinates of the straight line in three-dimensional cartesian rectangular coordinate system.The coordinate of straight line is characterized as The equation that the coordinate of arbitrfary point is met on straight line.

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 from the device for building plane Individual device, provides this coordinate of three devices in the three-dimensional cartesian rectangular coordinate system of structure respectively, recycles analytic geometry In space plane determine method, provide equation in coordinates of the plane in three-dimensional cartesian rectangular coordinate system.The coordinates table of plane Levy the equation met by the coordinate of arbitrfary point 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, any choose does not exist from each polyhedral surface Three devices on straight line, set up the plane equation on each surface, the equation group of polyhedron then to be met by each surface Into the space that is surrounded of inequation group；Characterize, do not exist optionally on each surface from cuboid for the coordinate of cuboid Collinear three summits, provide this coordinate of three summits in the three-dimensional cartesian rectangular coordinate system of structure respectively, then Using the determination method of the space cuboid in analytic geometry, cuboid is the inequality side that the equation met by each surface is constituted The space that journey group is 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 Straight line, straight line and face, straight line and body, face and face, face and body, body and body, and other space geometry relation judgement.

1. decision space point and the geometrical relationship put

, it is necessary to a point in two devices, respectively space during geometrical relationship between decision space point and point.If two The distance between cue ball centre of sphere of individual device is zero, then the two points are spatially to overlap, that is, are considered a point, it is only necessary to Want a device；If the distance of the cue ball centre of sphere of two devices is not zero, the two point be spatially it is misaligned, I.e. this 2 points are disjoint relationships；It can also be characterized according to coordinate of the point in rectangular coordinate system, according to analytic geometry cathetus side Relation between journey, judges the geometrical relationship between straight line；If coordinate of the cue ball centre of sphere of two devices in rectangular coordinate system 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）It 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 the utility model device has certain physical dimension, in practical operation, two devices Can not possibly be overlapping, therefore the relation between 2 points is only disjoint relationship.

2. the geometrical relationship of decision space point and straight line

The geometrical relationship of decision space point and straight line is, it is necessary to which three devices build point and straight line, and two of which device can structure Straight line is built, another device can be used as one, space point.If the cue ball centre of sphere of the 3rd device is just by having been built up Straight 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.This When, can be by the way that the method that point makees vertical line to straight line to be found to the intersection point a little on straight line, then the cue ball centre of sphere of the 3rd device is arrived The vertical range of straight line, as distance of the point to straight line.

Specific embodiment：Need four devices and two laser line generators.

（1）Conventional method：Two devices are taken, are respectively placed on two platforms in space, two of space are used as 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, any one axle of the first beam laser by 3rd device can be made, then be can determine that a little on straight line.If beam of laser is not Can then it be can determine that a little outside straight line by any one axle of 3rd device；It can also determine a little and straight line is in rectangular coordinate system Coordinate, whether the coordinate according to analytic geometry midpoint meet the equation of straight line, judge relation a little with straight line on straight line Or outside straight line.

It is determined that point can pass through following proposal to the distance of straight line：A laser line generator separately is taken, makes beam of laser can With by an axle of the 3rd device, and produced with the straight line that builds 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 The position of 4th 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 build the vertical line of straight line before, and wire length is distance of the point to straight line.The distance of point to straight line is not zero, 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.Take the 3rd device as a bit, be placed on this platform, if the 3rd device of holding Cue ball centre of sphere locus is constant, by rotating 3rd device, and the first beam laser can be made to pass through 3rd deviceXOrYAxle, then It can determine that a little on straight line.If beam of laser can not pass through 3rd deviceXOrYAxle, then can determine that a little outside straight line.

