CN105184868A - Triangular surface grid generation method based on three-dimensional entity model - Google Patents
Triangular surface grid generation method based on three-dimensional entity model Download PDFInfo
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Abstract
The invention discloses a triangular surface grid generation method based on a three-dimensional entity model. The method comprises the following steps: reading one surface in the three-dimensional entity model; reading one boundary of the surface; determining whether the boundary is already processed, if so, directly reading a processing result, and otherwise, processing the boundary; determining whether the boundaries of the surface are already completely processed; converting the boundary and the summit of the surface into a two-dimensional parameter space, and generating a two-dimensional grid in the two-dimensional parameter space; converting the generated two-dimensional grid into a three-dimensional parameter space; and determining all surfaces in the three-dimensional entity model already generate grids, if so, outputting a grid generation result, and generating an STL file. According to the invention, the grids are generated directly surface by surface, boundary of each surface is processed one by one, each surface or boundary is processed only once, and regulation and control parameters related to precision of the finally generated grids are arranged when the boundaries and surfaces are processed, such that the grids are generated efficiently and precisely.
Description
Technical field
The present invention relates to field of computer aided design, be specifically related to a kind of triangular surface mess generation method based on three-dimensional entity model.
Background technology
In recent years, 3D printing technique growth momentum is swift and violent.The data pre-processing program that 3D prints program of also namely cutting into slices carries out slicing treatment according to the model file of input to three-dimensional entity model, and produce slice of data, after this 3D printer manufactures object according to slice of data by the mode successively printed.At present, the form of the input model file of 3D printer adopts STL form usually.STL is a kind of file layout representing 3D solid geometric jacquard patterning unit surface with triangle.But, in field of computer aided design, support that the STEP form of the multiple geometric representation methods such as stream shape B reps has become international standard, and the most conventional in this field.For the model file of the STEP form of CAD Software Create, carry out 3D printing and usually have two kinds of solutions: one is directly carry out slicing treatment to the three-dimensional entity model represented with STEP form, and two is that the model file first model file of STEP form being converted to STL form carries out slicing treatment again.The former algorithm is comparatively complicated and section precision is comparatively difficult to ensure card, and the latter is then owing to existing many significant differences and cannot simple realization between two kinds of forms.
The core model file of STEP form being converted to the model file of STL form is the generation of the surface mesh of three-dimensional entity model.The surface mesh generation method used in different applications is usually different, generally speaking, surface mesh generation method of the prior art can be classified as following three classes: advanced layer method, the method based on grid and the triangulation methodology based on Delaunay.The quality of the grid generated based on the triangulation methodology of Delaunay mathematically has comparatively strict guarantee, even also can generating mesh to the geometrical body of some non-manifolds, but its algorithm is comparatively complicated, and it is very responsive to the error of floating number calculating, operation efficiency is lower, and the quality of institute's generating mesh still not high, precision is also difficult to regulation and control.Need noted its numerical value robustness or improve for obtaining the correct result that realizes.
Summary of the invention
The object of the invention is to address the deficiencies of the prior art, provide a kind of triangular surface mess generation method that operand is little, the quality of grid precision controllable, institute's generating mesh is secure, the technical scheme of employing is as follows:
Based on a triangular surface mess generation method for three-dimensional entity model, comprising:
S1, a face of reading in three-dimensional entity model;
S2, read the border in this face;
S3, judge this border whether through process, if so, direct reading process result, if not, this border is processed;
S4, judge that whether the border in this face is all processed and complete, if so, forward S5 to, if not, return S2;
S5, the border in this face and summit are transformed to two-dimensional parameter space, in two-dimensional parameter space, generate two-dimensional grid;
S6, the two-dimensional grid of generation is transformed to three-dimensional parameter space;
S7, to judge in this three-dimensional entity model if then export mess generation result, to generate whether all faces generating mesh all stl file, if not, then return S1.
As preferably, in described step S1, pre-sorting is carried out to the face of three-dimensional entity model, first read the curved surface in three-dimensional entity model, then read the plane in three-dimensional entity model.
The present invention carries out pre-sorting to the face of three-dimensional model, and when reading the face of three-dimensional model, first read curved surface and read plane again, this is because the generation of surface mesh is more more special than the generation of plane grid, the generation first carrying out surface mesh is more convenient and efficient.
As preferably, in described step S2, the reading on border adopts by the clear mode in face, namely read each bar border in this face one by one and process until the whole reading process in all borders in this face is complete.
