JPH11339071A - System for automatic polygon generation from dot group - Google Patents

Abstract

PROBLEM TO BE SOLVED: To generate detailed polygon meshes from a group of unarrayed dots distributed on the surface of a body in phase structure obtained by taking measurements through a measuring instrument, etc. SOLUTION: The minimum surface density of the unarrayed dot group distributed on the surface of the body obtained by taking measurements through the measuring instrument, etc., is calculated, a voxel size is determined according to the minimum surface density to generate a volume model of the voxel size, and a grating point connecting method is implemented for it to generate basic meshes. Then surface properties for relating the surface of the obtained basic meshes to the dot group are found and polygon meshes having all the dots of the dot group as vertexes are made detailed through vertex dividing operation to generate polygon meshes.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a CAD which can be used for a three-dimensional shape model generating device, particularly a shape input device for diverting design of existing products, an Internet VRML content generating device, and a non-contact measurement result analyzing device. / C
3D shape model automatic generation system using AM, and
The present invention relates to a method for automatically generating the model.

[0002]

2. Description of the Related Art In recent years, with the spread of multimedia on the Internet, the use of three-dimensional expressions has expanded, and the importance of three-dimensional modeling has increased. Among them, many three-dimensional modeling methods based on two-dimensional images have been proposed. A feature of a three-dimensional point group based on a two-dimensional image is that the density is sparse and not constant. Several methods have been proposed in the past for automatically generating a polygon model from a three-dimensional point group that is not aligned. [3] Hugues Hoppe, Tony DeRose, Tom Duchamp, John
McDonald, and Werner Stuetzle, Surfacereconstruction
from unorganized points.In Edwin E. Catmull, edito
r, Computer Graphics (SIGGRAPH'92 Proceedings), volum
e 26, pages 71-78, July 1992] assumes a point cloud of high and constant density, captured by a measuring instrument. Marc
hing Cubes method (an algorithm that generates a boundary surface (polygon mesh that separates 0 and 1) from a set of reference points having a value of 0 or 1 existing in a grid in a three-dimensional space.
A set of eight adjacent reference points that form a rectangular parallelepiped (Ce
In ll), it is checked whether the value of each reference point is 0 or 1, and a partial polygon mesh is generated based on the pattern. By performing this operation on all cells, a polygon mesh representing the boundary surface of all reference points can be generated. [[5] William E. Lorensen and Harvey E. Cli
ne.Marching cubes: A hige resolution 3D surface con
struction algorithm.In Maureen C.Stone, editor, Comp
uter Graphics (SIGGRAPH'87 Proceedigs), volume 21, pa
ges 163-169, July 1987.], they have to extend the grid spacing to the lowest density point cloud with sparsely varying density,
A polygon mesh generated from a point cloud that cannot create an accurate mesh is subjected to various post-processing such as noise removal, feature extraction, optimization, and simplification, but a mesh with poor accuracy is disadvantageous in any of the processes. . In general, point cloud data is stored and used to supplement it even after polygon mesh generation. [[1] Matthias Eck, Tony DeRose, T
om Duchamp, Hugues Hoppe, Michael Lounsbery, and Wer
ner Stuetzle.Multiresolution analysis of arbitrar
y meshes.InRobert Cook, editor, SIGGRAPH 95 Conferen
ce Proceedings, Annual ConferenceSeries, pages 173-1
82.ACM SIGGRAPH, Addison Wesley, August 1995.held in
LosAngeles, California, 06-11 August 1995.] and
[4] Hugues Hoppe, Tony DeRose, Tom Duchamp, John Mc
Dnald, and Werner Stuetzle.Meshoptimization.In Jame
s T. Kajiya, editor, Computer Graphics (SIGGRAPH'93 Pr
oceedings), volume 27, pages 19-26, August 1993]. On the other hand, the method of Veltkamp [[7] Remco C. Veltkamp. Boundaries through sc
attered points of unknown density.Graphical Models
and Image processing, 57 (6): 441-452,1995.]
γ-neighborhood graph [[6] RCVeltkamp.The γ-n
eighborhood graph.Comput.Geom.Theory Appl., 1 (4): 22
7 -246,1992.] Can be used as all the vertices of the polygon mesh. That is,
Although accurate polygon meshes can be created from sparse point clouds, they are limited to objects with simple phases and cannot reproduce through-holes. Polygon meshes that have lost their topological structure are not very problematic visually, but have the problem that they cannot be structurally analyzed technically. As the use of three-dimensional expressions expands, the use methods other than visual use also increase, and this problem tends to increase.