, can be by following proposal, it is determined that distance of the point to straight line if point is outside straight line：It is another to take a line laser generation Device, allows beam of laser to pass through the 3rd deviceXOrYAxle, and produced with the straight line that builds before and only produce a friendship Point.The 4th device is taken, is placed on this platform, keeps the cue ball centre of sphere locus of the 3rd device constant, passes through rotation the The position of the 4th 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 builds straight line before, and wire length is distance of the point to straight line.Point is to directly The distance of line is not zero, that is, puts 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 relation a little with straight line on straight line or outside 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 A plane can be built, another is then as a point in space., can be true if the vertical range of spatial point to plane is zero The fixed point is planar；Conversely, then can determine that the point outside plane；If point is outside plane, a little hanging down to plane can be determined Straight distance；Whether method that can also be according to analytic geometry, the coordinate according to point meets plane equation, or point to plane away from Whether from being zero, 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 which seven devices and five lines swash Optical generator.Four devices and four laser line generators are taken, the conventional method structure built according to this claims midplane A plane is built, four beam laser form a rectangle, and the cue ball centre of sphere of four devices is on that plane；Take the 5th device placement In on another platform, a bit in space is used as；The six, the 7 two devices are taken, is individually placed to build on the opposite side of rectangle, makes Two beam laser of rectangle are built respectively by the cue ball centre of sphere difference of an axle of the six, the seven devices, then the six, the 7 two devices On two opposite side；The 5th laser line generator transmitting laser beam is taken, it is passed sequentially through remaining two axles of the six, the seven devices Any one axle, then the 5th beam laser is all vertical with the opposite side where the six, the seven devices；If keeping the cue ball ball of the 5th 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 by 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 It can not 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 can be determined to the distance of plane by following proposal, at most needed Ten devices and seven laser line generators：On the basis of previously described embodiment, then the eight, the 9 two devices are taken, point It is not placed on another two opposite side of rectangle, makes the another two beams laser of structure rectangle respectively by an axle of the eight, the nine devices, then The cue ball centre of sphere of eight, the 9 two devices is respectively on another two opposite side；The 6th laser line generator transmitting laser beam is taken, is made It passes sequentially through any one axle of remaining two axles of the eight, the nine devices, then the 6th beam laser and opposite side where the eight, the nine devices be all Vertically；The 7th laser line generator transmitting laser beam is taken, pass through from an axle of the 5th device, make it can be with setting up before Plane produces intersection point, by rotating the 5th device, and parallel or vertical relation the base between the first six Shu Jiguang is still kept On plinth, along each side of rectangle（And on extended line）The position of the 6th to the 9th device is adjusted, can swash the five, the six, seven beams Light is intersected at a bit, the tenth device is placed on into point of intersection, and ensure that the five, the six, seven beam laser pass through the tenth device respectively 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 cue ball centre of sphere be space some upright projection point planar, the distance between the 5th and the tenth device cue ball centre of sphere is sky Between point to plane distance.In the plane whether whether the vertical range according to point to plane is zero, it is possible to determine that put.Schematic diagram See accompanying drawing 9, wherein, a）Upright projection point is in rectangular area, b）Upright projection point is outside rectangular area；

（3）It can also determine, a little with coordinate of the plane in rectangular coordinate system, whether the coordinate according to point meets plane side Journey, decision-point is in the plane or outside plane；Or whether can also be zero according to the distance at analytic geometry midpoint to plane, sentence The relation of breakpoint and straight line is on straight line or outside 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 complexity The relation of body, can be handled using similar method.The regional relation that space is split according to each surface for constituting body, judges Point and the position relationship on each surface of body, if point, which is located at, constitutes the space that each surface of body is surrounded, put in vivo；If point On each surface for constituting body, then put on body；If point, which is not located at, constitutes the space that each surface of body is surrounded, body is not Comprising point, i.e., point and body be from relation；Can also decision-point and each polyhedral surface, each bar seamed edge and each top Geometrical relationship between point；If the vertical range put to some surface of polyhedron is zero, this can be determined in the body On surface；If the vertical range of point to a certain seamed edge of polyhedron is zero, it can determine the point on seamed edge；If point arrives polyhedron The distance on a certain summit is zero, then can determine that the point is overlapped with summit；It can also determine a little and polyhedron is in rectangular coordinate system In coordinate characterize, according to point coordinate whether can make polyhedral inequation group be less than zero, equal to zero or more than zero, Decision-point is external in polyhedron, on polyhedron or in multiaspect；The judgement of point and cuboid geometrical relationship is similar to above-mentioned Point and polyhedron relation judgement.

