CN101110126A - Method for re-establishing three-dimensional model gridding - Google Patents
Method for re-establishing three-dimensional model gridding Download PDFInfo
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Abstract
The invention discloses a 3-D model grid reconstruction method, which is characterized in that: the method allocates an original 3-D model parameters into a 2-D parameter field, conducts sampling of importance in 2-D parameter field, decides the number and layout of sampling points according to the feature of the original model, carries out seamless sewing of the result of importance sampling, so as to realize optimal sampling in parameter field and the grid reconstruction based on it. Therefore, the method overcomes the defect of in the layout and control of grid peak in existing method and effectively lowers down the impact on grid reconstruction due to the distortion of parameter.
Description
Technical field
The invention belongs to field of Computer Graphics, be specifically related to a kind of mesh reconstruction method of three-dimensional model.
Background technology
In a lot of computer graphicss were used, three-dimensional model all was to use surperficial triangle gridding to represent, because triangle gridding is the simplest linear surface, graphic hardware is all extensively supported this method for expressing.At present, the model great majority generate automatically by 3-D scanning equipment and modeling software, like this model of Sheng Chenging usually owing to data volume too greatly, noise and leak etc. are arranged, and some are former thereby can not be satisfactory.These complex models have all proposed very high requirement to the transmission performance of memory property, processor performance and the data of computing machine.Though can reduce the complexity of model by the graticule model simplification algorithm, but Mesh simplification algorithm is mainly paid close attention to is the constant of the geometric configuration of model and topological structure, if in the process of model simplification, do not add special controlling mechanism, the details of model may be lost in this process, and results model does not well guarantee qualitatively leg-of-mutton yet.In order to satisfy the requirement of follow-up Digital Geometry Processing, the model quality that obtains still has much room for improvement.Factors such as the interconnectedness on the distribution of mesh reconstruction (Remeshing) by adjusting the summit, summit and leg-of-mutton size further improve model quality, and it has great significance to follow-up effective processing of grid.Mesh reconstruction all plays important effect, for example distortion of the generation of grid and editor, grid and simplification, denoising, compression, level of detail or the like in the application in a lot of fields such as Geometric Modeling and computer vision.
For a given three-dimensional model M, can obtain a new model M ' who is similar to master pattern by mesh reconstruction, and M ' can satisfy given quality requirements.For different application, the demand of mesh reconstruction is also different, and the yardstick of its quality relates to some aspects such as summit distribution, smoothness, systematicness, scale, leg-of-mutton shape.In the realization of mesh reconstruction, require these yardsticks can reach the combination of an optimum usually.
Relate in the application in engineering field of numerical operation at some, for example finite element analysis, the systematicness to grid has than higher requirement usually, comprises the systematicness of vertex connectivity and triangular shaped systematicness.A high-quality grid can reduce error in numerical operation, and saves operation time.And in the fields such as animation of computer graphics, how then relatively to pay close attention between the quality of grid and travelling speed and obtain a reasonable balance, the real effect to obtain in real time, this just requires in the mesh reconstruction process can be with the accurately representation model of few summit of trying one's best.