By adopting the border by the clear mode reading face in face, ensure that all borders in the face processed all can be read.
As preferably, in described step S2, closed bent limit is defined in three-dimensional parameter space two identical end points and be mapped as two different values, to represent the end points that in three-dimensional parameter space two are different.
The STEP form of three-dimensional entity model allows the existence on closed bent limit, and two end points that this type of curve defines in STEP statement are identical, therefore, these two end points need be mapped as two different values when boundary treatment carries out parameter space conversion, to represent two different end points respectively.
As preferably, in described step S3, ensure that the process on every bar border is only carried out once, and the result of boundary treatment is only kept in three-dimensional net result.
All borders all only process once, and the result of boundary treatment is only kept in three-dimensional net result, to make the grid of generation meet the restriction on the topology of triangle table surface grids, avoid occurring inconsistent error situation at the intersection place of not coplanar.
As preferably, comprise bent limit is converted into the set be made up of straight-line segment in described step S3 to the process on border, described set meets:
,
Wherein, p and q be three-dimensional model between three-dimensional parameter space empty in summit,
refer to two norms of this vector, the value of δ is then relevant with the concrete printing precision of 3D printer.
The important object of of boundary treatment is exactly the discretize on bent limit, is converted into several set be made up of straight-line segment by bent limit
Γ, and for wherein arbitrary two line segment f, g ∈
Γ, f ∩ g=f ∩ g., wherein f refers to the set of line segment f border (i.e. two end points of line segment).Owing to this collective entity being the fitting result on bent limit, for reaching good fitting effect, we control in definition (1) matching to bent limit, in fact, the special case that formula (1) is Hausdorff distance (Hausdorffdistance), certainly, the process of functional to border of other types is used to control also to be feasible.
As preferably, in described step S3, the result on border is met:
Boundary treatment is also the preliminary work that two-dimensional grid generates simultaneously, better result is had in order to two-dimensional grid generates, we make the result of boundary treatment meet formula (2), in fact in order to control the length of every bar straight-line segment after boundary treatment, if not using formula (2) to control border result, there will be some long-narrow triangular mesh in the two-dimensional grid of generation.The concrete geometric shape in the face that the value of ε processes because of us and concrete accuracy requirement and determine.For surface mesh generation, its value is only relevant with the concrete printing precision of 3D printer.Generate for plane grid, the value of ε is then more complicated.Here, for surface mesh generation, ε can get the machining precision of 3D printer, and carries out certain deviation.And plane grid is generated, ε gets the multiple of the mean value of line segment length after the shortest length of straight flange in border, face and the bent limit discretize that may exist.
As preferably, in described step S5, utilizing and map M:(x, y, z) borderline for the three-dimensional model in three-dimensional parameter space each summit transforms to two-dimensional parameter space by u; In described step S6, utilize inverse mapping M
1: the summit of the two-dimensional grid generated in two-dimensional parameter space is switched back to three-dimensional parameter space by u (x, y, z).
In the model described with B-rep, border is described separately.Especially, in STEP form, border is made up of the set on limit usually, and every bar limit is one-dimensional manifold.Therefore, we can define and map M:(x, y, z) each summit on three-dimensional model limit in three-dimensional parameter space all transforms to two-dimensional parameter space by u, and the character of one-dimensional manifold ensure that this mapping is a continuous dijection.Meanwhile, also there is a continuous inverse mapping M in it
1: u (x, y, z) is in order to become the summit in two-dimensional parameter space again three-dimensional parameter space.
As preferably, in described step S5, when two-dimensional parameter space generates two-dimensional grid, adopt the low-angle Introduced Malaria algorithm on the basis of ConstrainedDelaunay triangulation, and the up complex formed by linear unit is as input, in the space of the up complex of input, generate the triangular mesh in two-dimensional parameter space, and triangular mesh meets
, wherein К * is the triangular mesh generated at two-dimensional parameter space, A
τfor the area of triangle τ, θ is the upper limit of the area of triangle τ, and τ is triangle.
Wherein, the value of θ is relevant with the machining precision of 3D printer and to map T relevant.
In the present invention, the value of θ in fact also controls the precision of surface mesh generation.
