CN105022910B - A kind of access method of the topology element of three-dimensional CSG BRep models - Google Patents
A kind of access method of the topology element of three-dimensional CSG BRep models Download PDFInfo
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Abstract
The invention discloses a kind of CSG BRep model data structures, topological relation that the data structure can comprehensively inside careful record cast.Comprehensive analysis has angularly been carried out from sub- level body, topology location, topology direction to this special data structure, and has proposed two kinds of algorithms to solve the access problem of topological structure, has disclosed a kind of access method of the topology element of three-dimensional CSG BRep models.In addition, utilize the intersecting topological problem of the appropriate processing spatial model of Boolean calculation.Finally, with reference to the three-dimensional fine CSG BRep models of data structure proposed by the present invention structure, improved RANSAC algorithms or manual fitting parameter are utilized by the use of laser radar point cloud as the data source of model.Compared with common Triangulation Network Model, each component of model can be split the model, and shared internal memory is less, and possess more perfect topological relation, realize the inquiry and analysis of three dimensions object topology information.
Description
Technical field
The present invention relates to a kind of access method of the topology element of three-dimensional CSG-BRep models.
Background technology
The appearance of laser radar makes the mode of data acquisition become efficient and convenient.Modeling means general at present are according to sharp
The point cloud that optical radar measures is simplified and network forming.Although fine threedimensional model can be constructed.But its shortcoming is structure
The Triangulation Network Model built has data volume big, it is difficult to splits, does not have the shortcomings of topological relation.Not only it is not easy to manage, and not
Possesses the detailed description to model topology relation.Therefore, there is an urgent need to a kind of new method to solve these problems.At present, very
Expression and structure of more scholars to model topology relation are studied.
But three dimensions topology is also in initial stage at present, although different experts and scholars be proposed it is respective
Topological model, but also realize the access of topological structure without good method.To three-dimensional refined model inner topology knot
The research of structure is even more very few.Known the problem of existing, mainly there is at following 5 points：1) all assume that model has been present, then go
Probe into topological relation.2) all it is only to propose respective topological model, has no to probe into how to access topology.3) adjacent vacant mesosome is opened up
Though flutterring reconstruction has preferable method, difficult in the reconstruction of Topological Relation of the intersecting space body of processing.4) based on body and image come
Although realizing that three-dimensional reconstruction energy implementation model is rebuild, model forms against simple stretching, without fine structure, and
Model only has simple coordinate representation and lacks topological connection relation inside model.5) it is superfluous to there are data in most topological models
Remaining, topology merges incomplete phenomenon with geological information.
The content of the invention
The present invention is directed to these problems, according to the thought of object-oriented, using VS2010 and C Plus Plus as instrument, devises
The topology element expression of set of system and the mechanism accessed.Main contents are divided at 4 points：1. propose a kind of CSG-BREP Top Modules
The topological relation that type comes inside descriptive model.2. according to three-dimensional laser point cloud automatic Fitting parameter, or according to the point cloud after segmentation
Manual extraction parameter, with reference to topological model, realize CSG-BREP model creations so that CSG-BREP models paste with point cloud model
Close.3. construct complicated CSG-BREP models using Boolean calculation (shipping calculations, difference operation, union), by it is outer it is topological (model it
Between) turn to interior topological (within model) processing.4. the access of implementation model topological structure.The model and common Triangulation Network Model phase
Than each component of model can be split, and shared internal memory is less, and possess more perfect topological relation, realize three dimensions
The inquiry and analysis of object topology information, solving current Most models such as Triangulation Network Model does not have detailed topological relation, difficulty
The problem of with fractionation and topological relation access mechanism.
Technical scheme provided by the invention is：
A kind of access method of the topology element of three-dimensional CSG-BRep models, including：
The step of accessing the single model inner topology relation in the three-dimensional CSG-BRep models of building and Access Model
Between topological relation the step of；
By the topological relation for the three-dimensional CSG-BRep models for accessing building, to obtain in the building between each structure
Position relationship information；
Wherein, the step of sub- level topological structure of the described the step of accessing single model inner topology relation including accessing body
Parent topological structure step that is rapid and accessing body,
The step of topological relation between Access Model, including carrying out successively：Using Boolean calculation by opening up between model
Flutter and return the step of unified topology in single model accesses, and the step of access single model inner topology relation.
Preferably, in the access method of the topology element of described three-dimensional CSG-BRep models, the access body
The step of sub- level topological structure, specifically includes：
The topology element type of required lookup in the sub- level entity of body is traveled through,
When finding the topology element of required type,
By the information storage of the topology element into a mapping map,
So circulation, the topology element until finding all required types.
Preferably, in the access method of the topology element of described three-dimensional CSG-BRep models, the access body
The step of parent topological structure, specifically includes：
The body is traveled through, is found from the body positioned at all parent element structures physically,
Continue sub- level element structure of the traversal in the parent element structure in the parent element structure found,
Sub- level element structure to find assigns a unique mark,
The unique mark of the sub- level element structure and the parent element structure are put into according to key-value form
Into a mapping map,
The parent element structure being connected with the sub- level element structure is extracted from mapping map.
Preferably, will using Boolean calculation in the access method of the topology element of described three-dimensional CSG-BRep models
The step of unified topology in single model of topology recurrence between model accesses is included by entering to more than two objects
Row ships calculation, union or difference operation, to obtain in the form of a new object the step of, wherein, ship calculation, union described
With the form expression basic solid primitives that parametric equation is used in difference operation step.