In recent years, the mesh reconstruction technology has been subjected to very big concern.Some early stage technical mesh reconstruction algorithms simply improve mesh quality by the process of grid optimization technology such as model simplification, limit insertion, limit deletion, limit exchange, and the common speed of these class methods is all slow.Other some researchers then are devoted to study and can improve the speed of mesh reconstruction and the systematicness of grid vertex (Regularity) by the algorithm of global operation on the whole, and keep the original of model to levy in this process.From the systematicness angle of grid, the rambling grid of the interconnectedness on each summit is an irregular grid in the grid, can obtain semicircular canal grid then by the segmentation of irregular grid being carried out rule.The grid of the interconnectedness on each summit all identical (being generally 6) is called complete regular grid in the grid.The interconnectedness on most of summit all is the grid that 6 grid is called height rule.In order to improve the systematicness on summit, people such as Lee [LEE.A.W.F., SWELDENS, W., SCHROEDER, P., COWSAR, L., DOBKIN, D., 1998.MAPS:Multiresolution adaptive parameterization of surfaces.ComputerGraphics, Vol.32:pp.95-104,1998] and people [ECK.M such as Eck, DEROSE, T., DUCHAMP, T., HOPPE, H., LOUNSBERY, M., AND STUETZLE, W., 1995, Multiresolution analysis of arbitrary meshes, ACMSIGGRAPH 1995, pp 173-182] earlier with model parameterization to a base net lattice (Base Mesh), and then each faces of base net lattice is carried out uniform sampling carry out mesh reconstruction.People such as Guskov [GUSKOV, I., VIDIMCE, K., SWELDENS, W., SCHROEDER, P., 2000.Normal Meshes.Computer graphics proceedings, annual conference series:SIGGRAPH conference proceedings 2000, pp.95-102] with the similar method of Lee grid is cut into the plurality of sub grid with one, the sub-grid parametrization to the plane, is carried out uniform sampling respectively to the zone after the parametrization then and realized mesh reconstruction.Because the mapping of each parameter field is inequality, each parameter field is carried out same uniform sampling rebuild the distribution of new grid on each sub-dough sheet that obtain and inhomogeneous, and the interconnectedness on the summit of sub-dough sheet junction is also irregular, and the grid that obtains is a then grid of semicircular canal.People such as Gu [GU.x, GORTLER, S.J., HOPPE, H.2002.Geometry Images.ACM Transactionson Graphics, pp 355-36] notion of several picture (Geometry Images) has been proposed, he carries out rule sampling with a quadrature regular grids to parameter field then and obtains several picture by with mesh parameterization to a planar rectangular zone.Can directly reconstruct the new grid of complete rule by several picture.
These algorithms have been accelerated the speed of mesh reconstruction by parametrization.But owing to relate to the parametrization of three-dimensional model in this process to two dimensional surface, will inevitably introduce certain error, and these algorithms all are to utilize the segmentation grid of rule that parameter field is carried out rule sampling, their common drawback is: if sampling resolution is not enough, the zone that is twisted can be because of the very few loss in detail that causes in distribution summit, in mesh reconstruction, in order to keep certain local feature in the master pattern, may need that rule is all carried out in the entire parameter territory and be sub-divided into a very meticulous stage, caused the expansion of model vertices scale thus, and wherein a lot of summit may be redundant.In a lot of practical applications, owing to be subjected to the capacity of hardware and the restriction of processing speed, we always wish coming representation model with few summit of trying one's best, the quality that can guarantee model in reserving model detail is unaffected, it is less and some more relatively on the summit of model detail part promptly to try one's best on the summit that the part of model smoothing distributes, and this need be in algorithm distributes to the summit and control effectively.
