CN101465006B - Method for building grid surface by point cloud - Google Patents
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- CN101465006B CN101465006B CN2009100765498A CN200910076549A CN101465006B CN 101465006 B CN101465006 B CN 101465006B CN 2009100765498 A CN2009100765498 A CN 2009100765498A CN 200910076549 A CN200910076549 A CN 200910076549A CN 101465006 B CN101465006 B CN 101465006B
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Abstract
The invention relates to a method for constructing mesh surfaces by point clouds. The method comprises the following steps: firstly, input point clouds are converted into an implicit field; secondly, an initial cell complex is generated and modified, so that the cell complex on a topology can be correct; and finally, the mesh surfaces with consistent topology are generated by the cell complex. The method overcomes the deficiencies that the topology can not be ensured in constructing the mesh surface, and the density of the mesh is adjusted automatically according to the curvature of the surface by point clouds in the prior art, to ensure that the generated topology is correct, and well reserved mesh surfaces are obtained by geometrical characteristics.
Description
Technical field
The invention belongs to digital geometry models treated field, what particularly a kind of geometry and topology were responsive makes up the method for grid surface by a cloud.
Background technology
In digital geometry models treated field, a three-dimensional model often has three kinds of describing modes, and a kind of is a cloud mode, promptly mold surface is sampled, directly express model with sampled point, this method is fairly simple, and deal with data is relatively easy, it is the unprocessed form of a lot of scan model data, but this method also has its intrinsic shortcoming, and the some cloud can't be described the topology of object, and if, need very many points with higher precision description surface; Second kind is the grid mode, and promptly with there being the dough sheet of annexation to come the representation model surface, the topology that this describing mode can the accurate description object has a very wide range of applications in 3D modeling and animation field; The third is the spline surface mode, because this mode and relation of the present invention are little, so do not add to set forth.
In actual 3D modeling is used, often a cloud describing mode need be converted into the describing mode of grid.Method commonly used at present has following several: body method, by a three-dimensional implicit expression of a cloud match field, the place at zero point of this implicit expression field is the implicit expression surface, directly carry out the extraction of contoured surface then, thereby finish the structure of grid by very ripe Marching Cubes method or its mutation; Non-body method is promptly directly from a cloud, generating mesh.But these methods all have some great shortcomings: at first, the grid that these methods produced includes topological mistake probably, and these topology mistakes usually exist with the form of little ring or surface hole; Secondly, these methods mostly can not be made adaptive adjustment to the curved surface that is generated well, promptly, the description precision is strengthened in the place that changes greatly on the surface, reduce the description precision and change the place of comparatively relaxing on the surface, thereby the description to body surface is accurate inadequately, or the dough sheet number that is produced is too much, gives follow-up play up and processing causes burden.The commercial geometric modeling software of some maturations, as softwares such as Geomagic, free form, the point cloud that it provided is built grid function and is all more or less had these problems, especially, does not find that known business software can guarantee the correctness of topology at present as yet in a process of cloud reconstructed mesh.
In order enough to describe the topology of object, chamber born of the same parents' complex is a kind of describing method of using always.This method is described object with point, line, surface, body, if comprise a line, then must comprise two end points of this line, in like manner, if comprise a face or body, then must comprise its border.Describe object with chamber born of the same parents' complex a benefit is arranged, can clearly represent the topology of object exactly, calculate the topological invariants such as deficiency of object, simultaneously, can also protect the skeleton extract (skeleton itself also is chamber born of the same parents' complex) of topology to object, and the growth of opening up based on the guarantor of skeleton.In three dimensions, the expression mode commonly used of chamber born of the same parents' complex is signed Octree (ESO), and this is a kind of data structure commonly used in the computer graphics.In recent years, chamber born of the same parents complex technology in the application in Digital Geometry Processing field more and more widely.