Complete two-dimensional grid at two-dimensional parameter space to generate, some restrictions of the generation result demand fulfillment of grid.First, the result of generation is necessary for simplicial complex, and must want to coincide with predefined border, namely for the simplicial complex К * generated and predefined boundary B *,
, f. is the dough sheet (facet) of τ.Finally, the result К that the simplicial complex of generation transforms in three-dimensional parameter space will have enough good fitting effect to curved surface.Based on above-mentioned three requirements, the low-angle Introduced Malaria version DelaunayRefinement algorithm of our selective gist on the basis of ConstrainedDelaunay triangulation (CDT), it accepts up complex (piecewiselinearcomplex) the conduct input be made up of linear unit, in the up complex of input
xspace
middle generation triangular mesh, generates the definition that result meets simplicial complex, and the border defined in ensureing the border of generating mesh and inputting matches.So, front two requirements of mess generation easily meet, what is more important meets last requirement of mess generation. at this, we are to trickle amendment of having selected algorithm to carry out, the upper limit is set to the area of three-dimensional parameter space intermediate cam shape, and in the triangle that generates in parameter space of this upper limit practical function, namely
, but, triangle area has the upper limit and does not mean that the grid of generation has good fitting result to curved surface, but our algorithm of selecting can generate ideal grid meeting under above-mentioned restrictive condition.
Compared with conventional art, beneficial effect of the present invention: the present invention directly carries out mess generation by face, when carrying out the process on border and face, the regulation and control parameter that the length range of line segment during boundary treatment and the area upper limit of two-dimensional parameter space intermediate cam shape grid etc. are relevant with the precision of the triangular mesh finally generated is set, make each or border all only need process one time, can realize the regulation and control of the precision to final generating mesh, the quality of institute's generating mesh is also more secure.Meanwhile, method involved in the present invention does not need special grid optimization step, and operand is less, realization is simpler.In addition, mess generation method of the present invention also has the advantages such as numerical value robustness is higher, grid precision controllable.
Accompanying drawing explanation
Fig. 1 is the process flow diagram of the embodiment of the present invention;
Fig. 2 is the two-dimensional grid schematic diagram that a face of three-dimensional entity model in the embodiment of the present invention generates at two-dimensional parameter space;
Fig. 3 is the schematic diagram after the two-dimensional grid of Fig. 2 transforms to three-dimensional parameter space;
Fig. 4 is the two-dimensional grid schematic diagram generated when not using formula 2 pairs of border results to limit in the embodiment of the present invention;
Fig. 5 is the two-dimensional grid schematic diagram generated when using formula 2 pairs of border results to limit in the embodiment of the present invention;
Fig. 6 is the STEP file for testing in the embodiment of the present invention;
Fig. 7 is that the method for the application embodiment of the present invention is by the stl file of the STEP file transform of Fig. 6;
Fig. 8 is the actual measurement print result of the embodiment of the present invention.
Embodiment
Below in conjunction with drawings and Examples, the present invention is described in further detail.
Embodiment:
As shown in Figure 1, Figure 2 and Figure 3, a kind of triangular surface mess generation method based on three-dimensional entity model, comprising:
S1, a face of reading in three-dimensional entity model;
S2, read the border in this face;
S3, judge this border whether through process, if so, direct reading process result, if not, this border is processed;
S4, judge that whether the border in this face is all processed and complete, if so, forward S5 to, if not, return S2;
S5, the border in this face and summit are transformed to two-dimensional parameter space, in two-dimensional parameter space, generate two-dimensional grid;
S6, the two-dimensional grid of generation is transformed to three-dimensional parameter space;
S7, to judge in this three-dimensional entity model if then export mess generation result, to generate whether all faces generating mesh all stl file, if not, then return S1.
In described step S1, pre-sorting is carried out to the face of three-dimensional entity model, first read the curved surface in three-dimensional entity model, then read the plane in three-dimensional entity model.
The present embodiment carries out pre-sorting to the face of three-dimensional model, and when reading the face of three-dimensional model, first read curved surface and read plane again, this is because the generation of surface mesh is more more special than the generation of plane grid, the generation first carrying out surface mesh is more convenient and efficient.
In described step S2, the reading on border adopts by the clear mode in face, namely reads each bar border in this face one by one and processes until the whole reading process in all borders in this face is complete.
By adopting the border by the clear mode reading face in face, ensure that all borders in the face processed all can be read.
In described step S2, closed bent limit is defined in three-dimensional parameter space two identical end points and be mapped as two different values, to represent the end points that in three-dimensional parameter space two are different.
The STEP form of three-dimensional entity model allows the existence on closed bent limit, and two end points that this type of curve defines in STEP statement are identical, therefore, these two end points need be mapped as two different values when boundary treatment carries out parameter space conversion, to represent two different end points respectively.