Even more preferably, in the access method of the topology element of described three-dimensional CSG-BRep models, Boolean calculation is utilized
Topology between model is returned into the step of unified topology in single model accesses to specifically include：
Step 1: calculate the intersection point between the first and second voxels：Travel through all sides in the first voxel first, while time
All faces gone through in the second voxel, the first intersection point is sought into all faces in all sides in the first voxel and the second voxel,
Now, the side in the first voxel is divided into some sections by the first intersection point；In the same way, then by all sides in second element
Cap is carried out with all faces in the first element, obtains the second intersection point, now, the second intersection point is also by the side in the second voxel
It is divided into some sections；Enter step 2 afterwards,
Step 2: solve new intersection：Whether the intersection point first in determination step one is available point,
If the first intersection point is located on the border of the first element and in the border of second element, first intersection point is judged
For available point；
If the second intersection point is located on the border of second element and in the border of the first element, second friendship is also judged
Point is available point；
All available points are finally connected, to obtain new intersection；
Step 3: carry out classification processing to splitting later side in step 1：
Judge each section of the side in the first voxel and the position relationship of the second voxel, by positioned at the inside of the second voxel,
It is outside or each section with the second voxel in the first voxel overlapped is respectively divided into three classes,
Judge each section of the side in the second voxel and the position relationship of the first voxel, it is internal, outer the first voxel will to be located at
Portion or each section with the first voxel in the first voxel overlapped are also respectively divided into three classes；
Step 4: in the first and second voxels original border going or staying：Utilize the new intersection and step obtained in step 2
Classification results in rapid three,
When the first and second voxels do cap, retain positioned at the inside of the second voxel and overlapped with the second voxel side
The first voxel side two class sections, cast out a kind of section positioned at the first voxel side of the outside of the second voxel,
Retain the two class sections positioned at the inside of the first voxel and with the first voxel in the second voxel overlapped simultaneously, cast out
A kind of section positioned at the second voxel side of the outside of the first voxel；
When the first and second voxels do union or difference operation, retain positioned at the first voxel side of the outside of the second voxel
A kind of section, cast out the two class sections in the first voxel overlapped positioned at the inside of the second voxel and with the second voxel；
Step 5: the border that will be remained, a new voxel is constructed according to topology rebuilding thought.
Even more preferably, in the access method of the topology element of described three-dimensional CSG-BRep models, in the step 2,
First intersection point, which is located on the border of the first element and also includes the first intersection point in the border of second element, is located at first
On the border of element and on the border of second element,
Second intersection point is located on the border of second element and also includes the second intersection point in the border of the first element
On the border of second element and on the border of the first element.
Even more preferably, in the access method of the topology element of described three-dimensional CSG-BRep models, in the step 1,
Trying to achieve the detailed process of intersection point includes：
All parameter curves on side are collectively expressed as：C (t)=(x (t), y (t), z (t)),
All parametric surfaces in face are collectively expressed as：F (u, v)=(x (u, v), y (u, v), z (u, v)),
(1.1) parametric equation asks friendship to meet C (t)-F (u, v)=0, makes S (t, u, v)=C (t)-F (u, v),
(1.2) differentiate：
(1.3) each parameter differential display represents：
(1.4) dot product in (1.3)And makeFinally give following iterative equation：
(1.5) after the iterative equation in obtaining step (1.4), bounding volumetree is established respectively to curve and curved surface, when
When the bounding volumetree of curve intersects with the bounding volumetree leaf of curved surface, the parameter value in two leaves is taken as initial value t0, u0, v0
It is iterated, until meeting the condition of convergence, finally asks for intersection point.
Preferably, in the access method of the topology element of described three-dimensional CSG-BRep models, the topology rebuilding is thought
Want to build ring by side, then face is built by ring, finally build the mode of shell and body by face again.
Preferably, in the access method of the topology element of described three-dimensional CSG-BRep models, the building
In CSG-BRep models the adduction relationship of topology element be the topology element from complexity to simple topology element, and simply open up
Flutterring element can be shared by different complicated topology elements.
Even more preferably, in the access method of the topology element of described three-dimensional CSG-BRep models, the building
In CSG-BRep models the adduction relationship of topology element be shell and body quote face, ring is quoted in face, ring quote while and while invocation point.
The present invention comprises at least following beneficial effect：
The mode expression model that the CSG-BREP of the present invention is combined has the characteristics that：A. data volume can be largely reduced,
It is easy to the storage and management of model.B. it is capable of the generating process of clearly record cast.C. the Topology connection of model can be closed
System is handled.D. regular and irregular body can be handled simultaneously, broken through, the limitation of simple CSG expression.F. can locate
Manage the topological relation between model and model.
The present invention proposes two kinds of algorithms to solve the access problem of topological structure, realizes the sub- level and parent topology of enantiomorph
The access of structure.The topology between model can be returned unification in addition, carrying out Boolean calculation to voxel and constructing complex model
Topological issues inside to model, the access to the topological relation of building model is realized, be easy to clear and definite interior of building knot
The position such as the connection of structure and construction relation information.
Further advantage, target and the feature of the present invention embodies part by following explanation, and part will also be by this
The research and practice of invention and be understood by the person skilled in the art.
Brief description of the drawings
Fig. 1 is the topological model structure chart based on CSG-BREP of the present invention；
Fig. 2 is that topological model describes complicated body instance graph；
Fig. 3 is the geological information of the topology objects element of the present invention；
Fig. 4 is body shape member variables component relationship schematic diagram of the present invention；
Fig. 5 is according to point-cloud fitting parameter and the CSG voxel schematic diagrames of structure in the one of embodiment of the present invention；
Fig. 6 is the result schematic diagram that the upper side associated with summit of square is searched in the one of embodiment of the present invention；
Fig. 7 is the large timber construction illustraton of model based on CSG-BRep in the one of embodiment of the present invention；
Fig. 8 is the Triangulation Network Model figure that third party software Geomagic Studio12 generate large timber construction；
Fig. 9 is that the result for accessing its sub- shape side and summit in the one of embodiment of the present invention by box box shapes is shown
It is intended to；
Figure 10 is the result schematic diagram for accessing side in the one of embodiment of the present invention by summit；
Figure 11 is by the result schematic diagram of side access plane in the one of embodiment of the present invention.
Embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings, to make those skilled in the art with reference to specification text
Word can be implemented according to this.
It should be appreciated that such as " having ", "comprising" and " comprising " term used in the present invention do not allot one or
The presence or addition of a number of other elements or its combination.
