JP2001184528A - Method and device for reducing number of three- dimensional shape data - Google Patents

Abstract

PROBLEM TO BE SOLVED: To efficiently reduce the number of piece of measured three- dimensional shape data by exactly managing an approximate error in a polygon mode. SOLUTION: In the three-dimensional shape data measured by a three- dimensional shape measuring instrument 1, the number of pieces of data is reduced by contracting the edge of the polygon model by assembling two or more pieces of data into one piece of data. As for all approximate planes to be deformed by edge contraction, an evaluation value operating part 321 calculates a prescribed evaluation value based on a distance between each of planes and the first data of all three-dimensional shape data related to the deformation of each of planes. When the evaluation values is a tolerance or below, edge contraction corresponding to the evaluation value is performed in edge/plane contraction processing 323. By managing the distance to the approximate plane with respect to the first three-dimensional shape data, error management can comparatively exactly and intuitively easily be comprehended.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a data reduction method for three-dimensional shape data forming a polygon model and a data reduction apparatus using the method.

[0002]

2. Description of the Related Art For example, measurement data of high drawing quality obtained by a three-dimensional shape measuring apparatus having extremely high spatial resolution has a huge number of data. There is a problem that the load on the storage device is large and the processing speed is significantly reduced.
Therefore, it is necessary to reduce the number of measurement data to reduce the above problem as much as possible. In this case, a polygon model composed of the measurement data after the data reduction (that is, an approximated polygon model) ) And the polygon model composed of the actually measured three-dimensional shape data (hereinafter referred to as the first polygon model) is too large, so that the measured data after data reduction cannot be used effectively. In the data reduction processing, it is necessary to manage an error between the approximated polygon model and the first polygon model.

In particular, in the case of three-dimensional shape data obtained by a three-dimensional shape measuring device, since the actually measured three-dimensional shape data is converted into an approximate value by a data reduction process, the first polygon model and the approximated polygon are converted. It is preferable that error management with the model is performed based on the actually measured three-dimensional shape data.

On the other hand, conventionally, various methods have been proposed for reducing the number of three-dimensional shape data constituting a triangle polygon model by approximating the triangle polygon model within a desired allowable error range. ing.

For example, in the paper "Hierarchical approximation of a three-dimensional polygon model" (Horikawa, Totsuka, Proceedings of the 5th S)
ony Research Forum, pp3-7, 1995) evaluates the contribution of each edge constituting a triangular polygon model to the model shape using an evaluation function that represents the volume that changes when the edge is removed. A method is shown in which the number of three-dimensional shape data is reduced by removing edges having a small evaluation value, such as when the surface is parallel, when the surface is small, or when the edge is short.

[0006] Also, the paper "Simplification Envelope"
s "(Cohen Jonathan, Amitabh Varshney, Dinesh Ma
nocha, Greg Turk, Hans Weber, Pankai Agarwal, F
rederick Brooks and William Wright. Proceeding
s of SIGGRAPH 96 In Computer Graphics Proce
edings, Annual Conference Series, 1996, ACM SIG
GRAPH, pp. 119-128), a model in which the first polygon model is reduced by the error ε and a model in which the first polygon model is expanded by the error ε are created. A method for reducing the number of data of the first polygon model to be included is shown.

[0007] Also, the paper "Surface Simplification U"
sing Quadric Error Metrics "(Michael Garland
and Paul S. Heckbert. Carnegie Mellon Universi
In tyProceedings of SIGGRAPH 97. 1997), for example, two or more grid points (three-dimensional shape data) constituting an edge or a surface of a triangular polygon model are aggregated into one grid point (three-dimensional shape data). As a method of reducing the number of data of the three-dimensional shape data constituting the triangular polygon model, grid points gathered by edge contraction or surface contraction and the first triangle polygon model affected by edge contraction or surface contraction are used. The degree of the distance from the plane is managed as an error in the data reduction processing, and this error is within a predetermined allowable error range. A method for reducing the amount of the waste is shown.