A method of generating a volume model including a point cloud in a contour voxel is described in the method of Serita et al. [8] Yoichiro Serita, Daichi Watanabe, and Hiroaki Chiyokura. Automatic Model Regeneration.In 13th NICOGRAPH / MULTIMEDIA Contest Proceedings, volume 13, pages 70-79, 1997.], but the voxel size cannot be determined automatically, so the topological structure cannot be reproduced In some cases, contour voxels may be lost. Such a voxel or a polygon mesh generated by the voxel cannot be used for structural analysis or the like as a solid model reproducing an actual object. Regarding the generation of a polygon mesh from a volume model, there is the method described in [8] Serita et al., But once a polygon mesh having a vertex at an intermediate point formed on a line connecting the centers of voxels is adjusted, and then adjusted. The vertex is moved to the representative point in the voxel, and a polygon mesh having the representative point as the vertex is generated. However, at this time, the faces and ridge lines must be erased as the vertices move. Removal of faces and ridges requires complicated processing unless a system having a dedicated phase structure is constructed. For details on how to change the degree of detail of a polygon mesh while preserving its topological structure, see Hoppe et al. [[2] Hugues Hoppe. Prog
ressive meshes.In Holly Rushmeier, editor, SIGGRAPH
96 Conference Proceedings, Annual Conference Serie
s, pages 99-108.ACM SIGGRAPH, Addision Wesley, August
1996.held in New Orleans, Louisiana, 04-09 August 1
996.]. Where Progressive mesh
es is a technique for displaying a simplified mesh when displaying a detailed polygon mesh, and gradually creating a complex mesh. First, a detailed polygon mesh is decomposed into a set of a coarse mesh as a base and information (vertex division information) from the change of the detailed mesh to the coarse mesh. Next, a mesh having an arbitrary level of detail can be obtained by dividing the vertices of the coarse mesh and restoring the ridge line to the original (vertex division processing).
However, they propose a method for simplifying from a detailed polygon mesh, but a method for refining from a simple polygon mesh is realized only by following the history of simplification in reverse. Therefore, it cannot be used as a detailing method on the premise that a rough polygon mesh and points distributed on the surface of the object are given. Eck et al. [1] supra and Hoppe et al. [2] suppose that a method of obtaining an arbitrary detail polygon mesh from a point cloud is described. Make a mesh. Therefore, since a polygon mesh having an arbitrary level of detail cannot be directly generated from the point group, calculation cost is required for the pre-processing.

[0004]

SUMMARY OF THE INVENTION An object of the present invention is to solve the following seven problems. 1. When automatically generating a polygon mesh from an unaligned point cloud distributed on the surface of an object having a topological structure obtained by measuring with a measuring instrument, etc., Marching Cubes If the method is used, the accuracy becomes worse. 2. When automatically generating an accurate polygon mesh from unaligned points distributed on the surface of an object obtained by measuring with a measuring instrument, etc., the points distributed on the surface of an object with a topological structure If a γ-neighborhood graph is used, the phase structure is lost. 3. When automatically generating a volume model from unaligned point clouds distributed on the surface of an object obtained by measuring with a measuring instrument, if the voxel spacing is not set properly, the phase structure will be lost I will. 4. When automatically generating a volume model from unaligned point clouds distributed on the surface of an object obtained by measuring with a measuring instrument, contour voxels will be missing if the voxel spacing is not set properly. Would.

[0005] 5. When automatically generating a polygon mesh having a representative point in a contour voxel as a vertex from a volume model in which a three-dimensional surface is completely covered by a contour voxel, it is necessary to once generate a polygon mesh having a vertex at a center point of the voxel. 6. Generates a detailed polygon mesh from the coarse polygon mesh that has some of the unaligned points distributed on the surface of the object obtained by measurement with a measuring instrument and has the vertices as the points, and uses the remaining points in the points. In this case, it cannot be realized by the conventional method. 7. When generating a polygon mesh with an arbitrary degree of detail that has a part of the unaligned point group distributed on the surface of the object obtained by measurement with a measuring device, all points of the point group are used It is necessary to generate a detailed polygon mesh once.

