CN104821015A - Method for reconstructing alpha-shape curved surface topology of object surface sample point - Google Patents
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Abstract
The invention provides a method for reconstructing alpha-shape curved surface topology of an object surface sample point, which belongs to the field of product reverse engineering. The method is characterized by comprising the steps of constructing a Delaunay grid partition of the object surface sample point and constructing a space index KD tree; solving an alpha-shape scale threshold interval which corresponds with each patch, and obtaining a left end point set and a right end point set of the interval; selecting a patch with a least end point summation of the interval as an initial patch; obtaining a curved surface local sample with an optimized gain for estimating a sample point distribution density, performing alpha-shape scale threshold adaptive adjustment according to the sample point distribution density, then performing Delaunay patch filtering, and obtaining an initial grid curved surface; and extracting an external grid patch of the initial grid for obtaining a two-dimensional manifold grid. The method of the invention has functions of substantially preventing holes and rib dents on the grid curved surface, better keeping shape and position accuracy of the rib characteristic, reducing non-manifold patches in a primary filtering result, and furthermore realizing a relatively high reconstruction efficiency.
Description
Technical Field
The invention provides a sample point on the surface of a real objectαThe shape surface topology reconstruction method can be used for constructing a mesh surface model of a real object surface sampling point, and belongs to the field of product reverse engineering.
Background
The curved surface topology reconstruction is also called curved surface reconstruction, is a core technology of reverse engineering, mainly solves the problem of restoration of the adjacency relation of randomly distributed object surface sample points only containing coordinate information, and an output result is embodied as a polygonal mesh curved surface of a two-dimensional orientable manifold structure. The form and position accuracy of the reconstruction result of the edge characteristics of the object surface sample points has important influence on the subsequent design analysis and remanufacturing process, but the prior curved surface topology reconstruction technology cannot realize the accurate reconstruction of the edge characteristics, and has no more perfect solution for the problem of the curved surface topology reconstruction of mass object surface sample points with the data volume exceeding the physical memory capacity of a computer, so that the curved surface topology reconstruction is still a research hotspot in the fields of reverse engineering, computer aided design and manufacturing, scientific calculation visualization and the like.
The existing surface topology reconstruction algorithm can be mainly divided into a Delaunay mesh filtering algorithm and an implicit surface fitting algorithm. The Delaunay mesh filtering algorithm firstly constructs Delaunay mesh subdivision on the surface sample points of the object, then extracts a polygonal mesh curved surface from the Delaunay mesh subdivision by utilizing corresponding constraint conditions such as the distance between the sample points, the vector of a sample point method, the middle axis transformation and the like, and the constructed mesh curved surface is interpolated on the sample points at the edge characteristics, so that the form and position accuracy of the mesh curved surface can be well maintained. Implicit surface fitting algorithms, e.g. Poisson's method[13]The implicit function curved surface is subjected to overall approximation on the sampling points, the method has certain advantages in the aspect of curved surface topology reconstruction with noise data, and is widely applied to the fields of computer aided design, scientific calculation visualization and the like. Therefore, it is required toAnd under the condition of accurately reconstructing the edge characteristics, a Delaunay mesh filtering algorithm is selected to perform surface topology reconstruction.
A typical representation of the Delaunay lattice filtering algorithm isαShape algorithm and Cocone algorithm.αCalculating a corresponding scale threshold interval when the Delaunay surface patch is positioned in the grid curved surface by using a shape algorithm, and selecting a scale thresholdαAnd establishing a mesh curved surface by using the patch corresponding to the scale threshold interval. The Cocone algorithm selects a Voronoi pole to estimate a sample point normal vector, a complementary space of a coaxial symmetrical biconical space is established by taking the Voronoi pole as an axis, and Delaunay surface patches with dual Voronoi edges intersected with the space are selected to construct a grid curved surface. The Cocone algorithm requires infinite sampling density of edge features to ensure accuracy of normal vector estimation, and sampling density of physical surface sample point acquisition equipment, such as a structured light raster scanner and a laser measuring machine, can only reach a limited value, so that face selection errors occur during Cocone reconstruction, and the obtained edge features consist of a large number of tiny dents. DEY, etc., constructing an approximate edge curve, resampling from the curve as an edge feature point, and avoiding using a normal vector of the edge feature point when selecting a patch by a Cocone algorithm, so as to obtain an edge feature with a more optimized shape. In contrast to the Cocone algorithm,αthe shape algorithm does not depend on the local flatness of the curved surface described by the sampling point normal vector, and can better reconstruct the geometric characteristics of large-curvature areas such as edges, round corners, transition curved surfaces and the like of the sample points on the surface of the real object obtained by common data acquisition equipment, but when the sample points are not uniformly distributed, holes and a small number of edge dents are easily and wrongly reconstructed in a sparse area.