[0008]

Since the data reduction method described in the above-mentioned paper "Hierarchical approximation of a three-dimensional polygon model" only removes an edge by an evaluation value, the characteristic part of the polygon model is three-dimensionally reduced. Although data remains, errors in approximating the model by edge removal cannot be evaluated. Therefore, CG (Computer Graph
ics), such as VR (Virtual Reality), games, etc., is effective when simply reducing the number of polygon model data in order to simply display a three-dimensional image. This method cannot be an effective method when it is necessary to manage the error between the first measurement data and the data of the approximate model after data reduction like data.

On the other hand, the above-mentioned paper "Simplification Envelop"
The data reduction method shown in “es” allows strict error management, but it is necessary to create polygon models that have been enlarged and reduced with the error ε during the data reduction process, and hold the data of those polygon models. Therefore, there is a problem that the number of data related to the processing becomes enormous, and the load of arithmetic processing for reducing memory capacity and data is large.

In addition, the above-mentioned paper "Surface Simplification"
The data reduction method shown in `` Using Quadric Error Metrics '' manages, as an error, the degree of separation between the lattice points that make up the approximated polygon model with respect to the surface that makes up the first polygon model. This method is not necessarily appropriate when it is desired to reduce the data by managing the error of the polygon model after approximation to the lattice points constituting the first polygon model as in the measurement data.

In the case of measurement data obtained by measuring a rough surface or a cut surface of an object to be measured by a three-dimensional shape measuring apparatus, for example, the direction of the surface may suddenly change zigzag locally in a polygon model. In such a case, an error with respect to the zigzag plane is evaluated. Therefore, as the data reduction proceeds, the error is largely evaluated, and there is a problem that the data is not sufficiently reduced.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned problems, and has been made in consideration of the above-described problems. A data reduction method and a data reduction device using the data reduction method are provided.

[0013]

According to the first aspect of the present invention,
Two or more grid points are gathered into one grid point and the edge or surface of the polygon model is contracted to reduce the number of data of a plurality of three-dimensional shape data constituting the polygon model. A data reduction method, wherein for all surfaces that are deformed by contracting edges or surfaces of the polygon model, a predetermined value based on a distance between each surface and all first grid points involved in deformation of each surface. A first step of calculating an evaluation value; a second step of comparing the evaluation value with a preset allowable value; and performing the shrinkage of the edge or surface when the evaluation value is equal to or less than the allowable value. To reduce the above three-dimensional shape data
And the steps of

According to a second aspect of the present invention, a plurality of three-dimensional polygons constituting the polygon model are formed by condensing two or more lattice points into one lattice point and contracting an edge or surface of the polygon model. What is claimed is: 1. A data reduction device for three-dimensional shape data for reducing the number of coordinate data, wherein each surface and all the surfaces that are deformed by contracting edges or surfaces of the polygon model are involved in the deformation of each surface and each surface. Evaluation value calculation means for calculating a predetermined evaluation value based on the distance to all the first grid points, comparison means for comparing the evaluation value with a preset allowable value, and wherein the evaluation value is equal to or less than the allowable value. There is provided a data reduction means for reducing the three-dimensional shape data by contracting the edge or the surface.

[0015] According to the above arrangement, for all the surfaces that are deformed by contracting the edges or surfaces of the polygon model, the predetermined values based on the distance between each surface and all the first grid points involved in the deformation of each surface. Is calculated, and this evaluation value is compared with a preset allowable value. And
When the evaluation value is equal to or less than the allowable value, the edge or surface is contracted to reduce the three-dimensional shape data constituting the polygon model.

The evaluation value may be an error ε defined by the following equation (1).

[0017]

(Equation 4)

According to this configuration, the error ε defined by the equation (1) is calculated as an evaluation value for determining whether or not the edge or the surface contracts, for the edge or the surface constituting the polygon model. Is less than or equal to a predetermined allowable value, the edge or surface is contracted to reduce the number of grid points (three-dimensional shape data) forming the polygon model.