For having data volume big come the Triangulation Network Model built by discrete point cloud at present, it is impossible to split, without topology
The shortcomings of relation, the present invention propose a kind of special CSG-BRep model data structures, and the data structure can be comprehensively careful
Topological relation inside record cast.To this special data structure from sub- level body, topology location, topology is towards angularly
Comprehensive analysis has been carried out, and has proposed two kinds of algorithms to solve the access problem of topological structure.In addition, boolean's fortune is carried out to voxel
Calculation, which constructs complex model, to return unification to the topological issues inside model by the topology between model.Finally utilize laser
Data source of the radar points cloud as model, basic solid primitives parameter is fitted using improved RANSAC algorithms, is carried with reference to the present invention
The data structure construction CSG-BRep model voxels gone out, the data structure analyzed and accessed in the voxel are verified.
The present invention provides a kind of access method of the topology element of three-dimensional CSG-BRep models, including：
The step of accessing the single model inner topology relation in the three-dimensional CSG-BRep models of building and Access Model
Between topological relation the step of；
By the topological relation for the three-dimensional CSG-BRep models for accessing building, to obtain in the building between each structure
Position relationship information；
Wherein, the step of sub- level topological structure of the described the step of accessing single model inner topology relation including accessing body
Parent topological structure step that is rapid and accessing body,
The step of topological relation between Access Model, including carrying out successively：Using Boolean calculation by opening up between model
Flutter and return the step of unified topology in single model accesses, and the step of access single model inner topology relation.
The present invention proposes two kinds of algorithms to solve the access problem of topological structure, realizes the sub- level and parent topology of enantiomorph
The access of structure.The topology between model can be returned unification in addition, carrying out Boolean calculation to voxel and constructing complex model
Topological issues inside to model, the access to the topological relation of building model is realized, be easy to clear and definite interior of building knot
The position such as the connection of structure and construction relation information.
Preferably, the step of sub- level topological structure of the access body, specifically includes：
The topology element type of required lookup in the sub- level entity of body is traveled through,
When finding the topology element of required type,
By the information storage of the topology element into a mapping map,
So circulation, the topology element until finding all required types.
Preferably, the step of parent topological structure of the access body, specifically includes：
The body is traveled through, is found from the body positioned at all parent element structures physically,
Continue sub- level element structure of the traversal in the parent element structure in the parent element structure found,
Sub- level element structure to find assigns a unique mark,
The unique mark of the sub- level element structure and the parent element structure are put into according to key-value form
Into a mapping map,
The parent element structure being connected with the sub- level element structure is extracted from mapping map.
Preferably, the topology between model is returned what the unified topology in single model accessed using Boolean calculation
Step is included by carrying out shipping calculation, union or difference operation to more than two objects, in the form of obtaining a new object
The step of, wherein, express basic solid primitives with the form of parametric equation in described ship in calculation, union and difference operation step.
Preferably, in above-mentioned scheme, the topology between model is returned into unification using Boolean calculation and arrives single mould
The step of topology in type accesses specifically includes：
Step 1: calculate the intersection point between the first and second voxels：Travel through all sides in the first voxel first, while time
All faces gone through in the second voxel, the first intersection point is sought into all faces in all sides in the first voxel and the second voxel,
Now, the side in the first voxel is divided into some sections by the first intersection point；In the same way, then by all sides in second element
Cap is carried out with all faces in the first element, obtains the second intersection point, now, the second intersection point is also by the side in the second voxel
It is divided into some sections；Enter step 2 afterwards,
Step 2: solve new intersection：Whether the intersection point first in determination step one is available point,
If the first intersection point is located on the border of the first element and in the border of second element, first intersection point is judged
For available point；
If the second intersection point is located on the border of second element and in the border of the first element, second friendship is also judged
Point is available point；
All available points are finally connected, to obtain new intersection；
Step 3: carry out classification processing to splitting later side in step 1：
Judge each section of the side in the first voxel and the position relationship of the second voxel, by positioned at the inside of the second voxel,
It is outside or each section with the second voxel in the first voxel overlapped is respectively divided into three classes,
Judge each section of the side in the second voxel and the position relationship of the first voxel, it is internal, outer the first voxel will to be located at
Portion or each section with the first voxel in the first voxel overlapped are also respectively divided into three classes；
Step 4: in the first and second voxels original border going or staying：Utilize the new intersection and step obtained in step 2
Classification results in rapid three,
When the first and second voxels do cap, retain positioned at the inside of the second voxel and overlapped with the second voxel side
The first voxel side two class sections, cast out a kind of section positioned at the first voxel side of the outside of the second voxel,
Retain the two class sections positioned at the inside of the first voxel and with the first voxel in the second voxel overlapped simultaneously, cast out
A kind of section positioned at the second voxel side of the outside of the first voxel；
When the first and second voxels do union or difference operation, retain positioned at the first voxel side of the outside of the second voxel
A kind of section, cast out the two class sections in the first voxel overlapped positioned at the inside of the second voxel and with the second voxel；
Step 5: the border that will be remained, a new voxel is constructed according to topology rebuilding thought.
Preferably, in the step 2, first intersection point is located on the border of the first element and is located at second element
Border in also include the first intersection point and be located on the border of the first element and be located on the border of second element,
Second intersection point is located on the border of second element and also includes the second intersection point in the border of the first element
On the border of second element and on the border of the first element.
In above-mentioned scheme, preferably, in the step 1, trying to achieve the detailed process of intersection point includes：
All parameter curves on side are collectively expressed as：C (t)=(x (t), y (t), z (t)),
All parametric surfaces in face are collectively expressed as：F (u, v)=(x (u, v), y (u, v), z (u, v)),
(1.1) parametric equation asks friendship to meet C (t)-F (u, v)=0, makes S (t, u, v)=C (t)-F (u, v),
(1.2) differentiate：
(1.3) each parameter differential display represents：
(1.4) dot product in (1.3)And makeFinally give following iteration side
Journey：
(1.5) after the iterative equation in obtaining step (1.4), bounding volumetree is established respectively to curve and curved surface, when
When the bounding volumetree of curve intersects with the bounding volumetree leaf of curved surface, the parameter value in two leaves is taken as initial value t0, u0, v0
It is iterated, until meeting the condition of convergence, finally asks for intersection point.