To make it possible toαThe shape algorithm correctly reconstructs a sparse region when sampling points are unevenly distributed, the size of a scale threshold is mainly adjusted according to the sparsity degree of the distribution of the sampling points in a local region where a patch is located, wherein the sparsity degree of the distribution of the sampling points in the local region can be obtained by analyzing a local surface sample at the sampling points, and the main analysis method comprises the following steps of Jiang et al (Advanced Material)als Research, 2013, 821: 765-768.), The mean of The distances between samples, Giesen et al in The consistent alpha shape file (The Visual Computer, 2006, 22 (8): 531-540), and Teichmann et al, in Surface retrieval with anatomical consistency-scaled alpha maps (Proceedings of the conference on Visualization'98. IEEE Computer Society Press, 1998: 67-72) neutralization Xu et al in Automatic surface recovery with alpha-shape method (The Visual Computer, 2003, 19 (7): 431-443), and the like. Whether the holes and the edge dents in the reconstruction result can be effectively reduced by the method depends on whether the local surface sample can correctly reflect the shape of the area near the sampling points or not, but according to the literature, the acquisition of the local surface sample is mainly based on the Euclidean distance and usually deviates to the area with dense local sampling point distribution, and if a certain area simultaneously comprises the area with sparse sampling point distribution and the area with dense sampling point distribution, the holes and the edge dents are still easily reconstructed at the certain area.
Disclosure of Invention
The invention aims to solve the problems at presentαThe main problem of shape algorithm is to provide a real object surface sampling pointαAnd the shape surface topology reconstruction method optimizes the surface reconstruction result without obviously reducing the reconstruction efficiency.
The purpose of the invention is realized by the following technical scheme:
material object surface sampling pointαThe shape surface topology reconstruction method is characterized by sequentially comprising the following steps: (1) set of sample points on the surface of the objectPBased on QuickHull algorithm constructionPDelaunay mesh subdivision to obtain a set of patchesF(P) (ii) a (2) Point setPConstructing spatially indexed KD trees to facilitate fast acquisition of target sample pointskTaking the neighborhood point set as an initial curved surface local sample of the corresponding position of the surface of the object; (3) reference classicα-shape algorithm, solving each patchCorrespond toαShape scale threshold intervalObtaining the left end point of the scale threshold intervalSet of (2)And a right endpointSet of (2)(ii) a (4) Selecting the sum of endpoints of intervalsThe smallest patch is used as the initial patchT 0I.e. byT 0Satisfy the requirement of(ii) a (5) Obtaining an initial patchT 0 Then, fromQuery inFromQuery inAnd is calculated according toIs calculated by the formula (2)，
(1)
Wherein,is composed ofTThe three vertices of the three-dimensional graph,as the weight coefficient,，and is，Is composed ofA sample point distribution density estimation function; (6) obtaining a gain-optimized curved surface local sample, using the optimized sample for estimating the distribution density of sampling points, and performing the estimation according to the distribution density of the sampling pointsα-shape scale threshold value self-adaptive adjustment, and then performing Delaunay surface patch filtering to obtain an initial mesh surfaceQ(ii) a (7) Estimating sampling point normal vector by using curved surface local sample at each sampling point, calculating and unifying each surface patch normal vector, and finally extracting initial meshQThe two-dimensional manifold mesh is obtained by the external mesh surface patch.