Turk[TURK, G., 1992, Re-tiling polygonal surfaces.Computer graphics proceedings, annualconference series:SIGGRAPH conference proceedings 1992, pp.55-64] at first proposed and can heavily pave algorithm mesh reconstruction the algorithm----grid that the distribution on summit is controlled.The distribution of the algorithm of Turk by coming control vertex based on the concentration of model curvature information, but this algorithm spreads the summit up to convergence by the lax algorithm of an overall situation on original mesh, and speed is very slow.Frey[frey, p.j.About Surface Remeshing.In Proceedings of the 9th Int.MeshingRoundtable (2000), pp.123-136], people such as Rassineux [Ostromoukhov, V.A Simple And EfficientError-Diffusion Algorithm, ACM press, 2001, pp.567-572] the 3D grid optimization method that proposes, insert and remove mainly that technology and limit subside and the limit splitting operation is controlled sampling rate by the summit, and constantly relax and generate the distribution of adjusting the summit, speed is also very slow, and the number of the grid vertex that obtains at last of difficult control.People's such as Turk and Frey algorithm is all directly directly handled on 3D grid.People such as Surazhsky [Surazhsky vitally and craiggotsman.Explicit Surface Remeshing.In SGP ' 03:Proceedings of the 2003 Eurographics/ACMSIGGRAPH symposium on Geometry Processing, pp.20-30.Aire-la-Ville, Switzerland, 2003.Eurographics Association] work also be based on a series of edge contractions, the limit exchange, limit division and summit operation such as are moved and are realized mesh reconstruction, but it calculates local mesh parameterization in the plane position on new summit in the method for carrying out having adopted when move on the summit local parameterization, and utilize the method for area balance that grid is sampled based on vertex curvature, because most of operation all is based on local grid in this algorithm, with the method for front mutually specific rate be greatly improved.People such as Alliez [Alliez, p., meyer, m.Desbrun, m.2002.Interactive geometry remeshing.ACM Transactions onGraphics 2002,21 (3): pp.347-354] the mutual mesh reconstruction algorithm of Ti Chuing is compared with former persons and is had greatly improved, he is divided into a topological structure a little dough sheet identical with disk with 3D grid, with its parametrization to two dimensional surface, to each sub-dough sheet, according to the character of model itself, can come perfect representation with the discrete geometric maps figure (Geometry Maps) of some pairs.Then according to the concentration of each control chart definition, the summit distribution situation of geometric maps figure being sampled and deciding three-dimensional surface with the error diffusion method in the halftone technique, the method by mesh reconstruction and optimization gets new grid to the end again.In this algorithm,, therefore, in this process, still can't avoid parameter field is carried out regular discrete sampling because error-diffusion method can only be applicable to the rectangular image with fixed resolution.In addition, the sewing process of a plurality of sub-dough sheets also is the process of a more complicated.
Summary of the invention
The objective of the invention is to solve the deficiency of existing method on grid vertex distributes control, propose a kind of mesh reconstruction method based on two-dimensional parameterization and importance sampling.This method to two-dimensional space, is carried out importance sampling at two-dimensional space with the three-dimensional model parametrization, determines the number and the distribution of sampled point by the character of master pattern, thereby reaches best parameter spatial sampling and mesh reconstruction based on this.
The present invention realizes above-mentioned purpose by following technical solution:
A kind of method for re-establishing three-dimensional model gridding, its step comprises:
1) read in the original mesh data,
2) with the original mesh parametrization to the two-dimensional parameter territory, set up the mapping relations on summit in original mesh and the parameter field, make a mapping point in the two-dimensional parameter territory uniquely corresponding to a summit in the original 3D grid,
3) importance sampling is carried out in the two-dimensional parameter territory, obtains the sampling point set of grid vertex,
4) frontier point with parameter field joins in the sampled point set, and the importance sampling point set is carried out seamless stitching,
5) sampled point carry out mesh trianglesization, mesh reconstruction reproduces three-dimensional model.
Described with the original mesh parametrization to the two-dimensional parameter territory, be zero model for deficiency, utilize based on the sphere parametrization of barycentric coordinates method and with regular octahedron as intermediary's parameter field, with model parameterization to the unit square parameter field; Model for any deficiency, under the guiding of parametrization distortion tolerance, automatically the line of cut of search model arrives circular parameter field with model parameterization on this basis, and point on the line of cut and limit are extended to frontier point and the boundary edge that becomes parameter field in the plane parameter territory.
The described step that importance sampling is carried out in the two-dimensional parameter territory is:
1) to sampled concentrations of two-dimensional parameter territory definition,
2) use based on the multi-level importance sampling method of Penrose Tiling and [see Ostromoukhov, M., Donohue, C., Jodoin, P.2004.Fast Hierarchical Importance Sampling with Blue Noise Properties.SIGGRAPH ' 04, pp.488-495] importance sampling is carried out in the two-dimensional parameter territory, obtain the sampling point set that concentration is directly proportional with defined sampled concentrations.
Described method for re-establishing three-dimensional model gridding need carry out feature extraction to original mesh, obtains characteristic edge and unique point.