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 builds a bit in space.After the locus of point and body is determined, it is possible to determine that point The position relationship on each surface of the regional relation that space is split 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, whether the coordinate according to point can make the inequation group of cuboid be less than zero, equal to zero or Person is more than zero, and decision-point is in cuboid, on cuboid or rectangular external.

5. judge the geometrical relationship of straight line and straight line

Judge the geometrical relationship between straight line and straight line, it is necessary to which four devices, build two straight lines respectively.By geometry Xue Zhi Know and understand, three points being arbitrarily not arranged on the same straight line can determine a plane.From four devices, optionally not at one Three devices on straight line, build a plane.The plane that another device is built to first three device carries out upright projection, root Distance of the strong point to plane, it may be determined that the geometrical relationship between this two straight lines, if vertical range is zero, this device also exists In plane, i.e., this two straight lines are coplanar line；Conversely, if vertical range is not zero, this device not planar, this two Straight line is different surface beeline.

If the geometrical relationship of two straight lines is 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 is 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 it is the parallel relation in plane that can determine two former straight lines； 3）If obtaining two intersection points, but rectangle can not be formed；Or two intersection points are overlapped；It can then judge two straight lines as in plane Overlapping relation；Wherein, if two intersection points are overlapped, two straight lines be can be determined that for 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. Upright projection is done into plane building out-of-plane straight line, 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 to be called two antarafacials straight for the straight line that all intersects vertically of two different surface beelines The common vertical line of line.

It 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 third and fourth device builds second Bar straight line, and any three devices are not point-blank.Appoint and take three devices to build a plane, according to this claims In " relation between decision-point and plane " embodiment, whether planar the 4th device is judged, if device is flat In face, then two former straight lines are coplanar line, if not planar, for different surface beeline.

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 the geometrical relationship of two straight lines is 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 The plane that individual device is built to first three device does upright projection, finds the upright projection point in plane, takes the 5th device to put At subpoint, then the three, the five devices construct Article 3 straight line, are the projection line of Article 2 straight line 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, are individually placed on two platforms, make First, two beam laser separately take a laser line generator respectively by any one axle of the six, the seven devices, produce the 7th beam Laser, passes through from the axle in remaining two axle of the 6th 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 remaining two axle of the 7th device, because the axle of the utility model device three is vertical two-by-two, Then the 7th beam laser is vertical with first and second article of straight line, and the laser beam between the six, the seven devices is that the public affairs of two articles of different surface beelines are hung down Line.

It 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 which six devices build straight line and plane, four dresses therein A plane can be built by putting, and two other builds the straight line in space.Gained knowledge from geometry, straight line is parallel flat Straight line in face, then this straight line is parallel with plane.During the geometrical relationship of judgement straight line and plane, by two on straight line Device carries out upright projection to plane respectively, then two subpoints can planar set up straight line.If space line and Projection straight line is overlapped, and decision space straight line is planar；If the subpoint of straight line in the plane be overlap, space line and Plane is the relation intersected vertically；It is overlapping relation if space line and projection straight line are intersecting；If space line and projection are straight Line is parallel, can determine that it is parallel relation, then the distance of straight line and plane is the distance between space line and projection straight line.If empty Between straight line and plane it is intersecting, then straight line and the angle of plane are the angle between space line and projection straight line；

It can also be characterized according to the coordinate of straight line and plane in rectangular coordinate system, according to analytic geometry cathetus and plane Relation between equation, judges the straight line between straight line and plane in face, straight line intersects with plane, intersected vertically, straight line and The relation such as plane is parallel.