Summary of the invention
The purpose of this invention is to provide and a kind ofly make up the method for grid surface, to overcome the existing defectives such as topology control and self-adaptation adjustment dough sheet scale of from a technology of cloud generating mesh face, can't carrying out by some cloud.
In order to achieve the above object, technical scheme of the present invention proposes a kind of by a method of cloud structure grid surface, may further comprise the steps:
The point cloud of input is changed into the implicit expression field;
Utilize described implicit expression field to produce to have the Octree of symbol, produce initial chamber born of the same parents' complex and make amendment, make described chamber born of the same parents' complex correct on topology according to described Octree;
Generate the consistent surface mesh of topology by described chamber born of the same parents' complex, specifically comprise:
Cube leafy node to Octree segments, and up to one of meeting the following conditions: the symbol on described cube of a. and border thereof is entirely for just or complete in bearing; B. described cubical border can be divided into two connected components and this cubical each face also meets this condition according to symbol;
For negative, two end points are positive limit to each symbol, and segmentation once;
Adopt the DC method to finish the generation of surface mesh.
Above-mentioned by in the method for cloud structure grid surface, the described some cloud that will import changes into the implicit expression field and adopts the MPU method to finish.
In the above-mentioned method that is made up grid surface by some cloud, chamber born of the same parents' complex made amendment specifically to be comprised:
Described initial chamber born of the same parents' complex is carried out refinement ask skeleton, remove the topological mistake on the skeleton, obtain the correct chamber born of the same parents' complex skeleton of topology;
Carrying out how much responsive chamber born of the same parents' complex that keep with topology by the correct chamber born of the same parents' complex skeleton of described topology rebuilds.
In the above-mentioned method that is made up grid surface by some cloud, described the number of plies of the Octree of symbol is arranged is 7～8 layers.
Above-mentioned by in the method for cloud structure grid surface, describedly initial chamber born of the same parents' complex is carried out refinement ask skeleton and remove topology on the skeleton when wrong, if run into the topological mistake that shows as ringlet on the skeleton arranged, then ringlet is disconnected, further then refinement skeleton finally obtains the skeleton that does not have topology wrong.
Above-mentioned by in the method for cloud structure grid surface, describedly carry out the how much responsive chamber born of the same parents' complex that keep with topology when rebuilding by the correct chamber born of the same parents' complex skeleton of topology, the solid surface is investigated, strengthen the description precision of chamber born of the same parents' complex in the violent place of variation, and strengthen the description precision in the wrong place of former topology.
Technical scheme of the present invention is being made up by a cloud in the process of grid surface, overcome the deficiency that conventional art can not guarantee network topology, and can adjust the description precision automatically at the degree that the surface changes, the grid of Sheng Chenging can guarantee topology at last, can guarantee geometric detail again.
Description of drawings
Fig. 1 is made up the method embodiment process flow diagram of grid surface by a cloud for the present invention;
Fig. 2 is the Octree example of embodiment of the invention model;
Fig. 3 is an example of embodiment of the invention chamber born of the same parents' complex;
Fig. 4 is the refinement example of the embodiment of the invention;
Fig. 5 is segmentation and a skeleton growth example in the embodiment of the invention;
Fig. 6 is that the grid surface of the embodiment of the invention generates example (two-dimensional case);
Fig. 7 is that the grid surface of the embodiment of the invention generates example.
Embodiment
Following examples are used to illustrate the present invention, but are not used for limiting the scope of the invention.
Fig. 1 makes up the method embodiment process flow diagram of grid surface for the present invention by some cloud, and its input data are the some cloud that has normal direction information, is output as the grid that guarantees with topology for how much.As shown in the figure, present embodiment may further comprise the steps: S101, the some cloud that will import change into the implicit expression field; S102, the initial chamber born of the same parents' complex of generation are described; S103, initial chamber born of the same parents' complex is carried out refinement ask skeleton, remove the topological mistake on the skeleton, obtain the correct chamber born of the same parents' complex skeleton of topology; S104, carry out the how much responsive chamber born of the same parents' complex that keep with topology by the correct chamber born of the same parents' complex skeleton of topology and rebuild; S105, generate the consistent surface mesh of topology by chamber born of the same parents' complex.