Described sampled concentrations is the curvature value after the normalization and the product of triangle torsion resistance, and sampled concentrations can be come linear the adjustment by multiply by a coefficient:
Wherein, K
MeanBe the mean curvature on summit, A
3dAnd A
2dBe respectively the summit in three dimensions and two-dimensional space in the leg-of-mutton area in place, wherein k is an arithmetic number, can be used for linear regulation summit sampled concentrations.
Described frontier point and unique point with parameter field joins the sampled point set, and for any deficiency model, what need adding is the borderline point of unit circle parameter field.For deficiency is zero model, carries out the extension field expanding method by the unit square parameter field and obtains, and the steps include:
1) 1 * 1 unit square is launched into 3 * 3 big square,
2) sampled point that produces in the unit square is copied to 3 * 3 big square area according to symmetry,
3) do not comprise the triangle of the sampled point in the central area in deletion 3 * 3 big square area, and delete its respective vertices.Described mesh reconstruction method needs sampled point is screened, and the steps include:
1) between the distance between boundary edge and the characteristic edge, establish a threshold value at sampled point,
2) whether judge distance between sampled point and boundary edge and the characteristic edge less than threshold value,, otherwise keep this sampled point if less than threshold value then delete this sampled point.
Described structure grid is for [seeing SHEWCHUK by limiting the Delaunay trigonometric ratio, J.R.Triangle:Engineering a 2DQuality Mesh Generator and Delaunay Triangulator.In Proceedings of the First workshop onApplied Computational Geometry, Philadelphia, Pennsylvania (1996), PP.123-133.] in the two-dimensional parameter territory all sampled points and unique point are made up triangle gridding, wherein limiting the limit is characteristic curve and boundary sections.Make up and adopt the limit exchanging policy [to see HOPPE, H., DEROSE in the grid process, T., DUCHAMP, T., MCDONALD, J., ANDSTUETZLE, W.1993.Mesh optimization.SIGGRAPH 1993, pp 19-26] and Laplacian smoothing [ALLIEZ, P., MEYER, M.DESBRUN, M.2002.Interactive geometry remeshing.ACM Transactionson Graphics 2002,21 (3): pp.347-354] improve leg-of-mutton quality.
The present invention is converted into the sampling problem in two-dimensional parameter space with the summit control problem of 3D grid, is intended to the importance sampling technology is applied to the reconstruction of 3D grid, and the quantity by improving two-dimentional sampled point is improved the quality of rebuilding grid with distributing.
Advantage of the present invention can be summarized as following several aspect:
1) the present invention improves the plane parameter method, has adopted new two-dimensional parameter framework, and the model of different deficiencys is adopted the parametric method that adapts to it, and this effectively reduces the influence of parametrization distortion to mesh reconstruction.
2) will the sample blue noise method of sampling in field and theory of the present invention is applied to 3D grid and rebuilds, and the plane parameterization of importance sampling technology and 3D grid combined, to reach best parameter spatial sampling and mesh reconstruction based on this.
Description of drawings
Fig. 1 is a systems approach process flow diagram of the present invention,
Fig. 2-a is to be the process flow diagram that zero model carries out two-dimensional parameterization to deficiency,
Mapping generates several picture to Fig. 2-b through three steps by original mesh,
(a) master pattern (b) sphere parametrization result (c) is mapped to the final several picture that generates of octahedron (d)
Fig. 3 is the process flow diagram that the model of any deficiency is carried out two-dimensional parameterization,
Fig. 4 is that line of cut launches synoptic diagram,
Fig. 5 is an importance sampling concentration control chart,
A figure is mean curvature figure, and B figure is area distortion figure, and C figure is both constitutional diagrams
The multi-level importance sampling synoptic diagram that Fig. 6-a paves based on Penrose,
A1 is that the n layer is paved,
A2 further segments for the n layer is paved,
A3 is that the n+1 layer after the a2 segmentation is paved,
The multi-level importance sampling point position adjustment that Fig. 6-b paves based on Penrose,
B1 directly paves the sampled point that obtains,
B2 carries out Lloyd relaxation synoptic diagram for the sampled point to the b1 kind,
B3 is the optimization sampled point after lax,
Synoptic diagram is expanded in Fig. 7-a sampling territory,
Fig. 7-b sampling point set is expanded instance graph,
(1) be the interior sampling point set of unit square,
(2) be the sampling point set that are extended in 3 * 3 zones,
(3) divide for carrying out Delaunay trigonometric ratio gained plane trigonometry 2,
(4) final sampling point set and the set of corresponding triangle thereof for obtaining after the deletion redundant points.