Preferably, in above-mentioned scheme, the topology rebuilding thought is to build ring by side, then builds face by ring, most
Build the mode of shell and body by face again afterwards.
Preferably, the adduction relationship of topology element is the topology member from complexity in the CSG-BRep models of the building
Element arrives simple topology element, and simple topology element can be shared by different complicated topology elements.
Preferably, in the CSG-BRep models of the building topology element adduction relationship for shell and body quote face,
Face quote ring, ring quote while and while invocation point.
Based on CSG-BRep building topology models
1st, CSG-BRep model topologies element
Model is made up of fundamental, and these fundamentals are conceptualized as points, edges, faces, ring, shell, body and complicated body
And complex, show progressive relationship from simple to complex.As shown in table 1.
Each key element of the topology of table 1 and its meaning
Wherein, the position on summit is represented with geometric point.Point is most basic element in geometric modeling, free curve, song
Face or its allothimorph can use orderly point set representations.Side includes being not belonging to the undermined edge in any face, be pertaining only to face from
By while and belong to two or more faces it is shared while.Side includes several geometric representations：Curve in three dimensions, this is side
Basic representation mode；The parameter curve of two-dimensional space, for representing the side for belonging to face.The multistage also represented by one group of three-dimensional point
Line, multi-section-line can also be represented by the index put on one group of triangulation face.Face is by the curved surface of bottom and one or more
Individual ring describes.
2nd, topological model structure
Include the topological connection relation of complexity among model.It can be facilitated using the method (CSG) of constructive solid geometry
The different models of processing between topology constructing, still, it is only body mould that single CSG method for expressing, which is confined to minimum unit,
Type, model inner topology relation can not be embodied.Set forth herein the CSG modes combined with BRep to carry out building topology model.Entity
Border be to be represented by the union in face, and each face is represented by the definition of the curved surface where it plus its border, the side in face
Boundary is the union on side, and side is represented by putting again.As shown in Figure 1.
In topology, summit can form side, and side can form ring, and ring may be constructed face again, face in further composition shell or
Person's body.The topology objects of higher levels are built into step by step by the topology objects of lower-level.Centre can not across level establishment.It can not lead to
Cross topology objects side direct construction face or shell object (summit structure ring, face structure body except).Meanwhile by different bodies (solid)
Complicated body (compsolid) can be set up into, and can be unified to form complex by above-mentioned all topology objects
(compound)。
The topology element of higher level includes the reference to the element subordinate topology element.All references are all opening up from complexity
Element is flutterred to simple topology element.Meanwhile simple topology element can be shared by different complicated topology elements.With one
Exemplified by individual complicated body, according to set forth herein topological model the topological relation inside complex model is described, as shown in Figure 2.
Only three kinds of topology objects are directly associated with geometric object：Summit (vertex), side (edge), face (face),
Respectively Geo_Vertex, Geo_Edge, Geo_Face.In addition, summit, side, face are respectively allocated a tolerance
(Tolerance) value, for judging whether generate in error range inner vertex, side and face.Summit tolerance T geometric meaning be with
Summit is the ball that center of circle radius is T.This ball must include the end points of the curve on all sides being connected with this summit.The appearance on side
Difference is the maximum deviation between its three-dimensional curve and other any representations.It using tolerance is radius along side that its geometric meaning, which is exactly,
A three-dimensional curve comprising side and the pipe that represents of other any forms.The geometric meaning of the tolerance in face is the one of enveloping surface
The individual plate with thickness.Under normal circumstances, it is necessary to meet following condition：When side is located on face, and summit is located on side, the appearance in face
Difference<The tolerance on=side<The tolerance on=summit.More complicated geometry can be further associated with by geometry point-line-surface basic object
Object, then, topology information and geological information just directly or indirectly associate completely.Carrying out various computings and operation
In, it is possible to these geological informations are directly obtained by topology information, geological information reverse topology information can also be passed through.With opening up
The relation for flutterring the associated geometric element of object elements and tolerance is as shown in Figure 3.
In topology element, each element belongs to the object of entity (model is in itself).It is located at the topology of intermediate level
Object has the associated parent connect and sub- level topology objects simultaneously.Therefore, the access of topological relation is also classified into two kinds：It is a kind of
To access the topology objects annexation with its parent topology objects in itself, another kind be access topology objects in itself with its sub- level
The annexation of topology objects.The present invention realizes the access of both topological relations.Three are included wherein in arbitrary topology object
Variable, topology location CSGLocation are topological towards CSGOrientation and sub- level entity CSG_Subshape.Such as Fig. 4 institutes
Show, the sub- level topology objects being connected with shape are recorded in sub- level entity, and position records topology objects relative to world coordinate system
Spin matrix, towards record topology objects between orientation.