Further above-mentioned steps S101～S105 is elaborated below.
S101, the some cloud that will import change into the implicit expression field.
This step directly adopts MPU commonly used at present (Multi-level Partition of UnityImplicits, multi-level unit implicit surface decomposes) method.The implicit expression field of output is a function, is defined on the three dimensions, and value is on real number axis, and implicit surface of its place's definition at zero point is greater than zero place definition interior of articles, less than zero place definition object outside.
S102, the initial chamber born of the same parents' complex of generation are described.
Chamber born of the same parents' complex of this step is described with tape symbol Octree (ESO), and whether each element all has been assigned with a symbol and writes down it and belong in the body and (just representing that negative indication is external in the body) in ESO.Here, element has comprised point (point, 0 dimension element), limit (edge, 1 ties up element), face (face, 2 dimension elements) and chamber (cell, 3 dimension elements), and as shown in Figure 2, wherein, (a) part is original Eight model; (b) part is the model inner bulk structure of Octree; (c) part is complete space Octree.It should be noted that the symbol of each element is two different notions with symbol in the implicit expression field.Main purpose of this step is to describe to initial topology of object, so the number of plies of Octree generally can be very not dark.A given implicit expression field obtains initial chamber born of the same parents' complex by following steps:
I. specify the bottommost layer number of Octree, be generally 7 or 8, Octree has only one deck under the initial situation;
Ii. at will specify cube of lattice in surperficial somewhere, the size of cube lattice is relevant with the bottommost layer number, and the bottommost layer number is dark more, and cube lattice are more little; Then Octree is segmented, make this cube lattice become a leaf node of Octree; Set up an empty queue q again, cube lattice are put into formation.
Iii. as if formation q sky, then change step v, otherwise from formation q, take out a cube of lattice C (leaf node of Octree).
Iv. each face of C is done following operation, if the leafy node that 4 symbols of summit in the implicit expression field of this face cube identical or that C is relative with this face has been an Octree, then change iii, otherwise further segment Octree, make that the C cube relative with this face is a leafy node of Octree, the leafy node of correspondence is added formation q, change step I ii.
V. generation chamber born of the same parents complex, if the symbol of certain point in the implicit expression field is for just in the Octree, then its symbol is being for just, otherwise for negative, if the symbol of the end points on Octree bar limit is being all for just, then this limit is being for just, otherwise is to bear.If all boundary edge of certain face are being all for just, then this face is being for just, otherwise is to bear.If all boundary surfaces in certain chamber (also claiming body, i.e. leaf cube lattice) are being all for just, then this chamber is being for just, otherwise is to bear.
By above-mentioned steps i～v, a tape symbol Octree (ESO) has just generated, and it is exactly initial chamber born of the same parents' complex.
S103, initial chamber born of the same parents' complex is carried out refinement ask skeleton, remove the topological mistake on the skeleton, obtain the correct chamber born of the same parents' complex skeleton of topology.
At first will carry out refinement to initial chamber born of the same parents' complex, in the hope of its skeleton, as shown in Figure 3, wherein, (a) part is the original, and (b) part is its skeleton, can see a circle on the corresponding skeleton diagram of ring on the original.The process of refinement realizes (as shown in Figure 4) by removing " simply to ", if promptly a low-dimensional element is only contained by a higher-dimension element, then these two elements can be removed simultaneously, and do not influence the topology of whole object.This is the new method that proposes in Digital Geometry Processing field.Can obtain a skeleton after handling like this.A ring on the skeleton one corresponding original of circle disconnects corresponding a ring of removing on the original with the circle on the skeleton, if this ring is a topological mistake, equals to have removed a topological mistake.