Embodiment
Below in conjunction with accompanying drawing of the present invention, describe specific implementation method of the present invention in detail according to the order of technical scheme.
Fig. 1 has illustrated main technical flows of the present invention:
1) with the original mesh parametrization to the two-dimensional parameter territory:
2) importance sampling is carried out in the two-dimensional parameter territory;
3) original mesh is carried out mesh reconstruction.
At first read in the original mesh data, then model carry out two-dimensional parameterization.The present invention has adopted two kinds of parametrization frameworks, different models is adopted different Parameterization Scheme: for deficiency is zero model, utilization based on the sphere parametrization of barycentric coordinates method and with regular octahedron as intermediary's parameter field, with model parameterization to unit square.For the model of any deficiency, under the guiding of parametrization distortion tolerance, the line of cut of search model arrives circular parameter field with model parameterization on this basis automatically.Select circle as parameter field, both be convenient to parameterized concrete enforcement, also help to reduce parameterized torsion resistance.
For deficiency is zero model, and the parametrization framework that the present invention adopts is shown in Fig. 2 (a).Sphere is the most natural parametrization territory of 0-deficiency model, utilizes the sphere parametrization based on the barycentric coordinates method, the original mesh model can be mapped to regular octahedron.Utilize the spatial symmetry of regular octahedron, can be unit square with its " expansion ", and directly generate a several picture, said process need not model is cut, thus some problems when having avoided sewing up.
In order to generate several picture, need be at the surperficial S of plane parameter territory I and model M
MBetween set up mapping, that is: to arbitrary sampled point in the I, need to calculate it corresponding to S
MThe 3D coordinate information.By introducing sphere, the generative process of several picture (promptly can be shone upon I → S with octahedra
M) be divided into three mappings: model surface S
MWith unit sphere S
0Between mapping, regular octahedron O and unit sphere S
0Between mapping and the mapping between regular octahedron O and the plane parameter territory I, shown in Fig. 2 (b).
For a model M of representing with triangle gridding, can construct one from model surface S
MTo unit sphere S
0Mapping: p:S
M→ S
0The result who represents the sphere mapping with M.A given regular octahedron O, by above-mentioned same sphere parametric method with it parametrization to unit sphere, remember that the gained result is O, in fact, S
0=O.Mapping between from the regular octahedron to the planar I then can be summed up as " folding ", and the simplicity of this process is derived from the spatial symmetry of regular octahedron.Mapping from unit sphere O process regular octahedron to unit square I is designated as g:g=O → [0,1]
2
The key problem that generates several picture is will realize one from [0,1]
2To master pattern surface S
MMapping f (x, y)=(gp)
-1: [0,1]
2→ S
MThis mapping is [0,1]
2Any point t=in the space (x, y) ∈ [0,1]
2Be mapped to master pattern surface S uniquely
MOn corresponding point v.The present invention adopts barycentric coordinates method interpolation method, as " intermediary ", realizes this mapping with sphere on sphere.
The sphere parametrization O of given regular octahedron O, the sphere parametrization M of original triangle gridding M, and O is in [0,1]
2On reflection G, for [0,1]
2Interior any point t, we at first find out the triangle t that comprises t corresponding among the G
I0, (U)Then, pass through t
I0, (U)The triangle t of correspondence in O
I0, (O)T is mapped to unit sphere S
0, establishing institute's invocation point is t
S0In M, find to comprise a t
S0Triangle t
I1, (S0), and then obtain t
I1, (S0)At master pattern surface S
MOn corresponding triangle t
I1, by barycentric coordinates method interpolation method, calculate t at last at S
MOn the position.So just, set up the mapping one by one from the original mesh to the unit square.