In described step S3, ensure that the process on every bar border is only carried out once, and the result of boundary treatment is only kept in three-dimensional net result.
All borders all only process once, and the result of boundary treatment is only kept in three-dimensional net result, to make the grid of generation meet the restriction on the topology of triangle table surface grids, avoid occurring inconsistent error situation at the intersection place of not coplanar.
Comprise the process on border in described step S3 and bent limit is converted into the set be made up of straight-line segment, described set meets:
，
Wherein, p and q be three-dimensional model between three-dimensional parameter space empty in summit,
refer to two norms of this vector, the value of δ is then relevant with the concrete printing precision of 3D printer.
The important object of of boundary treatment is exactly the discretize on bent limit, is converted into several set be made up of straight-line segment by bent limit
Γ, and for wherein arbitrary two line segment f, g ∈
Γ, f ∩ g=f ∩ g., wherein f refers to the set of line segment f border (i.e. two end points of line segment).Owing to this collective entity being the fitting result on bent limit, for reaching good fitting effect, we control in definition (1) matching to bent limit, in fact, the special case that formula (1) is Hausdorff distance (Hausdorffdistance), certainly, the process of functional to border of other types is used to control also to be feasible.
In described step S3, the result on border is met:
Boundary treatment is also the preliminary work that two-dimensional grid generates simultaneously, better result is had in order to two-dimensional grid generates, we make the result of boundary treatment meet formula (2), in fact in order to control the length of every bar straight-line segment after boundary treatment, if do not use formula (2) to control border result, in the two-dimensional grid of generation, there will be some long-narrow triangular mesh.The concrete geometric shape in the face that the value of ε processes because of us and concrete accuracy requirement and determine.For surface mesh generation, its value is only relevant with the concrete printing precision of 3D printer.Generate for plane grid, the value of ε is then more complicated.
As shown in Figure 4, if do not use formula (2) to control boundary treatment, there will be some long-narrow triangular mesh in the two-dimensional grid generated, for this situation, we are before carrying out two-dimensional grid generation, first can detect on this face and whether have bent limit, using the length of the line segment after this bent limit process as the value determined with reference to value in formula (2), straight flange be processed.As shown in Figure 5, can see, after such process, the quality of the two-dimensional grid of generation improves greatly, in the final two-dimensional grid formed, do not occur long-narrow triangular mesh.
In described step S5, utilizing and map M:(x, y, z) borderline for the three-dimensional model in three-dimensional parameter space each summit transforms to two-dimensional parameter space by u; In described step S6, utilize inverse mapping M
1: the summit of the two-dimensional grid generated in two-dimensional parameter space is switched back to three-dimensional parameter space by u (x, y, z).
In the model described with B-rep, border is described separately.Especially, in STEP form, border is made up of the set on limit usually, and every bar limit is one-dimensional manifold.Therefore, we can define and map M:(x, y, z) each summit on three-dimensional model limit in three-dimensional parameter space all transforms to two-dimensional parameter space by u, and the character of one-dimensional manifold ensure that this mapping is a continuous dijection.Meanwhile, also there is a continuous inverse mapping M in it
1: u (x, y, z) is in order to become the summit in two-dimensional parameter space again three-dimensional parameter space.
In described step S5, when two-dimensional parameter space generates two-dimensional grid, adopt the low-angle Introduced Malaria algorithm on the basis of ConstrainedDelaunay triangulation, and the up complex formed by linear unit is as input, in the space of the up complex of input, generate the triangular mesh in two-dimensional parameter space, and triangular mesh meets
, wherein К * is the triangular mesh generated at two-dimensional parameter space, A
τfor the area of triangle τ, θ is the upper limit of the area of triangle τ, and τ is triangle.
Wherein, the value of θ is relevant with the machining precision of 3D printer and to map T relevant.
In the present invention, the value of θ in fact also controls the precision of surface mesh generation.
