CN105184868B - A kind of triangle table surface grids generation method based on three-dimensional entity model - Google Patents
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Abstract
The present invention discloses a kind of triangle table surface grids generation method based on three-dimensional entity model, including：Read a face in three-dimensional entity model；Read a line circle in the face；Judge whether the boundary has already passed through processing, if so, handling result is directly read, if it is not, handling the boundary；Judge the face boundary whether all it is processed at；The boundary in the face and vertex are transformed into two-dimensional parameter space, two-dimensional grid is generated in two-dimensional parameter space；The two-dimensional grid of generation is transformed to three-dimensional parameter space；Judge whether all faces have all generated grid in the three-dimensional entity model, is generated if then exporting grid as a result, generating stl file.The present invention directly carries out grid generation by face, the boundary in each face is handled one by one, each face or boundary need to only be handled one time, and the setting regulation and control parameter related with the precision of the grid ultimately generated when into the processing of row bound knead dough, realized high efficiency and accurately generated grid.
Description
Technical field
The present invention relates to field of computer aided design, and in particular to a kind of triangular surface based on three-dimensional entity model
Grid generation method.
Background technology
In recent years, 3D printing technique growth momentum is swift and violent.The data pre-processing program of 3D printing namely slice program according to
The model file of input carries out slicing treatment to three-dimensional entity model, generates slice of data, hereafter 3D printer is according to number of slices
Object is manufactured according to by layer-by-layer printing.Currently, the format generally use STL lattice of the input model file of 3D printer
Formula.STL is a kind of file format indicating 3D solid geometric jacquard patterning unit surface with triangle.However, in field of computer aided design,
The STEP formats of a variety of geometric representation methods such as manifold B reps are supported to have become international standard, and the most normal in the field
With.For the model file for the STEP formats that CAD software generates, carrying out 3D printing, usually there are two types of solutions：When pair
Slicing treatment is directly carried out with the three-dimensional entity model that STEP formats indicate, second is that being first converted to the model file of STEP formats
The model file of STL formats carries out slicing treatment again.The former algorithm it is complex and slice precision be relatively difficult to guarantee, and the latter then by
It can not simple realization there are many significant differences between two kinds of formats.
The core that the model file of STEP formats is converted to the model file of STL formats is the surface of three-dimensional entity model
The generation of grid.Surface mesh generation method used in different application fields is usually different, generally speaking, existing skill
Surface mesh generation method in art can be classified as three classes：It advanced layer method, the method based on grid and is based on
The triangulation methodology of Delaunay.The quality for the grid that triangulation methodology based on Delaunay generates mathematically have compared with
For stringent guarantee, or even grid can also be generated to the geometrical body of some non-manifolds, but its algorithm is complex, and to floating-point
The errors that number calculates are very sensitive, and operation efficiency is relatively low, and the quality of generated grid is not still high, precision also is difficult to.For
It obtains correctly realizing that result needs that its numerical value robustness is noted that or is improved.
Invention content
Present invention aim to address the defect of the prior art, provide that a kind of operand is small, grid precision is controllable, gives birth to
At the secure triangle table surface grids generation method of the quality of grid, the technical solution of use is as follows：
A kind of triangle table surface grids generation method based on three-dimensional entity model, including：
A face in S1, reading three-dimensional entity model；
S2, a line circle for reading the face；
S3, judge whether the boundary has already passed through processing, if so, handling result is directly read, if it is not, being carried out to the boundary
Processing；
S4, judge whether the boundary in the face is all processed at if so, S5 is gone to, if it is not, returning to S2；
S5, the boundary in the face and vertex are transformed into two-dimensional parameter space, two-dimensional grid is generated in two-dimensional parameter space；
S6, the two-dimensional grid of generation is transformed to three-dimensional parameter space；
S7, judge whether all faces have all generated grid in the three-dimensional entity model, if then export grid generate as a result,
Stl file is generated, if it is not, then returning to S1.