The sample points on the surface of the objectαThe shape surface topology reconstruction method is characterized in that in the step (6), gain-optimized surface local samples are obtained before Delaunay surface patch filtering is carried out, and the optimized samples are used for reconstructionα-shape scale threshold adaptive adjustment, comprising the specific steps of: (1)，the total number of patches in the Delaunay grid; (2) from F(P) Taking out dough sheetThe vertex is(ii) a (3) FromTaking outFromTaking out(ii) a (4) If it isStep (5) is executed, otherwise, step (2) is repeated; (5) facing sheetsEach vertex of (2)Obtaining gain optimizedλ(p i )，i=1,2,3, for one pointpLocal sample of the initial surface ofThe specific steps for gain optimization are as follows: from sampled data on the surface of a real objectpIs/are as followsk-neighbor set；To determine the gain optimization direction, a mean shift vector is calculatedIs of the formulaWhereinIs composed ofThe corresponding kernel density estimation mode point is,is calculated by the formula
(2)
Wherein,，G(x) In the form of a gaussian kernel function,nis composed ofNumber of samples in, bandwidthhTake a value ofpToThe maximum value of the distance between each point in the middle;in thatIn the opposite direction of (1)AboutpPoint of symmetry of； Query in physical surface sampling dataIs/are as followsk-neighbor set；FromIn the selection pairSubsets with gain optimizationS； If it isJump to r; ；⑧ (ii) a NinthlyTo (v); rThe gain optimization process is terminated; the above stepsFromFor the time selectedSubsets with gain optimizationSThe specific algorithm is as follows:to pairAccording to whichpAre arranged in ascending order to form an ordered set； ，； ；If it isThen fromSDeletion inThen jumping to (7); ；repetition ofTo；Return toS(ii) a (6) Using the previously determined、Andcalculating the resultFor any dough sheetT，The calculation formula of (2) is as follows:
(3)
whereinFor fine adjustment of the coefficients, it can be set manually,is composed ofpThe sample point distribution density of (a) is estimated,as the weight coefficient,，and is(ii) a (7) If it isAnd isThen, then；(8) (ii) a (9) If it isRepeating (2) to (8), otherwise executing (10); (10) return toQ。
The sample points on the surface of the objectα-shape surface topology reconstruction method, characterized in that sampling point density estimation function is adoptedThe calculation formula is
(4)
Whereinm(λ(p) Is a local sample of a curved surface) The number of the sampling points of (a),is composed ofThe volume of the distribution space is such that,Nset of surface sample points for objectPNumber of samples in (1).
The sample points on the surface of the objectα-shape surface topology reconstruction method, characterized in that weight coefficients are adopted1/3 is taken.
The physical surface sample according to claim 2α-shape surface topology reconstruction method, characterized in that the adopted fine tuning coefficientThe calculation formula of (2) is as follows:
(5)
whereinNThe number of the sample points on the surface of the object,ρ j the distribution density of the sampling points is calculated for each point,j=1，2，…N，is the average value of the density of each point.
Compared with the prior art, the invention has the following advantages:
(1) the gain optimization is carried out on the local samples used for the curved surface topology reconstruction, the topology neighborhood information loss caused by the uneven data distribution can be compensated to a certain extent, the completeness of the shape reflection of the curved surface local samples on the area near the sampling point is improved, and the improvement of the shape reflection of the curved surface local samples on the area near the sampling point is facilitatedαThe shape algorithm reconstructs the correctness of the result in the sampling point distribution sparse region;
(2) combining the gain-optimized curved surface local samples and utilizingαThe shape scale threshold value self-adaptive adjustment criterion realizes the self-adaptive adjustment of the scale threshold value, the curved surface topology reconstruction is carried out, the number of holes, edge dents and non-manifold surfaces in the non-uniform sampling point reconstruction result can be obviously reduced, and the edge characteristic shape and position precision can be well kept;
(3) establishing spatial index KD tree for real object surface sampling data, and facilitating rapid acquisition of target sampling pointskThe neighborhood data is used as an initial curved surface local sample, so that the gain optimization process of the curved surface local sample has small influence on the efficiency of curved surface topology reconstruction;
(4) in the referenceαWhen the shape algorithm carries out Delaunay surface patch filtering, the inspection rule of the filtering process simultaneously considersα-shapeThe left end point and the right end point of the scale threshold interval are more than the normalαThe shape surface topology reconstruction algorithm only considers the left endpoint of the scale threshold interval to obtain a more accurate mesh model, and the number of non-manifold patches in the mesh surface can be reduced;
(5) according to the space distribution characteristics of the optimized curved surface local sample, describing the distribution density of the sampling points in the curved surface local sample by the distribution number of the sampling points in unit volume, establishing a local self-adaptive sampling point distribution density function, and being beneficial to improving the accuracy of the sampling point distribution density result;
(6) through experimental research, the values of the key parameters in the curved surface topology reconstruction method are optimized, and the reconstruction efficiency and the reconstruction result accuracy are improved.