3rd, topology location
In order to track the position of topology element, each shape defines a local coordinate system CSGLocation.It is local to sit
Mark system can be represented by the following two kinds mode：Three mutually perpendicular vectors that one right-hand rule represents；One relative
In the conversion of world coordinate system；Location variable illustrates a series of coordinate system that elementary matrix obtains after conversion, for protecting
The result after accumulation conversion is deposited, this is avoided that recalculating for matrixing.If the matrix deposited in the location variable is Q, Q
1) and 2) it is necessary for 3*4 matrix, and Q must is fulfilled for following two conditions：
1)
2)
Matrix Q is the matrix of a linear transformation, and a point (x, y, z) can be transformed into addition a little by it by matrix multiplication
(u,v,w)：
Wherein Q is also likely to be the combination of basic transformation matrix.Basic transformation matrix includes translation transformation matrix, rotation transformation
Matrix, scale transformation matrix, centra-symmetric transformation matrix, axial symmetry transformation matrix, plane symmetry transformation matrix.Pass through these changes
Complex transformation matrix can be obtained by changing the combination of matrix
Parent shape location can have an impact to the sub- level shape of the shape.For example, to an edge type
Shape do translation transformation along vector (100,200,0) vector, the location in edge now deposit relative to generation
The transformation matrix of boundary's coordinate system is：
Now travel through the sub- level shape in edge, the transformation matrix deposited in vertex v ertex location variables
It is still matrix (4).If doing translation transformation and rotation transformation (rotating PI/2 along X-axis) to the shape of edge types simultaneously,
The matrix of location variables storage in edge and edge level body vertex is all relative to world coordinate system
Complex transformation matrix：
4th, topological direction
In addition, topological direction has an extremely important effect for the orientation for recording topology element, and topological direction and
Border has closely contact.Due to based on parameter representing that there is simple structure, calculating easy, numerical stability, and join
Number representation is easy to the scope of regulation curve and surface, so the parameter that curve and curved surface designed in the present invention all uses represents
Method.In parameter representation, the boundedness of curve and surface is inherently derived by the boundedness in parameter section.Need to use topology side
To shape by three kinds：By the curve of point constraint, the curved surface constrained by side and the space constrained by face.Either
Any shape border of the space geometry region higher as dimension (shape in itself), defines two local segments, its
In one be designated as give tacit consent to section.For a curve by point constraint, the parameter of curve first represents that song must be provided
One direction (natural direction) of line, such as sets a≤u≤b, and curve C (u) directions are and the acquiescence of the curve from C (a) to C (b)
Section is exactly the set of some row of along a curved path point bigger than vertex parameter., should for a curved surface constrained by side
The acquiescence section of curved surface is located at the left side of side direction of advance.While direction of advance refer to while natural direction, i.e., counterclockwise.It is right
In the space that one is constrained by face, the acquiescence section in the space is located at the opposite side of curved surface normal direction.
Topological direction is defined based on this acquiescence section come the inside (another local segment) to shape.Topological direction
The inside for defining shape shares four kinds of situations, as shown in table 2.
2 topological direction of table is to four kinds of definition inside shape
Topological direction is very general, in CSG-BRep models, as long as having segmentation or the place of border appearance to use
To topological direction.
Place forward and backward in topological direction is the most extensive.Shape direction determines the shape level shapes
Direction.The direction on wherein summit does not have direct geometric meaning, if summit CSG_Vertex's is oriented CSG_FORWARD,
It must just be matched with the small end of parameter value for the curve for representing side.Correspondingly, if summit is oriented CSG_REVERSED,
Then the big end of the parameter value of curve of the summit with representing side matches.If topology side CSG_Edge's is oriented CSG_
FORWARD, then it represents that the logical direction on side is identical with the natural direction of parameter curve；If CSG_REVERSED, then it represents that
Logical direction is opposite with the natural direction of parameter curve.Similarly, if topology face CSG_Face's is oriented CSG_FORWARD,
Then the direction in face and the normal direction of parametric surface are identical；If face is oriented CSG_REVERSED, the direction and parametric surface in face
Normal direction it is opposite.Shape direction is correctly set, and takes topological direction inversion, supplement etc. to operate, for shape
Material is added, correctly shows that shape, and the shape built carry out correct Boolean calculation and played to pass weight in which way
The effect wanted.Wherein, inversion operation is done to a topology objects so that the object topology direction is intercoursed forward and backward,
It is outwardly and constant inwardly.One topology objects is done supplement operate cause the object is exchanged with each other forward and backward, outwardly with
Also it is exchanged with each other inwardly.
5th, sub- level shape
For a body, CSG_Shape list is contained in its sub- level body CSG_Subshape,
All sub- level bodies related to body are housed in the list.Each body includes the reference of an antithetical phrase level body,
When simply quoting not abundant enough for one, for example run into a line and shared by two faces of a solid, now may be used
Energy side direction in two different faces is different, now needs two information：The reference of one topology location and a topology
The reference of direction.Only in this way, just can guarantee that will not malfunction when two topology elements at the same level share subordinate's topology element.
Embodiment 1
The access mechanism of topology element based on topological model
1st, the three-dimensional fine voxel model of structure
Before the mechanism for accessing topological structure is introduced, it is necessary first to constructed according to topological model structure above
Three-dimensional fine voxel model.The present invention proposes one three-dimensional point of selection in a cloud, utilizes RANSAC innovatory algorithms, joint line
Property least square method is extracted and is fitted quadratic surface, the selection mode of primary iteration point in RANSAC algorithms is improved, just
It is secondary to solve the area for carrying out cloud data after quadratic surface parameter automatically using the method for iteration according to the scanning density of spatial point
Regional partition, finally calculate the exact value of quadratic surface parameter after segmentation, the quadratic surface using linear least square to segmentation
Carry out Accurate Curve-fitting.The size of CSG voxels is obtained by fitting.CSG voxels are made up of basic topology key element, by above-mentioned
CSG-BRep model data structures, geometry and topology are merged, with reference to the speed-raising size after fitting, from bottom summit
Vertex constructs model voxel step by step.Naive model voxel mainly includes cuboid, cylinder, cone, spheroid, annulus
Body or the free form surface of closing etc..As shown in figure 5, the cylinder sphere fitted according to discrete point cloud, and generate CSG basic solid primitives
Cylinder, spheroid.
2nd, topological structure algorithm is accessed
In order to realize access of the CSG-BRep topologies for coupled shape up and down, it is necessary to be walked as follows
Suddenly：
Access shape level topological structure
Because directly containing variable CSG_Subshape in any one topology objects shape, and CSG_Subshape
In contain shape list, what is deposited in the list is the set of topology objects level, so, directly from the set
The topological classification searched required for middle traversal.In addition, if if a topology element is repeatedly quoted, then may
Travel through that the element is multiple, for example a line in square is generally shared by two faces, it is ensured that only to one in ergodic process
The individual topology element being shared accesses once, then must all be put into these topology elements in one mapping map.Implementation process
It is as follows：
Wherein S is the body to be traversed, and T is sub- level body to be accessed, and M is a mapping of oneself definition.Profit
The subobject of any one topology objects can be accessed with the algorithm.Such as can be in lookup face side, the summit in face, side
In summit etc..