Preferably, carrying out pre-sorting to the face of three-dimensional entity model in the step S1,3D solid mould is first read
Curved surface in type, then read the plane in three-dimensional entity model.
The present invention carries out pre-sorting to the face of threedimensional model, when reading the face of threedimensional model, first reads curved surface and reads again
Plane first carries out the generation of surface mesh more this is because the generation of surface mesh is more more special than the generation of plane grid
It is convenient and efficient.
Preferably, in the step S2 the reading on boundary reads each item in the face one by one by the way of clear by face
Boundary is simultaneously handled until all boundary whole reading process in the face finish.
By using the boundary by the clear mode reading face in face, it ensure that all boundaries in the face handled can be read
It gets.
Preferably, curl identical two endpoints mapping defined in three-dimensional parameter space will be closed in the step S2
For two different values, to indicate two different endpoints in three-dimensional parameter space.
The STEP formats of three-dimensional entity model allow the presence for being closed curl, and such curve is defined in STEP sentences
Two endpoints it is identical, therefore, BORDER PROCESSING carry out parameter space transformation when the two endpoints need to be mapped as to two differences
Value, to indicate two different endpoints respectively.
Preferably, in the step S3, ensure that the processing of each edge circle only carries out once, and the result of BORDER PROCESSING is only
It is stored in the final result of three dimensions.
Only processing is primary on all boundaries, and the result of BORDER PROCESSING is only stored in the final result of three dimensions,
So that the grid generated meets the limitation of triangle table surface grids on the topology, avoid occurring not at the intersection of different sides
Consistent error situation.
Preferably, including converting curl to the collection being made of straight-line segment to the processing on boundary in the step S3
It closes, the set meets：
,
Wherein, p and q is vertex of the threedimensional model in the space of three-dimensional parameter space,Refer to the two of the vector
Norm, and the value of δ is then related with the specific printing precision of 3D printers.
One important purpose of BORDER PROCESSING is exactly the discretization of curl, i.e., converts curl to and be made of straight-line segment
Several setΓ, and for any of which two lines section f, g ∈Γ, f ∩ g=f ∩ g., wherein f refer to line
The boundaries section f（That is two endpoints of line segment）Set.It is preferable to reach due to being the fitting result of curl on the collective entity
Fitting effect, we define (1) to control the fitting of curl, in fact, formula (1) is Hausdorff distance
（Hausdorff distance）A special case processing on boundary is controlled using other kinds of functional certainly
It is feasible.
Preferably, in the step S3, the handling result on boundary is met：
BORDER PROCESSING simultaneously be also two-dimensional grid generate preparation, in order to two-dimensional grid generation have preferably as a result,
We make the result of BORDER PROCESSING meet formula（2）, actually to control the length of every straight-line segment after BORDER PROCESSING, if
Boundary handling result is controlled without using formula (2), some long-narrow triangular mesh are will appear in the two-dimensional grid of generation.ε
The specific geometric shape in face that handles by us of value and specific required precision depending on.For surface mesh generation, its value
It is only related with the specific printing precision of 3D printer.Plane grid is generated, the value of ε is then increasingly complex.Herein, for
Surface mesh generation, ε can take the machining accuracy of 3D printer, and carry out certain deviation.And plane grid is generated, ε takes
The multiple of most short length of straight flange and the average value of line segment length after curl discretization that may be present in the boundary of face.
Preferably, in the step S5, mapping M is utilized:（x, y, z）U is by the three-dimensional mould in three-dimensional parameter space
The borderline each vertex of type transforms to two-dimensional parameter space；In the step S6, inverse mapping M is utilized−1: u ↦（x, y, z）It will
The vertex of the two-dimensional grid generated in two-dimensional parameter space switches back to three-dimensional parameter space.