Here, the denominator in the equation (1) is, for all of the surfaces constituting the polygon model, which are deformed by edge contraction or surface contraction, the relevant surface and the first one involved in the deformation of the surface. The sum of squares of the distance to the lattice point is shown, and the numerator of the expression (1) indicates the total number of terms of the sum of squares of the distance of the denominator. Therefore, the error ε indicates an average value of the degree of separation (square of distance) indicating how far a surface subjected to deformation due to edge contraction or surface contraction is away from the first grid point involved in the deformation of the surface. I have.

According to a fifth aspect of the present invention, in the three-dimensional shape data reduction apparatus according to the fourth aspect, the evaluation value calculating means includes an error matrix for each of the lattice points v constituting the first polygon model. Kv is calculated beforehand,
When two or more lattice points v _p (p = 1, 2,...) _Are gathered into one lattice point v _q , the sum of the error matrices Kv _p of each gathered lattice point v _p is calculated as the lattice point v _{p The} error ε is calculated by the above equation (1) as the error matrix Kvq of _q .

According to the above configuration, at the time of the data reduction processing, the error matrix Kv is calculated for each of all the lattice points v constituting the first polygon model, and two or more lattice points v are obtained by the edge contraction processing or the plane contraction processing. _p (p
= 1, 2,...) _Are gathered at the lattice point v _{q of} 1
When will assemble the lattice point v _q in the next edge shrinking or surface shrinkage, error matrix of error matrix Kv _p sum that grid point v _q of each lattice point v _p that is gathered at the lattice point v _q Kv _q ( = ΣK
v _p ), and the error ε is calculated by the above equation (1) using the error matrix Kv _q .

The error matrix of the grid points after the consolidation is calculated by adding the error matrix of the first grid point, so that the calculation becomes easy. Finally, the error evaluation can be performed by associating the sum of the error matrices of the first grid points related to the edge contraction or the surface contraction for each lattice point.

According to a sixth aspect of the present invention, in the three-dimensional shape data reduction apparatus according to the fifth aspect, the evaluation value calculating means calculates a diagonal element of an error matrix calculated for each of the first grid points and Only the element above the diagonal element is stored in the storage means, and the error matrix is restored using the diagonal element stored in the storage means and the element above the diagonal element. Is used to calculate the error ε according to the above equation (1).

According to the above configuration, the error matrix calculated for each of the first lattice points is a symmetric matrix, and the diagonal element of the error matrix and the element above the diagonal element are stored, so that the memory can be reduced. To contribute.

According to a seventh aspect of the present invention, in the three-dimensional shape data reduction device according to the fourth aspect, the evaluation value calculating means determines that a column vector V of the first three-dimensional shape data of the grid point is as follows: When expressed by equation (2), the total number of equations (1) is calculated by adding the elements at the lower right corner of the error matrix ΣKv _j (j = 1, 2,..., M _i ) calculated for each plane p _i. Σm
_i (i = 1, 2,..., n).

[0026]

(Equation 5)

According to the above configuration, when the intense vector V of the three-dimensional shape data of the lattice point v is represented by the equation (2), the error matrix Kv of the lattice point v is represented by the following equation (A). ,
The element in the lower right corner is always "1". Therefore, since the total number of ShigumaKv _j is the sum of the elements in the lower right corner of each error matrix Kv _j, there is no need to calculate the sum separately by calculating it.

[0028]

(Equation 6)

Further, an invention according to claim 8, in data reduction unit of the three-dimensional shape data according to claim 4, wherein said evaluation value calculating means, weighted in place of the error matrix Kv _j of the lattice point v _j The error ε is calculated by the above equation (1) using the error matrix w _j · Kv _j .

According to the above configuration, the error ε is determined by the lattice point v _j
Is calculated by the above equation (1) using a weighted error matrix w _j · Kv _j instead of the error matrix Kv _j .

[0031]

FIG. 1 is a block diagram of a processing system for three-dimensional shape measurement data to which a data reduction method according to the present invention is applied.