Specific embodiment is：Plane and the method for straight line are built according to this specification, six devices and five lines are used Laser generator builds a plane and straight line respectively；Two devices on space line are carried out to the plane of structure respectively Upright projection, according to the embodiment of " geometrical relationship of decision-point and plane " in this specification, can be respectively obtained on straight line Two devices upright projection point in the plane, can build 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, intersected vertically, 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 again The spatial relationship of miscellaneous body, can use similar method.The regional relation that space is split according to each surface for constituting body, sentences The geometrical relationship on each surface of boning out and body, if the point on straight line has the space surrounded positioned at each surface for constituting body, Then straight line and body phase are handed over；If straight line is located on each surface for constituting body or overlapped with seamed edge, straight line is on body；If on straight line Point be not located at and constitute the space that each surface of body is surrounded, then straight line and body be from relation；Can also decision-point with Geometrical relationship between each polyhedral surface, each bar seamed edge and each summit；According to straight line and body in rectangular coordinate system In coordinate characterize, according to the relation between analytic geometry cathetus equation and the inequation group of body, judge straight line and body Between on the face of body, it is intersecting or from etc. relation.Straight line and the judgement of cuboid geometrical relationship are similar to above-mentioned straight line With the judgement of polyhedron relation.

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., can be by the space on each surface of straight line and cuboid after the locus of straight line and body is determined Geometrical relationship, so as to finally judge the geometrical relationship of straight line and cuboid；It can be determined that each surface, each of straight line and cuboid Geometrical relationship between bar seamed edge and each summit, is closed using point and straight line, straight line and straight line and straight line and plane geometry The decision method of system, judges summit and straight line, straight line and each seamed edge and straight line and the geometrical relationship on each surface；According to straight line and Coordinate of the cuboid in rectangular coordinate system is characterized, according to the inequation group of 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 which 8 devices build two planes respectively.

（1）Four devices in one plane carry out upright projection to another plane respectively, are filled according to four devices to projection Putting the distance between a little can determine the geometrical relationship between plane.If the cue ball centre of sphere of four devices of a plane is to another The distance of individual plane is equal to zero, then can determine that the two planes are overlapped；Conversely, then can determine that the two planes are misaligned；If The cue ball centre of sphere of four devices of one plane is all equal and be all not equal to zero, and four cue balls to the distance of another plane 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 four devices of a plane is to another The distance of individual plane is all unequal, although or apart from 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, That is dihedral angle, is perpendicular to the straight line of intersection and its angle between the upright projection straight line of another plane in one side；

（2）Gained knowledge from geometry, two intersecting straight lines are respectively parallel to two in another plane in a plane Bar intersecting straight lines, then the two planes are parallel.Therefore, three devices adjacent in a plane are thrown to another plane respectively Shadow, if the subpoint obtained in another plane can only build straight line, two planes intersect vertically；If subpoint can be with Two intersecting straight lines, and two straight line parallels that two intersecting straight lines created are built with original three devices respectively are set up, Then two planes are parallel；If in two straight lines that two intersecting straight lines created are built with original three devices respectively at least It is not parallel to have a pair, then two planes intersect.After the intersection for finding two planes, the angle between two planes, i.e., two Face angle, is perpendicular to the straight line of intersection and its angle between the upright projection straight line of another plane in one side；