Complete two-dimensional grid at two-dimensional parameter space to generate, some restrictions of the generation result demand fulfillment of grid.First, the result of generation is necessary for simplicial complex, and must want to coincide with predefined border, namely for the simplicial complex К * generated and predefined boundary B *,
, f. is the dough sheet (facet) of τ.Finally, the result К that the simplicial complex of generation transforms in three-dimensional parameter space will have enough good fitting effect to curved surface.Based on above-mentioned three requirements, the low-angle Introduced Malaria version DelaunayRefinement algorithm of our selective gist on the basis of ConstrainedDelaunay triangulation (CDT), it accepts up complex (piecewiselinearcomplex) the conduct input be made up of linear unit, in the up complex of input
xspace
middle generation triangular mesh, generates the definition that result meets simplicial complex, and the border defined in ensureing the border of generating mesh and inputting matches.So, front two requirements of mess generation easily meet, what is more important meets last requirement of mess generation. at this, we are to trickle amendment of having selected algorithm to carry out, the upper limit is set to the area of three-dimensional parameter space intermediate cam shape, and in the triangle that generates in parameter space of this upper limit practical function, namely
, but, triangle area has the upper limit and does not mean that the grid of generation has good fitting result to curved surface, but our algorithm of selecting can generate ideal grid meeting under above-mentioned restrictive condition.
As shown in Figure 7, it is the schematic diagram of the stl file utilizing method of the present invention to be become by STEP file transform shown in Fig. 6, the result schematic diagram of the stl file shown in Fig. 7 being carried out to printing test as shown in Figure 8, as can be seen from the figure, the format conversion that the surface mesh generation method utilizing the present invention to propose is carried out and printing have the beneficial effects such as conversion accuracy is controlled, realization is simple, versatility is good.
Claims (9)
1., based on a triangular surface mess generation method for three-dimensional entity model, it is characterized in that, comprising:
S1, a face of reading in three-dimensional entity model;
S2, read the border in this face;
S3, judge this border whether through process, if so, direct reading process result, if not, this border is processed;
S4, judge that whether the border in this face is all processed and complete, if so, forward S5 to, if not, return S2;
S5, the border in this face and summit are transformed to two-dimensional parameter space, in two-dimensional parameter space, generate two-dimensional grid;
S6, the two-dimensional grid of generation is transformed to three-dimensional parameter space;
S7, to judge in this three-dimensional entity model if then export mess generation result, to generate whether all faces generating mesh all stl file, if not, then return S1.
2. a kind of triangular surface mess generation method based on three-dimensional entity model according to claim 1, it is characterized in that, in described step S1, pre-sorting is carried out to the face of three-dimensional entity model, first read the curved surface in three-dimensional entity model, then read the plane in three-dimensional entity model.
3. a kind of triangular surface mess generation method based on three-dimensional entity model according to claim 1, it is characterized in that, in described step S2, the reading on border adopts by the clear mode in face, namely reads each bar border in this face one by one and processes until the whole reading process in all borders in this face is complete.
4. a kind of triangular surface mess generation method based on three-dimensional entity model according to claim 1, it is characterized in that, in described step S2, closed bent limit is defined in three-dimensional parameter space two identical end points and be mapped as two different values, to represent the end points that in three-dimensional parameter space two are different.
5. a kind of triangular surface mess generation method based on three-dimensional entity model according to claim 1, it is characterized in that, in described step S3, ensure that the process on every bar border is only carried out once, and the result of boundary treatment is only kept in three-dimensional net result.
6. a kind of triangular surface mess generation method based on three-dimensional entity model according to claim 1, is characterized in that, comprise bent limit is converted into the set be made up of straight-line segment in described step S3 to the process on border, and described set meets
,
Wherein, p and q be three-dimensional model between three-dimensional parameter space empty in summit,
refer to two norms of this vector, the value of δ is then relevant with the concrete printing precision of 3D printer.
7. a kind of triangular surface mess generation method based on three-dimensional entity model according to claim 1, is characterized in that, in described step S3, meets the result on border
。
8. a kind of triangular surface mess generation method based on three-dimensional entity model according to claim 1, it is characterized in that, in described step S5, utilize and map M:(x, y, z) borderline for the three-dimensional model in three-dimensional parameter space each summit transforms to two-dimensional parameter space by u; In described step S6, utilize inverse mapping M
1: the summit of the two-dimensional grid generated in two-dimensional parameter space is switched back to three-dimensional parameter space by u (x, y, z).
9. a kind of triangular surface mess generation method based on three-dimensional entity model according to claim 1, it is characterized in that, as preferably, in described step S5, when two-dimensional parameter space generates two-dimensional grid, adopt the low-angle Introduced Malaria algorithm on the basis of ConstrainedDelaunay triangulation, and the up complex formed by linear unit is as input, in the space of the up complex of input, generate the triangular mesh in two-dimensional parameter space, and triangular mesh meets
, wherein К * is the triangular mesh generated at two-dimensional parameter space, A
τfor the area of triangle τ, θ is the upper limit of the area of triangle τ, and τ is triangle.
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