[0006]

A first aspect of the present invention is a system for automatically generating a polygon mesh from an unaligned point group distributed on the surface of an object obtained by measuring with a measuring instrument or the like. A polygon generating means for generating a basic polygon mesh from the point group, and a means for refining the polygon mesh from the obtained basic polygon mesh by using all the points of the point group as vertices. A system that generates meshes.

According to a second aspect of the present invention, in the system for generating a polygon mesh according to the first aspect, the means for generating a basic polygon mesh from the point group includes: means for calculating a minimum surface density of the point group; Means for determining a voxel size from the minimum surface density, means for generating a volume model of the voxel size, means for setting grid points, and means for generating a polygon mesh from the grid points, and A system for generating a polygon mesh, comprising: means for obtaining a surface attribute relating a surface of a basic polygon mesh to the point group; and means for refining the polygon mesh by a vertex dividing operation. It is.

According to a third aspect of the present invention, in the system for generating a polygon mesh according to the second aspect, the means for obtaining the surface attribute obtains a distance between a point coordinate and the surface as an attribute of the surface. This is a system for generating a polygon mesh.

According to a fourth aspect of the present invention, there is provided a system for generating a polygon mesh according to the second or third aspect,
The means for refining the polygon mesh refines, of all the points in the point cloud, a point having the largest distance to the surface and a surface to which the point belongs to which has the smallest distance energy. This is a system for generating a polygon mesh characterized by the following.

According to a fifth aspect of the present invention, there is provided a method for automatically generating a polygon mesh from a group of unaligned points distributed on the surface of an object obtained by measuring with a measuring instrument or the like. A method of generating a polygon mesh, comprising: a step of generating a polygon mesh; and a step of refining the polygon mesh from the obtained basic polygon mesh by using all points of the point group as vertices.

According to a sixth aspect of the present invention, in the method for generating a polygon mesh according to the fifth aspect, the step of generating a basic polygon mesh from the point group includes calculating a minimum surface density of the point group. Determining a voxel size from the minimum surface density, generating a volume model of the voxel size, setting grid points and generating a polygon mesh from the grid points, and refining the polygon mesh from the basic polygon mesh The system is a system for generating a polygon mesh, comprising the steps of: obtaining a surface attribute relating a surface of a basic polygon mesh to the point group; and refining the polygon mesh by a vertex division operation.

According to a seventh aspect of the present invention, in the method of generating a polygon mesh according to the sixth aspect, the vertex dividing operation has a maximum distance to a surface among all points in a point group. A method for generating a polygon mesh, wherein the method is performed for a point and a plane to which the point belongs, with a minimum distance energy.

According to the present invention, a polygon mesh having an arbitrary level of detail is generated having a part of an unaligned point group distributed on the surface of an object obtained by measurement with a measuring machine or the like as a vertex. The method is a method of generating a polygon mesh characterized by directly generating a polygon mesh having an arbitrary level of detail without once generating a detailed polygon mesh using all points of a point group.

According to a ninth aspect of the present invention, there is provided a method for automatically generating a polygon mesh from an unaligned point group distributed on the surface of an object obtained by measuring with a measuring instrument or the like. A method for generating a polygon mesh, comprising: a step of refining the polygon mesh by an operation of setting all the points of the point group as vertices from the obtained basic polygon mesh. Is a recording medium recording a computer-readable program to be executed by the computer.

A tenth aspect of the present invention is a method for automatically generating a polygon mesh from a non-aligned point group distributed on the surface of an object obtained by measuring with a measuring instrument or the like. Calculate the surface density, determine the voxel size from the minimum surface density, generate a volume model of the voxel size, set grid points, generate a basic polygon mesh from the grid points, and obtain the obtained basic polygon mesh A recording medium storing a computer-readable program for causing a computer to execute a method including a step of determining a surface attribute relating the surface and the point group and refining a polygon mesh by a vertex dividing operation. .

As described above, according to the present invention, the following effects can be obtained. That is, in a system and method for automatically generating a polygon mesh from an unaligned point group distributed on the surface of an object obtained by measuring with a measuring instrument,
(1) An accurate polygon mesh can be generated with all the points in the point group as the vertices of the polygon. (2) The topological structure can be reproduced even in the case of an object having a topological structure such as a hole.
(3) A volume model capable of reproducing a phase structure can be generated even in the case of an object having a phase structure such as a hole. (4)
A solid model that completely covers a solid with contour voxels can be automatically generated. (5) All representative points in a contour voxel can be directly set as vertices of the polygon mesh without once generating a polygon mesh having the center point of the voxel as a vertex. (6) A detailed polygon mesh can be generated while retaining the topological structure of the coarse polygon mesh.
(7) A polygon mesh having an arbitrary level of detail can be directly generated without once generating a detailed polygon mesh using all the points of the remaining point group.