For the closed model of any deficiency, the present invention will adopt the strategy that model is launched into a complete dough sheet, mainly consider the torsion resistance of surface tolerance parameterized the time, comprise angle distortion and area distortion etc.{ C} is to become model conversation a topological structure dough sheet D identical with disk for the tangent line limit collection of this method automatic search model under the guiding of the distortion tolerance of model parameterization.Distortion tolerance has adopted the geometric warping measure, and its formula is as follows:
Wherein, A ' (T
i) expression with the plane parameter territory in triangle T
iThe area of corresponding spatial triangle.
The grid cutting algorithm is formed by seeking two processes of initial tangent line and tangent line optimization, and obtains the parametrization of model in this process.As shown in Figure 3, the cutting of model and parameterized procedure can be realized as follows:
1) seeks the initial tangent line { C of model
Initial, initial torsion resistance L
MinBe set to infinity;
2) tangent line is launched, and in length of side ratio parametrization to the unit circle border;
3) with average (Mean-Value) parametric method [Floater, CoordOinates m.2003a.Mean-Value, ComputerAided Geometric Design, 20, pp 19-27]
4) the internal point parametrization is arrived unit circle inside;
5) if computational geometry torsion resistance L is L＜L
Min, find out the maximum triangle T of distortion
i, with current tangent line to T
iBee-line (limit that limits on the shortest path is necessary for the model limit) add tangent line to and { obtain new tangent line limit collection { C among the C}
New, got back to for the 2nd step. otherwise algorithm finishes;
Obtain line of cut to be launched into a ring after the tangent line, this is encircled border as parameter field.In this ring, the border tangent line occurs once, and other tangent lines respectively occur twice, and promptly a tangent line c will be split into { c, c ' }.For example, for tangent line limit collection as shown in Figure 4, the ring after the expansion is: a-b-c-b-d-e-f-e-g-e-d-h-d-b-i-b-a.The normal direction of hypothetical model all inwardly or outwardly, basic idea is the tangent line summit that all is attached thereto by a fixed-direction (clockwise or counterclockwise) traversal for each node (connecting the point greater than two tangent lines), and deeply travels through sub-tangent line limit collection thus up to arriving end points.Be similar to the depth-first method in the tree traversal.When looking for the triangle of torsion resistance maximum,, should adopt corresponding distortion to measure to determine the triangle of torsion resistance maximum for different cost functions.When looking for the shortest path of current line of cut some points in this triangle, need be that starting point is all attempted with each point on the line of cut, to find shortest path.
Constantly tangent line is optimized by this method, can make the model geometric distortion of expansion back reach minimum value, and model parameterization arrives circular parameter field the most at last.
When importance sampling is carried out in the two-dimensional parameter territory, the present invention uses control chart (control map) to come sampled point concentration in the defined parameters territory, and adopt the combination of surface curvature figure and area distortion figure to represent control chart, rebuild the summit number of back grid and the purpose of distribution to reach according to the geometric attribute decision of original mesh.By the curvature on estimation model summit, interpolation goes out the curvature value of each point on the surface mesh, and then obtains surface curvature figure; And calculate the area of each triangle before and after parametrization, calculate its area torsion resistance, and then obtain area distortion figure.The concentration on summit is the curvature value after the normalization and the product of triangle torsion resistance, and can come the linear sampled concentrations of adjusting by multiply by a coefficient.The concentration at each vertex v place can be expressed as:
Wherein, K
MeanBe the mean curvature on summit, A
3dAnd A
2dBe respectively summit leg-of-mutton area in place in 3d space and in the 2D space, k is an arithmetic number, is used for the linear concentration of adjusting.As shown in Figure 5.