Embodiment 2
Access shape parent topological structure
Due to being all from the top down (from CSG_ in the topological data structure of the CSG-BRep models designed by the present invention
Shell or CSG_Solid to CSG_Vertex) reference, it is impossible to directly from sub- level element as accessing sub- level topological structure
To access the parent element of the sub- level, so, the present invention proposes such a algorithm to solve the problem, using a square as
Example, as shown in fig. 6, in order to search three sides being connected with positioned at a summit of square, it is necessary to come according to following steps
Realize：
A. the square is traveled through, all side structures on the square are found from the square.
B. on the summit continued in structure on when traversal is located at this found.
C. to one coding of summit assignment found in b, a unique mark for being encoded to the summit is changed.
D. by the side (the just structure found in b) where the mark on summit in c and the summit according to key-value shape
Formula is put into map.
E. three side structures being connected with summit are extracted from map.
Specific implementation process is as follows：
Wherein, S is the body being traversed, and TS is exactly the side structure being connected with the summit if summit, then TA.
Using the algorithm, can dexterously solve the problems, such as that topology element causes data redundancy after repeatedly quoting, finally handle
The result such as table 3 of square, wherein, leftedge to rightedge is the direction of advance counterclockwise on side, and vertexID is summit
Unique mark：
Table 3：Access side associated with summit in quadrangle
Embodiment 3
The conversion of model inner topology relation is arrived between model
According to above-mentioned algorithm, it is possible to achieve the structure of single model inner topology relation and access, but between model
Topological relation is also untreated.Using Boolean calculation famous in CSG, the relation between model can be dexterously handled, by right
Different models carries out Boolean calculation, the topology between model can be returned into unification to the topology in model, utilize mould naturally
Algorithm in type can be with solution.
1st, typical voxel is represented with the geometric parameter equation
Cap is to construct the core content of CSG model boolean operations, and its efficiency and precision can directly influence boolean
The effect of computing, and then influence the reliability of construction entity.Friendship is asked including between straightway, between straightway and face
Ask friendship, the also intersection algorithm between face and face.Also, the realization of cap depends on the geometry implied in topology element will
Element, such as the curve and surface equation of key element.These curve and surface equations represent more in the form of parametric equation.The present invention be according to
The algorithm of sets classification and intersection realizes Boolean calculation.Table 4 is the parameter of geometric element in some typical basic solid primitives
Equation represents.
Several typical basic solid primitives parametric equations of table 4 represent
In table 4, straight-line data includes three-dimensional point P and three-dimensional vector D.Straight-line pass point P, and along D directions.Number of planes
According to including three-dimensional point P and three-dimensional orthogonal coordinate system N, Du, Dv.Plane is by point P, and its normal vector is N.The data on the face of cylinder
Include three-dimensional point P, Dv, Dx, Dy and nonnegative real number r of three-dimensional orthogonal coordinate system.The axle on the face of cylinder by point P, direction Dv,
The radius on the face of cylinder is r.The packet P containing three-dimensional point of circular conical surface, orthogonal coordinate system Dz, Dx, Dy, nonnegative real number r and real number ψ
(scope is (- pi/2, pi/2)).Circular conical surface is Dz by the direction of point P and axle.Cross point P and be with direction Dx, plane parallel Dy
The reference planes of circular conical surface.Reference planes truncated cone face is a circle, and its radius is r.The packet P containing three-dimensional point of sphere, three
Orthogonal dimension coordinate system Dz, Dx, Dy and nonnegative real number r.I.e. the centre of sphere of sphere is point P, radius r.The packet of anchor ring contains three
Tie up point P, three-dimensional orthogonal coordinate system Dz, Dx, Dy and nonnegative real number r1, r2.The axle of anchor ring by point P, direction Dz, r1 be from
To point P distance, the radius of the circle of anchor ring is r2 at the center of the circle of anchor ring.The packet in linear stretch face contains three-dimensional
Dv and three-dimensional curve.The packet P containing three-dimensional point of the surfaces of revolution, three-dimensional D and three-dimensional curve.The axle of surface of revolution passes through point P
And direction is D, rotating curve is that C and rotary shaft are coplanar.
2nd, Boolean calculation algorithm is created
Boolean operation method proposed by the present invention is based on the intersection algorithm of parameter curve and parametric surface.In basic body
After the form expression of element parametric equation, the Boolean calculation between voxel is carried out using following method.
A. the intersection point between two voxels is calculated.Assuming that two voxels of existing A, B.All sides (parameter song in A is traveled through first
Line represents), while travel through all faces in B (parametric surface expression).Face all in side all in A and B is found intersection.This
When, intersection point splits side.Similarly, then by all faces in all sides in B and A cap is carried out, obtains intersection point.
B. later side will be split and carry out classification processing.After a, the side intersected in A with face in B is divided into by intersection point
Some sections.It is in B inside, outside, or three kinds of situations of coincidence now to judge that these in A split later side.Similarly, B phases
Identical is taken to operate for A.
C. new intersection is solved.Need first to determine useful cross before new intersection is solved.I.e. if solved in a steps
Intersection point simultaneously meet (contain border) on A border and in B border, then the intersection point is available point.Similarly, B phases are judged
For A available point.After all available points are judged, these available points are subjected to line again, obtain new intersection.
The going or staying on original border in d.AB.New intersection completes Boolean calculation in classification results and c in b.
When A and B do cap, then the side in A is internal and border relative to B, as reservation, is cast out relative to outside B
Side, while take identical to operate relative to A B.When A and B do cup or difference operation, the side in A is relative to B
Outside, as reservation, cast out inside.