Drawings
FIG. 1 shows surface samples of the present inventionα-a program implementation flow chart of a shape surface topology reconstruction method;
FIG. 2 is a sample point of an objectpThe distribution diagram of the initial curved surface local sample is shown;
3-8 are schematic diagrams of constructing a KD tree index and obtaining an initial surface local sample;
FIG. 9 shows the result of gain optimization of the initial surface local samples shown in FIG. 2;
FIG. 10 is a sample pointpThe approximate spherical distribution space schematic diagram of the local sample of the curved surface;
FIGS. 11 to 14 are diagrams of a surface patch selection process for performing surface topology reconstruction on the point cloud shown in FIG. 5 by using the method of the present invention;
FIG. 15 is a Rabbit point cloud model as a sample point of a surface of an object used in a surface topology reconstruction test according to an embodiment;
FIG. 16 is a graph showing the effect of the global and local edge characteristics of the reconstruction result of the surface sample points of the object according to the first embodiment;
FIG. 17 is a surface sample point of a mechanical part used in the surface topology reconstruction test of the second embodiment;
FIG. 18 is a graph showing the effect of the global and local edge characteristics of the reconstruction results of the surface samples of the mechanical parts according to the second embodiment.
Detailed Description
The invention is further explained below with reference to the drawings and examples.
FIG. 1 shows surface samples of the present inventionαAnd a program implementation flow chart of the shape surface topology reconstruction method can be implemented by adopting a C programming language. Sample point on surface of objectαThe main program modules of the shape surface topology reconstruction method comprise the steps of constructing object surface sample points Delaunay mesh subdivision, establishing a dynamic spatial index KD tree, calculating the,αCalculating two end points of a shape scale threshold interval, selecting an initial surface patch on a mesh surface, optimizing the gain of a surface local sample used for surface reconstruction, adaptively adjusting a scale threshold, filtering a Delaunay surface patch, extracting manifold and the like.
FIG. 2 is a sample point of an objectpThe initial surface local sample of (1) is generally adoptedpIs/are as followskThe neighborhood point set is used as the initial surface local sample, butkThe neighborhood point set is obtained mainly based on euclidean distance, and usually biased to a local sample point distribution dense region (as shown in fig. 2), and if a certain region includes a sample point distribution sparse region and a sample point distribution dense region, a hole and an edge dent are likely to appear in a reconstruction result at the certain region. In addition, the acquisition speed of the initial curved surface local sample is a bottleneck problem influencing the overall efficiency of curved surface topology reconstruction, and in order to improve the acquisition speed of the initial curved surface local sample, a KD (K-dimension) tree dynamic spatial index is established for the physical surface sampling points, and the target sampling points are inquired based on the KD tree indexkThe neighborhood point set is used as an initial curved surface local sample, fig. 3-7 are construction process diagrams of nodes of each layer of the KD tree, and fig. 8 is a diagram for querying a target by using the KD treeOf spotskSchematic diagram of neighborhood point set.
Fig. 9 shows the result of gain optimization performed on the initial surface local sample shown in fig. 2, where the main steps of the gain optimization process are: from sampled data on the surface of a real objectpIs/are as followsk-neighbor set(as shown in FIG. 2);for determining the direction of gain optimization, according to the formulaCalculating a mean shift vectorWhereinCan be determined by reference to the formula (2), the position of which in space is shown in FIG. 2MPoint;in thatIn the opposite direction of (1)AboutpPoint of symmetry of； Query in physical surface sampling dataIs/are as followsk-neighbor set；FromIn the selection pairSubsets with gain optimizationS； If it isJump to r; ；⑧ (ii) a NinthlyTo (v); rThe gain optimization process is terminated,namely the gain-optimized surface local sample (see fig. 9).The above stepsFromFor the time selectedSubsets with gain optimizationSThe method comprises the following specific steps:to pairAccording to whichpAre arranged in ascending order to form an ordered set； ，； ；If it isThen fromSDeletion inThen jumping to (7); ；repetition ofTo；Return toS。
Fig. 10 is a schematic diagram of the spherical distribution space of the gain optimized local surface samples. After the gain-optimized curved surface local sample is obtained, the sample point distribution density of the area near the target sample point can be estimated by using the gain-optimized curved surface local sample, and specifically, the number of sample points in a unit volume in the curved surface local sample can be calculated according to a formula (4) to serve as the local sample point distribution density. In order to obtain the distribution volume of the curved surface local sample, the distribution space of the curved surface local sample can be regarded as a sphere, and the radius of the sphere is the maximum distance from each point in the local sample to the target sampling point.