In the model described with B-rep, boundary is individually described.Particularly, in STEP formats, boundary
Usually it is made of the set on side, and each edge is one-dimensional manifold.Therefore, we can define mapping M:（x, y, z）↦ u
Each vertex in three-dimensional parameter space on threedimensional model side is all transformed into two-dimensional parameter space, the property of one-dimensional manifold ensure that
The mapping is a continuous dijection.Meanwhile it there is also a continuous inverse mapping M−1: u ↦（x, y, z）Two dimension to be joined
Vertex in number space becomes three-dimensional parameter space again.
Preferably, in the step S5, when two-dimensional parameter space generates two-dimensional grid, using in Constrained
Low-angle Introduced Malaria algorithm on the basis of Delaunay Triangulation, and the fragment linearity complex that linear unit is constituted is made
For input, the triangular mesh in two-dimensional parameter space, and network of triangle are generated in the space of the fragment linearity complex of input
Lattice meet, wherein К * are the triangular mesh generated in two-dimensional parameter space, AτFor triangle τ's
Area, θ are the upper limit of the area of triangle τ, and τ is triangle.
Wherein, the value of θ is related with the machining accuracy of 3D printers and mapping T is related.
In the present invention, the value of θ actually also controls the precision of surface mesh generation.
Two-dimensional grid is completed in two-dimensional parameter space to generate, the generation result of grid needs to meet some limitations.First, raw
At result be necessary for simplicial complex, and must want to coincide with pre-defined boundary, i.e., for the simplicial complex К * of generation with
And pre-defined boundary B *,, f. is the dough sheet of τ（facet）.Finally, generation is simple multiple
The result К that deformation is changed in three-dimensional parameter space will have curved surface fitting effect good enough.It is required based on above-mentioned three,
We select to apply in Constrained Delaunay triangulations（CDT）On the basis of low-angle Introduced Malaria version
Delaunay Refinement algorithms, it receives the fragment linearity complex being made of linear unit（piecewise linear
complex）As input, in the fragment linearity complex of inputX SpaceMiddle generation triangular mesh generates result and meets
The definition of simplicial complex, and can guarantee that the boundary for generating grid matches with the boundary defined in input.So what grid generated
Preceding two requirements readily satisfy, what is more important meet grid generation last require here, we to select
Algorithm has carried out trickle amendment, and the upper limit is set to the area of three-dimensional parameter space intermediate cam shape, and this upper limit practical function
In the triangle that parameter space generates, i.e.,, but, triangle area is not meant to the upper limit
The grid of generation has preferable fitting result to curved surface, but the algorithm that we select can be generated in the case where meeting above-mentioned restrictive condition
Ideal grid.
Compared with traditional technology, beneficial effects of the present invention：The present invention directly carries out grid generation by face, into row bound
When the processing of knead dough, the area upper limit of the length range and two-dimensional parameter space intermediate cam shape grid of line segment when BORDER PROCESSING is set
Deng regulation and control parameter related with the precision of the triangular mesh ultimately generated so that each face or boundary need to only be handled one time,
The regulation and control of the precision to ultimately generating grid can be realized, the quality of generated grid is also more secure.Meanwhile involved by the present invention
And method do not need special grid optimization step, operand smaller, realize it is simpler.In addition, the grid of the present invention generates
Method also has many advantages, such as that numerical value robustness is higher, grid precision is controllable.
Description of the drawings
Fig. 1 is the flow chart of the embodiment of the present invention；
Fig. 2 is that the two-dimensional grid that a face of three-dimensional entity model in the embodiment of the present invention is generated in two-dimensional parameter space shows
It is intended to；
Fig. 3 is that the two-dimensional grid of Fig. 2 transforms to the schematic diagram behind three-dimensional parameter space；
Fig. 4 is the two-dimensional grid generated when being defined to boundary handling result without using formula 2 in the embodiment of the present invention
Schematic diagram；
Fig. 5 is that the two-dimensional grid generated when being defined to boundary handling result using formula 2 in the embodiment of the present invention is shown
It is intended to；
Fig. 6 is the STEP files for test in the embodiment of the present invention；
Fig. 7 is stl file made of converting the STEP files of Fig. 6 using the method for the embodiment of the present invention；
Fig. 8 is the actual measurement print result of the embodiment of the present invention.