（3）Characterized according to coordinate of the plane in rectangular coordinate system, according between analytic geometry midplane and plane equation Relation, 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.It can use（1）Decision method, The geometrical relationship between plane and plane is judged according to the distance between original device to subpoint；It can also use（2）Judge Whether method, optional three from four subpoints, builds projection line, according to being parallel relation between former straight line and projection line, Judge the geometrical relationship between plane and plane；Characterized according to coordinate of the plane in rectangular coordinate system, according in analytic geometry Relation between plane equation and plane equation, judges that the plane between plane and plane is overlapped 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 With the geometrical relationship of complicated body, it can be handled using similar method.The area that space is split according to each surface for constituting body Domain relation, judges the geometrical relationship on each surface of plane and body, if plane intersect with any one surface of body, plane with Body is intersecting；If plane is overlapped with any one polyhedral surface, plane is on body；If plane not with polyhedral One surface of meaning is intersecting or overlaps, then plane and body are non-intersect, i.e., plane and body be from relation.If plane is to polyhedron The vertical range on one surface is zero, can also determine the plane on the surface of body；Can also judge plane with it is polyhedral Geometrical relationship between each surface, each bar seamed edge and each summit；According to the coordinate of plane and body in rectangular coordinate system Characterize, according to the relation between analytic geometry midplane equation and the inequation group of body, judge flat between plane and body Face on the face of body, with body phase hand over or with body phase from etc. relation.The judgement of plane and cuboid geometrical relationship is similar to above-mentioned The judgement of plane and polyhedron relation.

Specific embodiment：By taking cuboid as an example, plane and the method for 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 is determined, each of plane and cuboid can be passed through The space geometry relation on individual surface, so as to finally judge plane and the geometrical relationship of 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 is to plane or puts down Upright projection is made on each surface towards cuboid, then judges summit with plane, each seamed edge and plane and each surface with putting down The geometrical relationship in face；Characterized according to the coordinate of plane and cuboid in rectangular coordinate system, according to analytic geometry midplane equation 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, between complicated body Spatial relationship, can use similar processing method.The regional relation that space is split according to each surface for constituting body, judges The space geometry relation on one each polyhedral surface and another each surface of polyhedron, or according to " judge plane with The method of the geometrical relationship of body ", judges an individual space geometry relation with each another individual surface, if two individuals have coincidence Surface and other surfaces of an individual are still located at the space that another polyhedron is surrounded, then polyhedron includes another Polyhedron；If a polyhedron intersects with another any one polyhedral surface, two polyhedrons intersect；If more than two Face body was both non-intersect, did not also include, then was disjoint relationship；Can also judge each polyhedral surface, each bar seamed edge with And the geometrical relationship between each summit and another each polyhedral surface, each bar seamed edge and each summit；According to body Coordinate in rectangular coordinate system is characterized, and according to the relation between the inequation group of two individuals in analytic geometry, judges body Body between body hand in vivo, with body phase or with body phase from etc. relation.Cuboid is similar with the judgement of cuboid geometrical relationship In the judgement of above-mentioned polyhedron and polyhedron relation.

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.After the locus of two cuboids is determined, according to one long Coincidence between each surface of cube and another cuboid surface, intersect, intersect vertically, the geometrical relationship such as parallel, or Geometrical relationship between the individual space geometry relation with each another individual surface of foundation one, the individual of synthetic determination two；Also may be used To judge each surface, each bar seamed edge and each summit and each surface of another cuboid, each bar of a cuboid Geometrical relationship between seamed edge and each summit；Characterized according to coordinate of the cuboid in rectangular coordinate system, it is several according to parsing Relation in what between the inequation group of two cuboids, 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, parse it is several What is gained knowledge and above-mentioned basic geometric relationship is built and judged.