Whether the following describes and how to discern a ring is topological mistake actually.A ring has two attributes, its size and thickness, and size refers to the area that will fill required at least filling to this ring, and thickness refers to will be with the minimum area of this loop slit tangent plane.In this step, if the size of a ring or thickness less than certain fixing threshold value, it just belongs to a topological mistake, this also is quite reasonable in actual applications.How measuring the size and the thickness of a ring, is a prior art during chamber born of the same parents' complex is handled, and repeats no more here.In order to remove topological mistake, only need on skeleton, disconnect ring (limit is wherein removed) and get final product, can proceed refinement then.Constantly carry out refinement and remove topological mistake, till not finding topological mistake.
S104, carry out the how much responsive chamber born of the same parents' complex that keep with topology by the correct chamber born of the same parents' complex skeleton of topology and rebuild.
This step comprises two sub-steps, promptly at first Octree is further segmented, and then from the resulting skeleton of step S103, protects the growth of topology.Because original Octree only for describing topology, so its number of plies is not dark, in order to make it can describe geometric detail, also will segment it.In order to take into full account how much and topological property, need to determine " feature " zone.Segment in these zones, regional contained " feature " is many more, and the precision of being segmented is just high more.The defined feature of this algorithm comprises two classes, and a class is a topological characteristic, and a class is a geometric properties.Topological characteristic refer in step S103, located contain the wrong place of topology, geometric properties refers to the surface to be changed greatly, the bigger place of curvature in other words, curvature is big more, its geometric properties of surface is just obvious more.In order to determine geometric properties, adopt the way of integrating sphere, this is a Digital Geometry Processing field method commonly used.That is, in order to determine the degree of crook of certain point of surface, be that a ball is made at the center with it, the common volume of ball and interior of articles is exactly the geometric properties at this place with the ratio of sphere volume, and obviously this value and 0.5 differs more little, and this locates just smooth more, otherwise then crooked more.
This method is further segmented Octree in topology mistake and the bigger place of Geometrical Bending, and Geometrical Bending is big more, and the precision of segmentation is just high more, referring to Fig. 5.Second step is that skeleton is grown, and the growth here is the inverse operation of refinement among the step S103, promptly increases by two " simply to " elements at every turn.In order to guarantee skeleton only in the interior of articles growth, it must be positive requiring the each symbol of 0 dimension element (i.e. point) in the implicit expression field that increases.
S105, generate the consistent surface mesh of topology by chamber born of the same parents' complex
This step adopts improved DC method.Its example shown in Fig. 6,7, wherein, (a) the corresponding original chamber born of the same parents' complex of part, (b) part is then corresponding to chamber born of the same parents' complex and grid surface after the special segmentation.The concrete grammar of realizing this step is as follows: the chamber born of the same parents' complex that is obtained by S104 may and be not suitable for direct generating mesh surface, need carry out special segmentation.So-called special segmentation is meant following steps:
I. the leafy node (cube) to Octree segments, up to one of meeting the following conditions:
1) symbol on this cube and border thereof is being entirely for just or complete in bearing,
2) this cubical border can be divided into two connected components according to symbol, and this cubical each face also meets this condition.
Ii. be negative to each symbol, two end points but are positive limits, and segmentation once.
After the above-mentioned special segmentation, can adopt existing DC (Dual contouring, antithesis contoured surface structured approach) method is carried out the generation of grid surface, that is: the leaf cube of sign change arranged for each, produce a summit, calculate with original DC method the position, is then to produce a face and connect each leaf cube pairing summit adjacent with this limit in every limit that sign change is arranged.Can prove on mathematics that the grid surface of Chan Shenging can keep the consistent of topology with chamber born of the same parents' complex like this.
Result to the generating mesh face analyzes, and can find the grid surface that the present invention can generate has geometry and topology to guarantee simultaneously.With respect to existing method, as ripe business softwares such as Geomagic, this method has not only remedied it can not guarantee the shortcoming of topology, and geometric detail that can the active detecting surface, describe precision local the increasing automatically that degree of crook is big, finally obtaining how much can both guaranteed grid surface with topology.