Specific implementation mode
Present invention is further described in detail with reference to the accompanying drawings and examples.
Embodiment：
As shown in Figure 1, Figure 2 and Figure 3, a kind of triangle table surface grids generation method based on three-dimensional entity model, including：
A face in S1, reading three-dimensional entity model；
S2, a line circle for reading the face；
S3, judge whether the boundary has already passed through processing, if so, handling result is directly read, if it is not, being carried out to the boundary
Processing；
S4, judge whether the boundary in the face is all processed at if so, S5 is gone to, if it is not, returning to S2；
S5, the boundary in the face and vertex are transformed into two-dimensional parameter space, two-dimensional grid is generated in two-dimensional parameter space；
S6, the two-dimensional grid of generation is transformed to three-dimensional parameter space；
S7, judge whether all faces have all generated grid in the three-dimensional entity model, if then export grid generate as a result,
Stl file is generated, if it is not, then returning to S1.
Pre-sorting is carried out to the face of three-dimensional entity model in the step S1, first reads the song in three-dimensional entity model
Face, then read the plane in three-dimensional entity model.
The present embodiment carries out pre-sorting to the face of threedimensional model, when reading the face of threedimensional model, first reads curved surface and reads again
It makes even face, this is because the generation of surface mesh is more more special than the generation of plane grid, first carries out the generation of surface mesh more
For convenience and efficiently.
In the step S2 the reading on boundary is read each boundary in the face and is handled one by one by the way of clear by face
Until all boundary whole reading process in the face finish.
By using the boundary by the clear mode reading face in face, it ensure that all boundaries in the face handled can be read
It gets.
It will be closed curl identical two endpoints defined in three-dimensional parameter space in the step S2 and be mapped as two not
Same value, to indicate two different endpoints in three-dimensional parameter space.
The STEP formats of three-dimensional entity model allow the presence for being closed curl, and such curve is defined in STEP sentences
Two endpoints it is identical, therefore, BORDER PROCESSING carry out parameter space transformation when the two endpoints need to be mapped as to two differences
Value, to indicate two different endpoints respectively.
In the step S3, ensure that the processing of each edge circle only carries out once, and the result of BORDER PROCESSING is only stored in three
In the final result of dimension space.
Only processing is primary on all boundaries, and the result of BORDER PROCESSING is only stored in the final result of three dimensions,
So that the grid generated meets the limitation of triangle table surface grids on the topology, avoid occurring not at the intersection of different sides
Consistent error situation.
Include converting curl to the set being made of straight-line segment, the set to the processing on boundary in the step S3
Meet：
,
Wherein, p and q is vertex of the threedimensional model in the space of three-dimensional parameter space,Refer to the two of the vector
Norm, and the value of δ is then related with the specific printing precision of 3D printers.
One important purpose of BORDER PROCESSING is exactly the discretization of curl, i.e., converts curl to and be made of straight-line segment
Several setΓ, and for any of which two lines section f, g ∈Γ, f ∩ g=f ∩ g., wherein f refer to line
The boundaries section f（That is two endpoints of line segment）Set.It is preferable to reach due to being the fitting result of curl on the collective entity
Fitting effect, we define (1) to control the fitting of curl, in fact, formula (1) is Hausdorff distance
（Hausdorff distance）A special case processing on boundary is controlled using other kinds of functional certainly
It is feasible.