（Five）The demarcation of image space

The utility model device is shot by camera or video camera, its perspective view in camera plane is can obtain Picture.When the image space after shooting is converted to two dimension or three-dimensional real space, it is necessary to be demarcated and schemed by image space Image space parses two steps.Image space is demarcated：Determine in real space the device cue ball of known real space coordinate and attached The respective coordinates that ball is represented in shooting image with pixel, are closed so as to set up their conversion according to different scaling methods System.Image space is parsed：The two-dimensional coordinate that any one is represented with pixel on image, using the inverse transformation in uncalibrated image space Method, is transformed to 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 The structure of spatial relationship, 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 the utility model device of capture apparatus primary optical axis as an example, a device is taken, is utilized Magnetic chuck below device, fixing device is on the flat board of a surfacing（Metallic plate, glass plate etc., it is same as below）, Build a three-dimensional cartesian rectangular coordinate system, a capture apparatus is placed on tripod, adjustment tripod, capture apparatus and Setting position, makes the cue ball of device be located at the center of device screen, and ensures in capture apparatus it can be seen that forecourt is in master It can be seen that forecourt and cue ball formation concentric circles on the center of ball, i.e. image, and left and right two ball is to the distance phase of cue ball Primary optical axis Deng, capture apparatus is located at forecourt, cue ball, on the line of rear ball center（Sagittal axis）.Now, the key light of capture apparatus The coordinate plane that axle is constituted perpendicular to left ball, upper ball, right ball（Coronal-plane）, the camera plane of capture apparatus and this coordinate plane are put down OK.For 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 by a certain seat constructed by the primary optical axis and a device of a capture apparatus Mark plane vertical；Another capture apparatus is placed on tripod again, left/right side or the up/down of First equipment is placed on Side, estimates its primary optical axis with the primary optical axis of First equipment in substantially vertical position, adjustment tripod, capture apparatus and device Position, also with method mentioned above A, by another coordinate constructed by the primary optical axis and device of second capture apparatus Plane is vertical, and this coordinate plane is perpendicular to previous coordinate plane, even the primary optical axis of First capture apparatus before device, After advocating peace on the line of the ball centre of sphere（Sagittal axis）, then ensure the primary optical axis of second capture apparatus in the left of device, right ball of advocating peace On the line of the centre of sphere（Trunnion axis）, on Huo Zheshang, the line of the cue ball centre of sphere（Vertical axis）.Now, the key light of two capture apparatus Axle is vertical relation.

Method C：Capture apparatus primary optical axis parallel coordinates plane

Two devices are separately fixed on the flat board of two surfacings, flat position is adjusted, makes stream oriented device substantially water It is flat.Beam of laser, and horizontal sheaf the utility model device are produced using laser line generator, two setting positions is adjusted, makes Light can be successively from two devices the same side ball enter device, passed by cue ball, and on the outside of another ball with not stopping, It can ensure that two devices can build space straight line.According to method mentioned above A, one of device is selected to build Descartes's rectangular coordinate system, the primary optical axis of capture apparatus is vertical with the coronal plane constructed by one of device, then this is clapped The primary optical axis for taking the photograph equipment 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 the flat board of two surfacings, flat position is adjusted, makes stream oriented device substantially water It is flat.Beam of laser, and horizontal sheaf the utility model device are produced using laser line generator, two setting positions is adjusted, makes Light can be successively from two devices the same side ball enter device, what is do not stopped passes by cue ball, and on the outside of another ball, It can ensure that two devices can build space straight line.Two capture apparatus are distinguished each one device of autoregistration and placed, According to method mentioned above A, optionally one of device builds Descartes's rectangular coordinate system, ensures every equipment key light respectively Axle is before corresponding intrument, 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 put down OK.

2. the demarcation of image space

The demarcation of image space is exactly by determining that the device cue ball and attached ball of known spatial coordinate in real space are being clapped Take the photograph on image and use the respective coordinates of pixel denotation coordination value, closed so as to set up their conversion according to different scaling methods It is, and it is usually the coordinate in two-dimentional or three-dimensional real space for obtaining any pixel on image to parse.

Specific embodiment is as follows：

（1）The selection of capture apparatus, its Choice is as follows：According to the purpose of graphical analysis and real space dimension not With it is necessary to consider the number of capture apparatus used, how place apparatus, and the locus of determining device and device therefor closes System；If it is sufficient to obtain the two-dimensional space coordinate of small range, single device, and if three dimensions is sat on a large scale Mark, then need two or more equipment sync pulse jammings；Digital camera single image can have higher resolution ratio, but continuously Shooting image frequency is not high, and digital camera camera function can be with continuously shot images, but the resolution ratio of image is general, frequency acquisition For 25 or 30 frames/second；High-speed camera then not only can be with continuously shot images, and can have very high resolution ratio and collection frequency Rate, but it is expensive；The image space demarcation that camera is shot be a width demarcated, video camera is then continuous shoots Image, need to be extracted and be converted to after image sequence by frame, width（Or ensemble average）Uncalibrated image space.