A processing system for three-dimensional shape measurement data (hereinafter, referred to as a shape data processing system) shown in FIG.
The three-dimensional shape measuring device 1 for measuring the three-dimensional shape data of the object G, the external storage device 2 for storing the three-dimensional shape data measured by the three-dimensional shape measuring device 1, and the three-dimensional shape measuring device 1 Shape data processing device 3 for reducing predetermined three-dimensional shape data using the data reduction method according to the present invention and performing predetermined data processing, and an external storage device for storing the three-dimensional shape data processed by the shape data processing device 3 4. Using the three-dimensional shape data after the data reduction, a display device 5 for displaying a three-dimensional shape image of the measurement object G such as a polygon model and the three-dimensional shape data processed by the shape data processing device 3 are used. CAD / CAM (computer aided des)
ign and computer aided manufacturing).

The three-dimensional shape measuring apparatus 1 measures the surface shape of the measuring object G using a conjugate autofocus system. As shown in FIG. 2, the three-dimensional shape measuring apparatus 1 includes an illumination unit 101 that generates illumination light, an illumination unit 101.
The illumination light reflected from the measurement object G is irradiated onto the measurement object G, and the illumination light reflected from the measurement object G is guided to the light receiving unit 103. A light receiving unit 103 that photoelectrically converts the signal into a signal and outputs the signal. A beam that splits the reflected light from the measurement target G that has passed through the confocal optical system 102 (hereinafter, referred to as the optical system 102) and guides the reflected light to the light receiving unit 103. It has a basic configuration including a calculation unit 105 that calculates the position coordinates of the surface of the measurement object G using the light reception signal output from the splitter 104 and the light reception unit 103.

The three-dimensional shape of the measuring object G is set on a measuring table 106 disposed in front of the three-dimensional shape device 1 and the measuring table 106 is placed at a predetermined pitch in the height direction. The measurement is performed by measuring the unevenness of the surface of the measurement object G at each height position while moving up and down. That is, the height direction of the measurement object G is set in the Y direction,
Assuming that the optical axis direction 2 is the Z direction, the Y direction, and the direction orthogonal to the Z direction is the X direction, the Y coordinate of the measurement object G is changed at a predetermined pitch while the measurement object G is positioned at each Y coordinate. The three-dimensional shape of the measurement object G is measured by measuring the Z coordinate of. Then, the three-dimensional shape data (x, y, z) of the measurement target G measured by the three-dimensional shape measuring device 1 is input to the shape data processing device 3.

The three-dimensional measuring apparatus 1 includes a photoelectric conversion element 103a composed of a line sensor arranged parallel to the X axis, and for each pixel of the photoelectric conversion element 103a (each pixel position corresponds to the X coordinate). The position coordinates (Z coordinate) of the surface of the measuring object G are measured using the light receiving signal. Therefore, the illumination unit 101 emits slit-shaped illumination light extending in the X direction so that the reflected light from the measurement target G is incident on the entire photoelectric conversion element 103a.

The Z coordinate of the measuring object G is measured as follows. First, a slit-shaped illumination light extending in the X direction is emitted from the illumination unit 101 disposed at the focal position on the image side of the optical system 102. The illumination light is condensed at a focus position on the object side of the optical system 102, and a line light extending in the X direction is formed at the focus position. Next, in this state, the object-side focal position of the optical system 102 (that is, line light) is moved in the optical axis direction until the focal position reaches the inside of the measurement object G, and the photoelectric conversion element is moved at a predetermined cycle. The exposure of 103a is repeated. Then, using the level of the light-receiving signal received at each exposure position, the calculation unit 105 calculates the exposure position having the maximum level for each pixel of the photoelectric conversion element 103a, and calculates the position on the surface of the measurement object G. Let it be the Z coordinate.

The shape data processing device 3 includes a polygon generation unit 31, a data reduction unit 32, an allowable value input unit 33, and a data output unit 34. The polygon generation unit 31 generates a polygon model of the measurement target G based on the three-dimensional shape data (x, y, z) of the measurement target G input from the three-dimensional shape measurement device 1. The data reduction unit 32 reduces three-dimensional shape data by contracting edges or surfaces of the polygon model. That is, FIG.
As shown in (1), the number of grid points (three-dimensional shape data) of the polygon model A is appropriately reduced so that the precise polygon model A based on the measurement data is approximated to the polygon model B within a predetermined allowable error range. It is.