E. the border that will be remained, ring is built by side according to topology rebuilding thought again, then face, face structure is built by ring
The mode of shell and body constructs the result S after A and B Boolean calculations.
The core of algorithm above be realize parameter curve and parametric surface in a steps seek friendship problem.By all parameters
Curve is collectively expressed as：C (t)=(x (t), y (t), z (t)) parametric surface all be collectively expressed as F (u, v)=(x (u,
V), y (u, v), z (u, v)) then the intersection point of parameter curve and parametric surface is determined by following formula.
A. parametric equation asks friendship to meet C (t)-F (u, v)=0, makes S (t, u, v)=C (t)-F (u, v).p
B. differentiate.
C. each parameter differential display represents
Both sides dot product in d.cAnd makeFinally give the iterative equation in e
E. iterative equation.
After iterative equation is obtained, bounding volumetree is established respectively to curve and curved surface, when bounding volumetree and the song of curve
When the bounding volumetree leaf in face is intersecting, the parameter value in two leaves is taken as initial value t0, u0, v0It is iterated, until meeting to receive
Condition is held back, finally asks for intersection point
According to above-mentioned algorithm, by the Boolean calculation between model, the topological relation between model is revert to mould again
The access of the structure and topological structure of type inner topology relation.
The present invention is programmed, the data source of this experiment is utilization by the use of VS2010 as development environment using C Plus Plus
Three laser sweep the cloud data of instrument acquisition, go out basic solid primitives cuboid, cylinder etc. by Points cloud Fitting, utilize article
RANSAC innovatory algorithms set forth above are fitted and calculated cuboid in a cloud, cylinder equidimension parameter, in combination with preceding
Topological model described in text, and the Forbidden City The Gate of Supreme Harmony large timber construction CSG-BRep with topological relation is constructed by Boolean calculation
Model, as shown in Figure 7.In order to compare, at the same with third party software Geomagic Studio12 generate large timber construction triangle
Pessimistic concurrency control, as shown in Figure 8.Accessed, the query analysis CSG-BRep large timber construction models, can obtained shown in Fig. 7 by topology
Model include 81 cylinders, 148 cuboids altogether.Model is detachable.With detailed topological relation.Committed memory it is big
Small is 336KB.And the common triangulation network large timber construction model as shown in Figure 8 directly generated according to discrete point, altogether comprising 3991
It is individual, 7475 tri patch.Model can not be split.The annexation on triangle summit is only included, is closed without complete topology
System.The size of committed memory is 1986KB.
Pass through visit of the programming realization CSG-BRep topologies for coupled shape up and down using above-mentioned algorithm
Ask, that is, realize the access to model topology element parent object and subobject.
By contrast it is recognised that set forth herein the fine CSG-BRep models of three-dimensional, be not only effectively reduced data
Amount, and model is detachable, and each several part component is clear, and possess can query analysis topological relation.
The advantages of another protrusion of the CSG-BRep models is the inquiry point for realizing three dimensions object topology information
Analysis.Below with algorithm previously described herein, programming realization CSG-BRep topologies are for coupled shape up and down
The access of shape, that is, realize the access to model topology element parent object and subobject.For convenience's sake, the large timber construction is extracted
In a basic body exemplified by, to verify the access reliability of topological structure pair.As Fig. 9 represent pass through a shape cuboid,
Its sub- level shape side and summit is accessed respectively.As Figure 10 represent to access respectively by a summit on shape box it is coupled
The three parent topology sides connect.Coupled two are accessed by a topological side on shape box respectively shown in Figure 11
Parent manifold.From a summit, the side that can be connected with queried access with the point；, can be with queried access from side
The face being connected with the side；From face, the body that can be formed with the queried access face.In turn, visit can be inquired about step by step from body
Ask any subobject of the body.
The component relationship of topology information and geological information in the shape that the present invention is represented CSG-BRep has been carried out in detail
Elaboration and analysis simultaneously, realize visit of any one topology objects for coupled father and object and sub- level object
Ask.
The present invention devises the topology data model based on CSG-BREP, and the group of topology element is contained in the data model
Into relation, the combination of topology element and geometric element, and three big mechanism of topology element：Topology location, topological direction, sub- level
Element list.And according to the thought of object-oriented, using VS2010 and C Plus Plus, by experiment, realize three-dimensional refined model
Generation, Boolean calculation, and the access of model inner topology element, work well.Topology data model based on CSG-BREP,
Annexation between model element understands, is advantageous to the query analysis of D spatial features.It this method solve at present
Most models such as Triangulation Network Model does not have detailed topological relation, and only has topological model but be unable to free access topology knot
The problem of structure.
Topology element and access mechanism described herein are the explanations for simplifying the present invention.The topology of the present invention is visited
Ask that the application of mechanism, modifications and variations will be readily apparent to persons skilled in the art.
Although embodiment of the present invention is disclosed as above, it is not restricted in specification and embodiment listed
With it can be applied to various suitable the field of the invention completely, can be easily for those skilled in the art
Other modification is realized, therefore under the universal limited without departing substantially from claim and equivalency range, it is of the invention and unlimited
In specific details and shown here as the legend with description.
Claims (10)
- A kind of 1. access method of the topology element of three-dimensional CSG-BRep models, it is characterised in that including：Between the step of accessing the single model inner topology relation in the three-dimensional CSG-BRep models of building and Access Model Topological relation the step of；By the topological relation for the three-dimensional CSG-BRep models for accessing building, to obtain the position in the building between each structure Put relation information；Wherein, it is described access single model inner topology relation the step of including access body sub- level topological structure the step of and The parent topological structure step of body is accessed,The step of topological relation between Access Model, including carrying out successively：The topology between model is returned using Boolean calculation The step of returning the unified topology in single model to access, and the step of access single model inner topology relation.
- 2. the access method of the topology element of three-dimensional CSG-BRep models as claimed in claim 1, it is characterised in that the visit The step of sub- level topological structure for asking body, specifically includes：The topology element type of required lookup in the sub- level entity of body is traveled through,When finding the topology element of required type,By the information storage of the topology element into a mapping map,So circulation, the topology element until finding all required types.