[0017]

Embodiments of the present invention will be described with reference to the drawings. In the embodiment of the present invention, regarding the point group distributed on the surface of the object obtained by measuring with a measuring instrument or the like, (1) the point group is distributed on the surface of the object.
(2) Point clouds are not aligned, that is, adjacent points are not clear in order, period, etc. (3) The density of point clouds is not constant And The present invention will be described with reference to the flowchart of FIG. First, generation of a basic mesh will be described, and then generation of a detailed mesh will be described.

1. Regarding basic mesh generation, first, a coarse basic mesh in which a topological structure is reproduced is generated. The generation of a basic mesh consists of the following steps. (A) Calculation of Minimum Surface Density of Point Group (S101) For example, the minimum surface density of the point group (5000 points) shown in FIG. 5 is calculated. With respect to a certain point p _i in the point group P = (p ₁ , p ₂ ,..., _Pn ), k neighboring points (K-neighborhood) are obtained. The K-neighborhood is obtained by acquiring k points in ascending order of the distance from a certain point. k is determined by the properties of the point cloud. A relatively small number is set for a point cloud having a constant density, and a large number is set for a point cloud having a sparse and inconsistent density. And P _nf farthest point from P _i the original point in K-neighborhood, calculates the area A _{while discs} of a circle the distance between the original point P _i and radius.

[0019]

(Equation 1)

The radius between the point P _nf and the point P _i is defined as a radius, and all points of the K-neighborhood are included in a sphere centered at the point P _i . Also, since the points are distributed on the surface of the object,
It is thought that it becomes a plane locally. Therefore, the point P
The surface density ρ at _i is

[0021]

(Equation 2)

## EQU1 ## The above calculation is performed for all points or representative points, and the minimum surface density ρ _min obtained therein is defined as the minimum surface density of the point group.

(B) Determination of Voxel Size (S102) The size L _vx of one side of the voxel is determined so as to satisfy the following condition using the minimum surface density ρ _min .

[0024]

(Equation 3)

C _α is a constant larger than 1 representing a margin. Since the size of the voxel is determined based on the minimum surface density of the point cloud, the surface of the object can be completely covered by the contour voxel. In addition, a phase structure such as a through-hole may not be reproduced when the voxel size is large. However, according to the method of the present invention, the voxel size is set to a minimum size as long as the contour voxel covering the surface does not have a defect. Therefore, all phases can be reproduced.

(C) Generation of volume model (S10
3) Generate a volume model of the voxel size determined in (b). The volume model is generated using the method [8] of Serita et al. As a result, for example, a volume model shown in FIG. 6 is generated in which voxels having attribute 1 are inside and voxels having attribute 0 are outside.

(D) Generation of Basic Mesh The grid point connection method is performed, and from the volume model, for example,
The basic mesh shown in FIG. 7 is generated. We use Marching Cubes to place the vertices of the basic mesh on the points in the point cloud.
Marching Lattice Points
Method). In this method, a polygon mesh in which the vertex coordinates adopt the point group coordinates in the point group can be directly generated without performing vertex movement, edge line deletion, and surface deletion after polygon generation. Determination of Grid Points and Values (S104) The representative points of eight adjacent voxels are applied to one Cell of Marching Cubes, and values are set to the grid points. The values of the grid points use the voxel attribute values 0 and 1 as they are. As the representative point, a point close to the center of the voxel is selected from the points included in the voxel. -Polygon generation (S105) A polygon is generated with the lattice point value being attribute value 0 outside the solid and attribute value 1 being inside the solid. There are 256 combinations of the attributes of the grid points, but if there are no combinations having the same phase due to rotation, there are 23 combinations. Among them, polygons are generated in 13 types as shown in FIG. A polygon is generated according to these.