The multi-level importance sampling method of paving based on Penrose that the present invention adopts that Ostromoukhov proposes, this method is paved whole sample area with the isosceles triangle that two kinds of length of sides have golden section proportion, by successively segmenting the purpose that reaches importance sampling, shown in Fig. 6-a.And by one calculate in advance good correction chart adjust the position of sampled point can be so that sampled point reaches blue noise character, shown in Fig. 6-b.Because this method does not have special requirement to the shape of sample area, reduce distortion so be applicable to the circular parameter field that we select.
For the model of any deficiency, for the tangent line that makes the grid after the reconstruction can unite by a seam, the borderline point of unit circle parameter field must be retained, and therefore, these points are forced to join behind importance sampling as a result in the sampled point.Simultaneously,, should be avoided on the tangent line and to insert new point for integrality and the symmetry that guarantees tangent line, its method for when sampled point when the distance of tangent line is within some threshold values, delete this sampled point, otherwise keep this sampled point.(for deficiency is zero model, as previously mentioned, because the algorithm that the present invention adopts does not need really model cutting to be opened, does not therefore need to consider the problem at point of contact.)
For deficiency is zero model, and the present invention utilizes the sphere parametrization, by means of regular octahedron, directly generates a several picture.Yet sphere and regular octahedron are closed, non-boundary, and unit square has the border.To introduce the change of topology information inevitably when octahedron is expanded into unit square or lose: octahedron is a non-boundary, and unit square has the border; Originally octahedra two adjacent faces may no longer be adjacent after being unfolded; Originally cross over the octahedra not triangle of coplanar, thereby corresponding triangle may cause two-dimentional triangle to overlap and deleted in unit square because cross over zones of different.In order to compensate the disappearance of topology information, keep the geometric properties of original mesh as far as possible, the present invention solves the problems referred to above (shown in Fig. 7-a and Fig. 7-b) by the unit square parameter field being carried out the extension field expanding method, the steps include:
1) 1 * 1 unit square is launched into 3 * 3 big square,
2) sampled point that produces in the unit square is copied to 3 * 3 big square area, (symmetry derives from octahedral geometrical property) according to symmetry;
3) do not comprise the triangle of the sampled point in the central area in deletion 3 * 3 big square area, and delete its respective vertices.
After the summit that obtains having blue noise character by above-mentioned importance sampling distributes, also need to produce connected relation between the summit to obtain required triangle gridding, this can carry out plane trigonometryization and realize by the sampled point to parameter space.The present invention will adopt and limit the Delaunay trigonometric ratio, and this method can keep characteristic specified point and characteristic curve after trigonometric ratio.Characteristic curve can obtain by two the adjacent leg-of-mutton dihedral angles of limit that calculate in the master pattern, and allow the trigonometric ratio method in needs, on characteristic edge, to add new summit to guarantee each leg-of-mutton quality, avoid long and narrow leg-of-mutton generation as far as possible.In order to optimize the quality of grid, the present invention adopts limit exchanging policy and Laplacian smoothing to improve leg-of-mutton quality, and the Lapalacian weights are defined as follows:
Wherein, A
i 3DAnd A
I-1 3DBe the adjacent area of two triangles in 3d space in limit that constitutes with summit p and its adjoint point q, D
I, jBe the corresponding respectively sampled concentrations value in leg-of-mutton three summits.Adopt in the algorithm
Come the integration of the control chart concentration on subtriangular, make after optimizing the summit with given control chart corresponding.Utilize the three-dimensional coordinate of linear interpolation method calculating sampling point to realize the mesh reconstruction after optimizing is reproduced three-dimensional model.
Foregoing is understood the implementation method based on the mesh reconstruction of two-dimensional parameterization and importance sampling specifically.By means of two-dimensional parameterization, the two-dimensional parameter territory is transferred in the sampling of master pattern, in this process, reduce the distortion that parametrization is brought as far as possible; Adopt the importance sampling technology, can obtain having the sampling point set of blue noise character, can keep the geometric properties of original mesh preferably; By mesh reconstruction and optimization, can obtain the summit quantity and the improved new grid that distributes.