More than be preferred forms of the present invention, according to content disclosed by the invention, those of ordinary skill in the art can expect some identical, replacement schemes apparently, all should fall into the scope of protection of the invention.
Claims (6)
1. one kind makes up the method for grid surface by some cloud, it is characterized in that, may further comprise the steps:
The point cloud of input is changed into the implicit expression field;
Utilize described implicit expression field to produce to have the Octree of symbol, produce initial chamber born of the same parents' complex and make amendment, make described chamber born of the same parents' complex correct on topology according to described Octree;
Generate the consistent surface mesh of topology by amended chamber born of the same parents' complex, specifically comprise:
Cube leafy node to Octree segments, and up to one of meeting the following conditions: the symbol on described cube of a. and border thereof is entirely for just or complete in bearing; B. described cubical border can be divided into two connected components and this cubical each face also meets this condition according to symbol;
For negative, two end points are positive limit to each symbol, and segmentation once;
Adopt the DC method to finish the generation of surface mesh.
2. made up the method for grid surface according to claim 1 by a cloud, it is characterized in that, the described some cloud that will import changes into the implicit expression field and adopts the MPU method to finish.
3. make up the method for grid surface according to claim 1 by a cloud, it is characterized in that chamber born of the same parents' complex is made amendment specifically to be comprised:
Described initial chamber born of the same parents' complex is carried out refinement ask skeleton, remove the topological mistake on the skeleton, obtain the correct chamber born of the same parents' complex skeleton of topology;
Carrying out how much responsive chamber born of the same parents' complex that keep with topology by the correct chamber born of the same parents' complex skeleton of described topology rebuilds.
4. made up the method for grid surface according to claim 1 by some cloud, it is characterized in that, described the number of plies of the Octree of symbol is arranged is 7～8 layers.
5. as make up the method for grid surface as described in the claim 3 by a cloud, it is characterized in that, describedly initial chamber born of the same parents' complex is carried out refinement ask skeleton and remove topology on the skeleton when wrong, if run into the topological mistake that shows as ringlet on the skeleton arranged, then ringlet is disconnected, further then refinement skeleton finally obtains the skeleton that does not have topology wrong.
6. as make up the method for grid surface as described in the claim 3 by a cloud, it is characterized in that, describedly carry out the how much responsive chamber born of the same parents' complex that keep with topology when rebuilding by the correct chamber born of the same parents' complex skeleton of topology, the solid surface is investigated, strengthen the description precision of chamber born of the same parents' complex in the violent place of variation, and strengthen the description precision in the wrong place of former topology.
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| CN102222134B (en) * | 2011-05-20 | 2012-10-03 | 山东大学 | Automatic grid density generation method applicable to finite element analysis during forging process |
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| CN111814384B (en) * | 2020-09-01 | 2020-12-11 | 北京应用物理与计算数学研究所 | High-performance numerical simulation pre-and-post-processing low-overhead connection data structure and method |
| CN112434637B (en) * | 2020-12-04 | 2021-07-16 | 上海交通大学 | Object identification method based on quantum computing line and LiDAR point cloud classification |
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| CN101192307A (en) * | 2006-11-17 | 2008-06-04 | 鸿富锦精密工业（深圳）有限公司 | Point cloud triangular topological relations construction method |
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Non-Patent Citations (3)
| Title |
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| Fakir S. Nooruddin et al.Simplification and Repair of Polygonal Models Using Volumetric Techniques.《IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS》.2003,第9卷(第2期), * |
| M. Botsch et al.Sampling Point-Set Implicits.《Eurographics Symposium on Point-Based Graphics》.2007, * |
| Qian-Yi Zhou et al.Topology Repair of Solid Models Using Skeletons.《IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS》.2007,第13卷(第4期), * |
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