2. Generation of Fine Mesh A fine mesh having all the points of the point group as vertices is generated from the basic mesh by the following steps. (A) Registration of Surface Attribute (S106) The point group is associated with the surface by projecting it onto the surface constituting the basic mesh, and the coordinates of the point and the distance between the surface are registered as the attribute of the surface. All points in the point cloud are attributes of any of the faces.
Regarding the point P _f having the largest distance to the surface among all the points and the surface to which the P _f belongs, that is, the surface F _f having the largest distance to the point, even if the vertex dividing operation described later is performed, Always keep and update so that the latest one can be referenced. The projection method is performed in the direction of the normal vector of the triangular surface, and points are registered on a surface that simultaneously satisfies the following conditions. (1) Triangular surface that can be projected inside (2) Triangular surface that can be projected at the shortest distance For points that cannot be projected on any surface, find the point or vertex on the ridge line that is the shortest distance from the point that cannot be projected on the surface, A vector connecting the point and the original point and a normal vector of a surface adjacent to the ridge line or the vertex are registered as attributes to a surface having the smallest angle.

(B) Refinement of Polygon Mesh by Vertex Split Operation In order to perform the refinement operation while maintaining the phase of the basic mesh, we have replaced the vertex split operation (vertex split) (see above [2]) with the forward operation. Expanded as a polygon mesh deformation function so that it can be used. The vertex split operation (vert
ex split) is an inverse operation to the edge line dividing operation (edge collapse) in the above [2] (Progressive Mesh), but is changed to the following function specification and used as a basic operation of detailing.

[0030]

(Equation 4)

Here, ↓ indicates an input argument, and ↑ indicates an output argument. V _s , V _t , V _u are vertices, F _l , F _r , F _lt , F _lu ,
F _rt and F _ru represent surfaces, and C _Vt , C _Vu and C _Vs represent coordinates, respectively, and the relationship between the elements is shown in FIG. For this vertex split operation function vsplit, V _s represents the vertex V _Ff in the plane F _f having the largest distance to the point, C _{Vt represents} the coordinates of the vertex V _Ff , and C _{Vu represents the} vertex V _Ff.
Distance between the surface to have the coordinates of the point P _f is the maximum, giving respectively. As a result, the point P _f farthest from the polygon mesh
It is a refinement of a new vertex V _n (S108).
FIG. 4 shows this state. Vertex V _Ff surface F _f to point P _f is projected exist three points. In addition, a plurality of candidates for F _lt , F _lu , F _rt , and F _ru exist _depending on a combination of surfaces around the vertex V _Ff . As described above, there are several candidates for the vertex division operation for a point, and a candidate having the minimum distance energy when the vertex division operation is performed is selected (S10).
9). Distance energy E of polygon mesh M
_dist (M) is the sum of squares of the distance between the points in the point group and the surface of the polygon mesh. Since the area where the surface that changes before and after the vertex division operation exists is limited, the energy difference calculation may be performed only for the surface within the range. The range of the surface that changes when the vertex division operation is applied is shown in the bold line in FIG. As described above, the points farthest from the polygon mesh are sequentially taken into the polygon mesh (11
0), if you continue that operation until there are no more capture points,
For example, a fine mesh shown in FIG. 8 in which all points in the point group are vertices is obtained. Further, the method for generating a polygon mesh described above can be implemented by a computer. That is, by recording a program for causing a computer to execute the method on a recording medium, the method can be easily performed on any computer.

[0032]

According to the present invention, a sparse polygon mesh having a non-uniform density and a non-uniform density distributed on the surface of an object having a phase structure obtained by measuring with a measuring instrument or the like. In the case of automatic generation, (1) a volume model with high accuracy, in which all points in the point group become vertices, which reproduces the topological structure of the original object and has no loss in contour voxels, is obtained. (2) When automatically generating a polygon mesh having a representative point in a contour voxel as a vertex from a volume model in which a three-dimensional surface is completely covered by a contour voxel, without once generating a polygon mesh having a vertex at a center point of the voxel. A polygon mesh having the representative point in the contour voxel as a vertex is obtained. (3) A part of an unaligned point cloud distributed on the surface of the object obtained by measuring with a measuring device or the like is defined as a vertex.
A detailed polygon mesh can be generated using the points of the remaining point group from the coarse polygon mesh. (4) A part of an unaligned point group distributed on the surface of the object obtained by measuring with a measuring device or the like is defined as a vertex.
When generating polygon meshes with different levels of detail using the points of the remaining point group from the coarse polygon mesh, any arbitrary polygon mesh using the points of the remaining point group without generating a detailed polygon mesh A polygon mesh with a detailed level is obtained. (5) By implementing the present invention in a three-dimensional CAD system or the like, a three-dimensional shape model can be automatically generated from a point cloud. Effects corresponding to the ninth and tenth aspects: The method for generating a polygon mesh according to the present invention can be easily implemented by an arbitrary computer.