Although disclose specific embodiments of the invention and accompanying drawing for the purpose of illustration, its purpose is to help to understand content of the present invention and implement according to this, but it will be appreciated by those skilled in the art that: without departing from the spirit and scope of the invention and the appended claims, various replacements, variation and modification all are possible.Therefore, the present invention should not be limited to most preferred embodiment and the disclosed content of accompanying drawing.
Claims (10)
1. method for re-establishing three-dimensional model gridding, its step comprises:
1) read in the original mesh data,
2) with the original mesh parametrization to the two-dimensional parameter territory, set up the mapping relations on summit in original mesh and the parameter field, make a mapping point in the two-dimensional parameter territory uniquely corresponding to a summit in the original 3D grid,
3) importance sampling is carried out in the two-dimensional parameter territory, obtains the sampling point set of grid vertex,
4) frontier point with parameter field joins in the sampled point set, and the importance sampling point set is carried out seamless stitching,
5) sampled point carry out mesh trianglesization, mesh reconstruction reproduces three-dimensional model.
2. method for re-establishing three-dimensional model gridding as claimed in claim 1 is characterized in that original mesh is carried out feature extraction, obtains characteristic edge and unique point.
3. method for re-establishing three-dimensional model gridding as claimed in claim 1 or 2, it is characterized in that for deficiency be zero original mesh, utilization based on the sphere parametrization of barycentric coordinates method and with regular octahedron as intermediary's parameter field, with model parameterization to the unit square parameter field.
4. method for re-establishing three-dimensional model gridding as claimed in claim 1 or 2, it is characterized in that original mesh for any deficiency, under the guiding of parametrization distortion tolerance, the line of cut of automatic search model, model parameterization is arrived circular parameter field, line of cut is launched into the boundary edge of parameter field, and the point of contact is a frontier point.
5. method for re-establishing three-dimensional model gridding as claimed in claim 1 or 2 is characterized in that described importance sampling step is:
1) to sampled concentrations of two-dimensional parameter territory definition,
2) use based on the multi-level importance sampling method of Penrose Tiling importance sampling is carried out in the two-dimensional parameter territory, obtain the sampling point set that concentration is directly proportional with defined sampled concentrations.
6. method for re-establishing three-dimensional model gridding as claimed in claim 5 is characterized in that described sampled concentrations is
Wherein, K
MeanBe the mean curvature on summit, A
3dAnd A
2dBe respectively the summit in three dimensions and two-dimensional space in the leg-of-mutton area in place, wherein k is an arithmetic number, can be used for linear regulation summit sampled concentrations.
7. method for re-establishing three-dimensional model gridding as claimed in claim 2 is characterized in that
1) between the distance between frontier point and the characteristic edge, establish a threshold value at sampled point,
2) whether judge distance between sampled point and boundary edge and the characteristic edge less than threshold value,, otherwise keep this sampled point if less than threshold value then delete this sampled point.
8. method for re-establishing three-dimensional model gridding as claimed in claim 3 is characterized in that described unit square parameter field is expanded:
1) 1 * 1 unit square is launched into 3 * 3 big square,
2) sampled point that produces in the unit square is copied to 3 * 3 big square area according to symmetry,
3) do not comprise the triangle of the sampled point in the central area in deletion 3 * 3 big square area, and delete its respective vertices.
9. method for re-establishing three-dimensional model gridding as claimed in claim 2, it is characterized in that described structure grid in the two-dimensional parameter territory all sampled points and unique point being made up triangle gridding by limiting the Delaunay trigonometric ratio, wherein limiting the limit is characteristic edge and boundary edge.
10. method for re-establishing three-dimensional model gridding as claimed in claim 1 or 2 is characterized in that adopting in the described structure grid process limit exchanging policy and Laplacian smoothing to improve leg-of-mutton quality.
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