Fig. 11 to 14 are diagrams illustrating a process of selecting a surface slice from the Delaunay mesh to construct a mesh surface. (1) Set of sample points on the surface of the objectPBased on QuickHull algorithm constructionPDelaunay mesh subdivision to obtain a set of patchesF(P) Fig. 11 shows a convex hull of the created Delaunay grid; (2) point setPConstructing a spatial index KD tree (as shown in figures 3-8) to facilitate rapid acquisition of target sampling pointskTaking the neighborhood point set as an initial curved surface local sample of the corresponding position of the surface of the object; (3) reference classicαShape algorithm for solving each patchCorrespond toαShape scale threshold intervalObtaining the left end point of the scale threshold intervalSet of (2)And a right endpointSet of (2)(ii) a (4) Selecting the sum of endpoints of intervalsThe smallest patch is used as the initial patchT 0I.e. byT 0Satisfy the requirement of(ii) a (5) Obtaining an initial patchT 0 Then, fromQuery inFromQuery inAnd is calculated according to the formula (1)Is calculated by the formula (2)Calculating the time weight coefficient1/3 is taken; (6) obtaining a gain optimized curved surface local sample, using the optimized sample to estimate the distribution density of sampling points according to a formula (4), and carrying out the estimation according to the distribution density of the sampling pointsα-shape scale threshold value self-adaptive adjustment, and then performing Delaunay surface patch filtering to obtain an initial mesh surfaceQ(ii) a (7) Estimating sampling point normal vector by using curved surface local sample at each sampling point, calculating and unifying each surface patch normal vector, and finally extracting initial meshQThe two-dimensional manifold mesh is obtained by the external mesh surface patch. The concrete process of the step (6) is (1)，(ii) a (2) From F(P) Taking out dough sheetThe vertex is(ii) a (3) FromTaking outFromTaking out(ii) a (4) If it isStep (5) is executed, otherwise, step (2) is repeated; (5) facing sheetsEach vertex of (2)Obtaining gain optimizedλ(p i )，i=1,2, 3; (6) using the previously determined、Andcalculating the scale threshold value according to the formula (3)Calculating the time weight coefficientTaking out the 1/3 (the weight ratio of the materials),the distribution density of the sample points is calculated according to the formula (5)Calculating according to the formula (4); (7) if it isAnd isThen, thenThe patch addition process is shown in fig. 12 and 13; (8)(ii) a (9) If it isRepeating (2) to (8), otherwise executing (10); (10) returning the constructed initial mesh surfaceQ(as shown in fig. 14).
The first embodiment is as follows: the surface sampling points of the mechanical part shown in fig. 15 are reconstructed by applying the curved surface topology reconstruction method of the invention. The sampling point set shown in fig. 15 includes 55685 sampling points, contains edge characteristics, boundary characteristics and a free-form surface, and is a point set with a large overall distribution non-uniformity degreeαThe shape scale threshold is adjusted more accurately, the phenomenon that the density of sampling points is over-estimated due to the fact that the local samples of the curved surface are seriously biased to the dense area of the sampled data is avoided, and the defects caused by mistaken deletion can be effectively reduced. From the reconstruction result of the method of the present invention shown in fig. 16, the overall reconstruction result has almost no holes, and can more accurately reflect the overall morphological characteristics of the point set with a large overall non-uniform local degree, the reconstruction effect of the local edge characteristics has good continuity and sharpness, and the holes near the edge are significantly reduced, the number of the surface patches in the reconstructed mesh model is 119162, and the reconstruction time is 19.35 seconds.
Example two: the model of the rabbitt point cloud, which is the sample point on the surface of the object shown in fig. 17, is reconstructed by applying the method for reconstructing the surface topology of the invention. The point cloud model shown in fig. 17 includes 34834 sample points, the overall distribution is approximately uniform, the local part is non-uniform due to large curvature change, and there is a sharp edge at the edge of the ear, because better local samples of the curved surface can be obtained under the non-uniform condition for the reconstruction process of the curved surface topology, the reconstruction result shown in fig. 18 has better reconstruction effects on the whole and the edge of the ear, the number of patches in the reconstructed mesh model is 100163, and the reconstruction time is 11.82 seconds.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
Claims (5)
1. Material object surface sampling pointαThe shape surface topology reconstruction method is characterized by sequentially comprising the following steps: (1) set of sample points on the surface of the objectPBased on QuickHull algorithm constructionPDelaunay mesh subdivision to obtain a set of patchesF(P) (ii) a (2) Point setPConstructing spatially indexed KD trees to facilitate fast acquisition of target sample pointskTaking the neighborhood point set as an initial curved surface local sample of the corresponding position of the surface of the object; (3) reference classicαShape algorithm for solving each patch Correspond toαShape scale threshold intervalObtaining the left end point of the scale threshold intervalSet of (2)And a right endpointSet of (2)(ii) a (4) Selecting the sum of endpoints of intervalsThe smallest patch is used as the initial patchT 0I.e. byT 0Satisfy the requirement of(ii) a (5) Obtaining an initial patchT 0 Then, fromQuery inFromQuery inAnd is calculated according toIs calculated by the formula (2)，
Wherein,is composed ofTThe three vertices of the three-dimensional graph,as the weight coefficient,，and is，Is composed ofA sample point distribution density estimation function; (6) obtaining a gain-optimized curved surface local sample, using the optimized sample for estimating the distribution density of sampling points, and performing the estimation according to the distribution density of the sampling pointsα-shape scale threshold value self-adaptive adjustment, and then performing Delaunay surface patch filtering to obtain an initial mesh surfaceQ(ii) a (7) Estimating sampling point normal vector by using curved surface local sample at each sampling point, calculating each surface patch normal vector and making itUniformizing and finally extracting initial gridsQThe two-dimensional manifold mesh is obtained by the external mesh surface patch.