- 3. the access method of the topology element of three-dimensional CSG-BRep models as claimed in claim 1, it is characterised in that the visit The step of parent topological structure for asking body, specifically includes：The body is traveled through, is found from the body positioned at all parent element structures physically,Continue sub- level element structure of the traversal in the parent element structure in the parent element structure found,Sub- level element structure to find assigns a unique mark,The unique mark of the sub- level element structure and the parent element structure are put into one according to key-value form Map in map,The parent element structure being connected with the sub- level element structure is extracted from mapping map.
- 4. the access method of the topology element of three-dimensional CSG-BRep models as claimed in claim 1, it is characterised in that utilize cloth Topology between model is returned the step of unified topology in single model accesses by your computing to be included by two or more Object carry out shipping calculation, union or difference operation, to obtain in the form of a new object the step of, wherein, shipped described Calculate, express basic solid primitives with the form of parametric equation in union and difference operation step.
- 5. the access method of the topology element of three-dimensional CSG-BRep models as claimed in claim 4, it is characterised in that utilize cloth Topology between model is returned the step of unified topology in single model accesses and specifically included by your computing：Step 1: calculate the intersection point between the first and second voxels：Travel through all sides in the first voxel first, while travel through the All faces in two voxels, the first intersection point is sought into all faces in all sides in the first voxel and the second voxel, now, Side in first voxel is divided into some sections by the first intersection point；In the same way, then by all sides in second element and the All faces in one element carry out cap, obtain the second intersection point, and now, the second intersection point also splits the side in the second voxel Into some sections；Enter step 2 afterwards,Step 2: solve new intersection：Whether the intersection point first in determination step one is available point,If the first intersection point is located on the border of the first element and in the border of second element, first intersection point is judged to have Effect point；If the second intersection point is located on the border of second element and in the border of the first element, also judge that second intersection point is Available point；All available points are finally connected, to obtain new intersection；Step 3: carry out classification processing to splitting later side in step 1：Each section of the side in the first voxel and the position relationship of the second voxel are judged, by positioned at the inside of the second voxel, outside Or each section with the second voxel in the first voxel overlapped is respectively divided into three classes,Judge each section of the side in the second voxel and the position relationship of the first voxel, will be located at the first voxel it is internal, it is outside or It is that each section with the first voxel in the first voxel overlapped is also respectively divided into three classes；Step 4: in the first and second voxels original border going or staying：Utilize the new intersection and step 3 obtained in step 2 In classification results,When the first and second voxels do cap, retain positioned at the inside of the second voxel and overlapped with the second voxel side the The two class sections on one voxel side, cast out a kind of section positioned at the first voxel side of the outside of the second voxel,Retain the two class sections positioned at the inside of the first voxel and with the first voxel in the second voxel overlapped simultaneously, cast out and be located at A kind of section on the second voxel side of the outside of the first voxel；When the first and second voxels do union or difference operation, retain being somebody's turn to do positioned at the first voxel side of the outside of the second voxel A kind of section, cast out the two class sections in the first voxel overlapped positioned at the inside of the second voxel and with the second voxel；Step 5: the border that will be remained, a new voxel is constructed according to topology rebuilding thought.
- 6. the access method of the topology element of three-dimensional CSG-BRep models as claimed in claim 5, it is characterised in that the step In rapid two, first intersection point is located on the border of the first element and also includes the first intersection point position in the border of second element In on the border of the first element and positioned at second element border on,Second intersection point is located on the border of second element and is also located in the border of the first element including the second intersection point On the border of second element and on the border of the first element.
- 7. the access method of the topology element of the three-dimensional CSG-BRep models as described in claim 5 or 6, it is characterised in that institute State in step 1, trying to achieve the detailed process of intersection point includes：All parameter curves on side are collectively expressed as：C (t)=(x (t), y (t), z (t)),All parametric surfaces in face are collectively expressed as：F (u, v)=(x (u, v), y (u, v), z (u, v)),(1.1) parametric equation asks friendship to meet C (t)-F (u, v)=0, makes S (t, u, v)=C (t)-F (u, v),(1.2) differentiate：(1.3) each parameter differential display represents：<mrow> <mfrac> <mrow> <mo>&part;</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>u</mi> </mrow> </mfrac> <mo>&times;</mo> <msub> <mi>d</mi> <mi>s</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>u</mi> </mrow> </mfrac> <mo>&times;</mo> <mfrac> <mrow> <mi>d</mi> <mi>C</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>u</mi> </mrow> </mfrac> <mo>&times;</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>u</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>u</mi> <mo>-</mo> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>u</mi> </mrow> </mfrac> <mo>&times;</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>v</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>v</mi> </mrow>(1.4) dot product in (1.3)And makeFinally give following iterative equation：(1.5) after the iterative equation in obtaining step (1.4), bounding volumetree is established respectively to curve and curved surface, works as curve Bounding volumetree when intersecting with the bounding volumetree leaf of curved surface, take the parameter value in two leaves as initial value t0, u0, v0Carry out Iteration, until meeting the condition of convergence, finally ask for intersection point.
- 8. the access method of the topology element of three-dimensional CSG-BRep models as claimed in claim 5, it is characterised in that described to open up It is to build ring by side to flutter and rebuild thought, then builds face by ring, finally builds the mode of shell and body by face again.
- 9. the access method of the topology element of three-dimensional CSG-BRep models as claimed in claim 1, it is characterised in that described to build The adduction relationship for building topology element in the CSG-BRep models of thing be the topology element from complexity to simple topology element, and letter Single topology element can be shared by different complicated topology elements.
- 10. the access method of the topology element of three-dimensional CSG-BRep models as claimed in claim 9, it is characterised in that described In the CSG-BRep models of building the adduction relationship of topology element be shell and body quote face, ring is quoted in face, ring quote while and while Invocation point.
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