（2）The selection of caliberating device, its Choice is as follows：According to the spatial dimension of IMAQ, real space not With dimension and the complexity of 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；The image calibration precision of multiple devices is higher than the demarcation of 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 one 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 it can use the caliberating device of more than three；Described according to multi-parameter Capture apparatus imaging model, then need multiple index points, is also accomplished by that multiple caliberating devices are applied in combination；

（3）Many devices are applied in combination, and it is as follows that scheme is applied in combination in it：The mark points provided due to single caliberating device 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 and block when taking the photograph, then the quantity of index point is also possible to reduce, therefore in actual use, it is necessary to more index point, can be with Using the combination of multiple devices come uncalibrated image.Conventional combination has the plane combination of four devices and the spatial group of eight devices Close.The plane combination of four devices is similar to the construction method of rectangle plane, and a device sets up three-dimensional cartesian coordinate system, four 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.The Spatial Coupling of eight devices is 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, symmetrical mounting and asymmetric unit difference 56 and 48 index points can be at most provided.

（4）Image space demarcates conventional method, and its specific scaling method is as follows：Change according to 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；Laser beam is projected, according to capture apparatus and the structure of device spatial relationship Method, build the spatial relationship of capture apparatus and caliberating device；The image shot is obtained, passes through 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 the rectangular coordinate system of the real space of each cue ball and each attached ball in structure；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, the parameters of capture apparatus are demarcated.

（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, the linear transformation method represented according to common coordinate, then need to obtain two of device or The space coordinate 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, figure has been demarcated Image space and the transformation matrix of coordinates of two-dimensional space；The linear transformation method represented according to homogeneous coordinates, then need to be filled The space coordinate for five or more the centre ofs sphere put, finds their corresponding pixel coordinate values respectively on image, passes through 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 the space coordinate of four of device or more the centre ofs sphere, in figure Their corresponding pixel coordinate values are found respectively as upper, are determined 8 transformation parameters needed in DLT methods, are 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 of image space demarcation, the linear transformation method represented according to common coordinate, then need to obtain three of device or The space coordinate 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, are demarcated The transformation matrix of coordinates of image space and three dimensions；The linear transformation method represented according to homogeneous coordinates, then need To the space coordinate of six or more the centre ofs sphere of device, find their corresponding pixel coordinate values respectively on image, pass through 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 changed, so that the transformation matrix in uncalibrated image space；According to conventional DLT methods, then need to obtain device Six or more the centre ofs sphere space coordinate, find their corresponding pixel coordinate values respectively on image, determine in DLT methods 11 transformation parameters needed, set up coordinate conversion relation, the transformation matrix in uncalibrated image space.

Claims (7)

1. The device that 1. 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；Consolidated on the downside of cue ball by the 6th connecting rod and 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 2. three-dimensional tree-shaped rectangular coordinate system as claimed in claim 1 is built and image space is demarcated, it is characterised in that The size of five attached balls 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, the physical dimension of connection cue ball and the six roots of sensation connecting rod of base and other five connecting rods can be with equal, can also 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 go up 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 3. 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 4. 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, can also be 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 go up 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 5. 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.
6. The device that 6. 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, base is circular or square, round diameter or the square length of side are more than 4 times of cue ball 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 more than, the diameter for the magnet that goes in ring No more than cup dolly diameter or the square base length of side.
7. The device that 7. a kind of three-dimensional tree-shaped rectangular coordinate system as claimed in claim 6 is built and image space is demarcated, its feature Be, forecourt, left ball, on outer surface of ball brush the color consistent or inconsistent with other spheroids respectively；

   Base bottom is embedded in annular magnet, and the height for the magnet that goes in ring is not higher than substructure height；

   Cue ball, base, attached ball, connecting rod can use metal, and plastics, glass, timber, high polymer material is made.