2. The physical surface sample according to claim 1αThe shape surface topology reconstruction method is characterized in that in the step (6), gain-optimized surface local samples are obtained before Delaunay surface patch filtering is carried out, and the optimized samples are used for reconstructionα-shape scale threshold adaptive adjustment, comprising the specific steps of: (1)，the total number of patches in the Delaunay grid; (2) from F(P) Taking out dough sheetThe vertex is(ii) a (3) FromTaking outFromTaking out(ii) a (4) If it isStep (5) is executed, otherwise, step (2) is repeated; (5) facing sheetsEach vertex of (2)Obtaining gain optimizedλ(p i )，i=1,2,3, for one pointpThe specific steps of performing gain optimization on the initial curved surface local sample are as follows: from sampled data on the surface of a real objectpIs/are as followsk-neighbor set；To determine the gain optimization direction, a mean shift vector is calculatedIs of the formulaWhereinIs composed ofThe corresponding kernel density estimation mode point is,is calculated by the formula
Wherein,，G(x) In the form of a gaussian kernel function,nis composed ofNumber of samples in, bandwidthhTake a value ofpToThe maximum value of the distance between each point in the middle;in thatIn the opposite direction of (1)AboutpPoint of symmetry of； Query in physical surface sampling dataIs/are as followsk-neighbor set；FromIn the selection pairSubsets with gain optimizationS； If it isJump to r; ；⑧ (ii) a NinthlyTo (v); rThe gain optimization process is terminated; the above stepsFromFor the time selectedSubsets with gain optimizationSThe specific algorithm is as follows:to pairAccording to whichpAre arranged in ascending order to form an ordered set； ，； ；If it isThen fromSDeletion inThen jumping to (7); ；repetition ofTo；Return toS(ii) a (6) Using the previously determined、Andcalculating the resultFor any dough sheetT，The calculation formula of (2) is as follows:
whereinFor fine adjustment of the coefficients, it can be set manually,is composed ofpThe sample point distribution density of (a) is estimated,is a rightThe coefficients of which are such that,，and is(ii) a (7) If it isAnd isThen, then；(8) (ii) a (9) If it isRepeating (2) to (8), otherwise executing (10); (10) return toQ。
3. The physical surface sample according to claim 1 or 2α-shape surface topology reconstruction method, characterized in that sampling point density estimation function is adoptedThe calculation formula is
Whereinm(λ(p) Is a local sample of a curved surface) The number of the sampling points of (a),is composed ofThe volume of the distribution space is such that,Nset of surface sample points for objectPNumber of samples in (1).
4. The physical surface sample according to claim 1 or 2α-shape surface topology reconstruction method, characterized in that weight coefficients are adopted1/3 is taken.
5. The physical surface sample according to claim 2α-shape surface topology reconstruction method, characterized in that the adopted fine tuning coefficientThe calculation formula of (2) is as follows:
whereinNThe number of the sample points on the surface of the object,ρ j the resulting sample distribution density, j =1,2, …, was calculated for each pointN，Is the average value of the density of each point.
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| CN107610228A (en) * | 2017-07-05 | 2018-01-19 | 山东理工大学 | Curved surface increment topology rebuilding method based on massive point cloud |
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| US11348260B2 (en) * | 2017-06-22 | 2022-05-31 | Interdigital Vc Holdings, Inc. | Methods and devices for encoding and reconstructing a point cloud |
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