[Brief description of the drawings]

FIG. 1 is a flowchart for explaining an automatic polygon creation process according to the present invention.

FIG. 2 is a diagram for explaining a polygon generation method in a grid point connection method.

FIG. 3 is a diagram illustrating an example of a vertex splitting operation according to the present invention.

FIG. 4 is a diagram showing an example of refinement by a vertex division operation according to the present invention.

FIG. 5 is a diagram showing a point cloud distributed on the surface of an object.

FIG. 6 is a diagram illustrating an example of a volume model according to the present invention.

FIG. 7 is a diagram showing an example of a basic mesh according to the present invention.

FIG. 8 is a diagram showing an example of a fine mesh according to the present invention.

Claims (10)

[Claims] 1. A system for automatically generating a polygon mesh from an unaligned point group distributed on the surface of an object obtained by measuring with a measuring device or the like, wherein a basic polygon mesh is generated from the point group. And a means for refining the polygon mesh from the obtained basic polygon mesh by using all the points of the point group as vertices. 2. The system for generating a polygon mesh according to claim 1, wherein said means for generating a basic polygon mesh from said point group comprises: means for calculating a minimum surface density of said point group; The means for determining a voxel size, the means for generating a volume model of the voxel size, the means for setting grid points, and the means for generating a polygon mesh from grid points, and the means for refining the polygon mesh are And a means for obtaining a surface attribute for associating the surface of the basic polygon mesh with the point group, and a means for refining the polygon mesh by a vertex dividing operation. 3. The system for generating a polygon mesh according to claim 2, wherein said means for obtaining a surface attribute obtains a distance between a coordinate of a point and a surface as an attribute of the surface. , A system that generates polygon meshes. 4. The system for generating a polygon mesh according to claim 2, wherein said means for refining said polygon mesh has a maximum distance to a surface among all points in a point cloud. A system for generating a polygon mesh characterized by refining a point and a plane to which the point belongs to which has the smallest distance energy. 5. A method for automatically generating a polygon mesh from an unaligned point group distributed on the surface of an object obtained by measuring with a measuring instrument or the like, wherein a basic polygon mesh is generated from the point group. A method for generating a polygon mesh, comprising the step of: refining a polygon mesh from the obtained basic polygon mesh by an operation of setting all points of the point group as vertices. 6. The method for generating a polygon mesh according to claim 5, wherein the step of generating a basic polygon mesh from the point group comprises calculating a minimum surface density of the point group and voxel from the minimum surface density. Determining a size, generating a volume model of the voxel size, setting grid points and generating a polygon mesh from the grid points, and refining the polygon mesh from the basic polygon mesh. A method for generating a polygon mesh, comprising: obtaining a surface attribute that associates a surface of a mesh with the point group; and refining the polygon mesh by a vertex dividing operation. 7. The method for generating a polygon mesh according to claim 6, wherein the vertex dividing operation includes, among all the points in the point group, a point having the largest distance to the surface and the point having the largest distance to the surface. A method of generating a polygon mesh, which is performed on a surface to which distance energy becomes minimum among belonging surfaces. 8. A method for generating a polygon mesh having an arbitrary degree of detail and having a vertex as a part of an unaligned point group distributed on the surface of an object obtained by measuring with a measuring machine or the like. A method for generating a polygon mesh characterized by directly generating a polygon mesh of an arbitrary level of detail without once generating a detailed polygon mesh using all the points. 9. A method for automatically generating a polygon mesh from an unaligned point group distributed on the surface of an object obtained by measuring with a measuring device or the like, wherein a basic polygon mesh is generated from the point group. And recording a computer-readable program for causing a computer to execute a method for generating a polygon mesh from the obtained basic polygon mesh, which includes the steps of refining the polygon mesh by operating all the points of the point group as vertices. Recording medium. 10. A method for automatically generating a polygon mesh from an unaligned point group distributed on the surface of an object obtained by measuring with a measuring instrument or the like, wherein a minimum surface density of the point group is calculated. Determining a voxel size from the minimum surface density, generating a volume model of the voxel size, setting grid points and generating a basic polygon mesh from the grid points, and obtaining the surface of the obtained basic polygon mesh and the points A recording medium storing a computer-readable program for causing a computer to execute a method including a step of determining a surface attribute relating a group and refining a polygon mesh by a vertex dividing operation.