In the step S3, the handling result on boundary is met：
BORDER PROCESSING simultaneously be also two-dimensional grid generate preparation, in order to two-dimensional grid generation have preferably as a result,
We make the result of BORDER PROCESSING meet formula（2）, actually to control the length of every straight-line segment after BORDER PROCESSING, if
Boundary handling result is controlled without using formula (2), some long-narrow triangular mesh are will appear in the two-dimensional grid of generation.ε's
It is worth because depending on the specific geometric shape in the face that we are handled and specific required precision.For surface mesh generation, its value is only
It is related with the specific printing precision of 3D printer.Plane grid is generated, the value of ε is then increasingly complex.
As shown in figure 4, if controlled BORDER PROCESSING without using formula (2), will appear in the two-dimensional grid of generation
Some long-narrow triangular mesh, for such case, whether before carrying out two-dimensional grid generation, can first detect on the face has song for we
Side is handled straight flange using the length of the curl treated line segment as the value in formula (2) is determined with reference to value.Such as
Shown in Fig. 5, it can be seen that after such processing, the quality of the two-dimensional grid of generation greatly improves, finally formed
Long-narrow triangular mesh is not occurred in two-dimensional grid.
In the step S5, mapping M is utilized:（x, y, z）U will be on the threedimensional model boundary in three-dimensional parameter space
Each vertex transform to two-dimensional parameter space；In the step S6, inverse mapping M is utilized−1: u ↦（x, y, z）By two-dimensional parameter
The vertex of the two-dimensional grid generated in space switches back to three-dimensional parameter space.
In the model described with B-rep, boundary is individually described.Particularly, in STEP formats, boundary
Usually it is made of the set on side, and each edge is one-dimensional manifold.Therefore, we can define mapping M:（x, y, z）↦ u
Each vertex in three-dimensional parameter space on threedimensional model side is all transformed into two-dimensional parameter space, the property of one-dimensional manifold ensure that
The mapping is a continuous dijection.Meanwhile it there is also a continuous inverse mapping M−1: u ↦（x, y, z）Two dimension to be joined
Vertex in number space becomes three-dimensional parameter space again.
In the step S5, when two-dimensional parameter space generates two-dimensional grid, using in Constrained Delaunay
Low-angle Introduced Malaria algorithm on the basis of triangulation, and using linear unit constitute fragment linearity complex as input,
The triangular mesh in two-dimensional parameter space is generated in the space of the fragment linearity complex of input, and triangular mesh meets, wherein К * are the triangular mesh generated in two-dimensional parameter space, AτFor the area of triangle τ, θ
For the upper limit of the area of triangle τ, τ is triangle.
Wherein, the value of θ is related with the machining accuracy of 3D printers and mapping T is related.
In the present invention, the value of θ actually also controls the precision of surface mesh generation.
Two-dimensional grid is completed in two-dimensional parameter space to generate, the generation result of grid needs to meet some limitations.First, raw
At result be necessary for simplicial complex, and must want to coincide with pre-defined boundary, i.e., for the simplicial complex К * of generation with
And pre-defined boundary B *,, f. is the dough sheet of τ（facet）.Finally, generation is simple multiple
The result К that deformation is changed in three-dimensional parameter space will have curved surface fitting effect good enough.It is required based on above-mentioned three,
We select to apply in Constrained Delaunay triangulations（CDT）On the basis of low-angle Introduced Malaria version
Delaunay Refinement algorithms, it receives the fragment linearity complex being made of linear unit（piecewise linear
complex）As input, in the fragment linearity complex of inputX SpaceMiddle generation triangular mesh generates result and meets
The definition of simplicial complex, and can guarantee that the boundary for generating grid matches with the boundary defined in input.So what grid generated
Preceding two requirements readily satisfy, what is more important meet grid generation last require here, we to select
Algorithm has carried out trickle amendment, and the upper limit is set to the area of three-dimensional parameter space intermediate cam shape, and this upper limit practical function
In the triangle that parameter space generates, i.e.,, but, triangle area is not meant to the upper limit
The grid of generation has preferable fitting result to curved surface, but the algorithm that we select can be generated in the case where meeting above-mentioned restrictive condition
Ideal grid.
As shown in fig. 7, being the signal for the stl file for being converted into STEP files shown in fig. 6 using the method for the present invention
Figure is the result schematic diagram that printing test is carried out to stl file shown in Fig. 7 as shown in Figure 8, it can be seen from the figure that utilizing
The format conversion that surface mesh generation method proposed by the present invention carries out and printing are controllable with conversion accuracy, it is simple, logical to realize
With the advantageous effects such as property is good.
Claims (8)
1. a kind of triangle table surface grids generation method based on three-dimensional entity model, which is characterized in that including：
A face in S1, reading three-dimensional entity model；
S2, a line circle for reading the face；
S3, judge whether the boundary has already passed through processing, if so, handling result is directly read, if it is not, to the boundary
Reason；
S4, judge whether the boundary in the face is all processed at if so, S5 is gone to, if it is not, returning to S2；
S5, the boundary in the face and vertex are transformed into two-dimensional parameter space, two-dimensional grid is generated in two-dimensional parameter space；
S6, the two-dimensional grid of generation is transformed to three-dimensional parameter space；
S7, judge whether all faces have all generated grid in the three-dimensional entity model, generated if then exporting grid as a result, generating
Stl file, if it is not, then returning to S1；
In the step S5, when two-dimensional parameter space generates two-dimensional grid, using in Constrained Delaunay triangles
Low-angle Introduced Malaria algorithm on the basis of subdivision, and using the fragment linearity complex of linear unit composition as input, defeated
The triangular mesh in two-dimensional parameter space is generated in the space of the fragment linearity complex entered, and triangular mesh meets Aτ≤ θ,Wherein K*For the triangular mesh generated in two-dimensional parameter space, AτFor the area of triangle τ, θ is the face of triangle τ
The long-pending upper limit, τ are triangle.
2. a kind of triangle table surface grids generation method based on three-dimensional entity model according to claim 1, feature
It is, pre-sorting is carried out to the face of three-dimensional entity model in the step S1, first reads the curved surface in three-dimensional entity model, then
Read the plane in three-dimensional entity model.
3. a kind of triangle table surface grids generation method based on three-dimensional entity model according to claim 1, feature
Be, in the step S2 boundary reading using clear by face by the way of, i.e., read one by one each boundary in the face and handle directly
All boundary whole reading process to the face finish.
4. a kind of triangle table surface grids generation method based on three-dimensional entity model according to claim 1, feature
Be, will be closed in the step S2 curl identical two endpoints defined in three-dimensional parameter space be mapped as two it is different
Value, to indicate two different endpoints in three-dimensional parameter space.
5. a kind of triangle table surface grids generation method based on three-dimensional entity model according to claim 1, feature
It is, in the step S3, ensures that the processing of each edge circle only carries out once, and the result of BORDER PROCESSING is only stored in three-dimensional space
Between final result in.
6. a kind of triangle table surface grids generation method based on three-dimensional entity model according to claim 1, feature
It is, includes converting curl to the set being made of straight-line segment to the processing on boundary in the step S3, the set is full
Foot
Wherein, p and q is vertex of the threedimensional model in three-dimensional parameter space, ‖ ‖2Refer to two norms of vector, Г is by straight
The set that line line segment is constituted.
7. a kind of triangle table surface grids generation method based on three-dimensional entity model according to claim 1, feature
It is, in the step S3, the handling result on boundary is metP and q is that threedimensional model exists
Vertex in three-dimensional parameter space, Г are the set being made of straight-line segment,It is the set of two endpoints of line segment f.
8. a kind of triangle table surface grids generation method based on three-dimensional entity model according to claim 1, feature
It is, in the step S5, utilizes mapping M:By the borderline each top of the threedimensional model in three-dimensional parameter space
Point transformation is to two-dimensional parameter space；In the step S6, inverse mapping M is utilized-1:It will be generated in two-dimensional parameter space
The vertex of two-dimensional grid switch back to three-dimensional parameter space.
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