The data reduction section 32 includes an evaluation value calculation section 321, an evaluation value sorting section 322, and an edge / plane contraction processing section 323 in order to execute a data reduction process described later.

The evaluation value calculation unit 321 shrinks the edges or faces constituting the polygon model by collecting two or more grid points and replacing them with one grid point (ie,
In order to approximate the polygon model), an evaluation value for determining whether or not each edge or each surface is contracted is calculated. This evaluation value will be described later.

The evaluation value sorting unit 322 includes the evaluation value calculation unit 32
The minimum evaluation value is calculated by rearranging a plurality of evaluation values calculated for each edge or each surface in ascending or descending order in step 1. The edge / surface contraction processing unit 323 compares the minimum evaluation value calculated by the evaluation value sorting unit 322 with the allowable value input from the allowable value input unit 33, and when the value is equal to or smaller than the allowable value, the edge / surface contraction processing unit 323 corresponds to the minimum evaluation value. The edge or surface is contracted. The evaluation value and the edge contraction method will be described later.

The allowable value input section 33 is for the operator to input an allowable value for determining whether or not edge contraction or surface contraction is possible. This allowable value corresponds to an allowable range in which, even when edge contraction or surface contraction is performed, the influence on the characteristic portion of the polygon model is small when approximating the polygon model. It is input as appropriate.

The data output unit 34 outputs the reduced three-dimensional shape data (three-dimensional shape data constituting the approximated polygon model) to the external storage device 4, the display device 5,
An interface for outputting to the external processing device 6.

The external storage device 4 records data on an external recording medium such as a magnetic disk, an optical disk, or a magnetic optical disk. When three-dimensional shape data is input from the shape data processing device 3, the external storage device 4 stores the data in a predetermined file format. Record on a recording medium.

The display device 5 is a display device including an electronic display device such as a cathode ray tube and a liquid crystal display device.
When the three-dimensional shape data is input from the shape data processing device 3 to the display device 5, an image of the polygon model of the measuring object G approximated based on the data is displayed (the polygon model B in FIG. reference).

The external processing device 6 is, for example, a device for producing a mold or a model having substantially the same shape as the surface shape of the measuring object G. When the three-dimensional shape data is input from the shape data processing device 3 to the external processing device 6, the workpiece is cut based on the three-dimensional shape data, and a mold or the like is automatically manufactured.

Next, a data reduction method according to the present invention will be described.

FIG. 4 is a conceptual diagram of a data reduction method by edge contraction. FIG. 5 is a conceptual diagram of a data reduction method by surface contraction.

FIG. 4 shows a data reduction method based on edge contraction.
If the polygon model as shown in is composed of grid points v ₁ to v _10, for example, grid point v ₁ and both the lattice point v ₁ to contract the edges Ed ₁₂ connecting the lattice points v _2, v ₂ Are gathered at the grid point v ₁ ′ to reduce the number of data.

Data reduction method by edge shrinkage (hereinafter referred to as
Abbreviated as the edge shrinkage method. ), First, for all edges Ed _ij (i, j = 1, 2,... 10, where i ≠ j is a combination of lattice points adjacent to each other), the influence of the edge contraction on the shape change of the polygon model is described. calculating an evaluation value for evaluating the minimum of the evaluation grid points at both ends of the edge Ed _ij which value corresponds to the evaluation value is equal to or less than the allowable value v _i, v _j
Are collected at a predetermined grid point v _i ′ to reduce data.

Next, gather the polygon model grid points v _i, the v _j to the lattice point v _i '(approximated polygon model)
Is performed in a similar manner, and the data is further reduced. Then, in the same manner, the edge contraction is performed on the polygon model after the edge contraction one by one until the edge contraction becomes impossible (that is, the approximation of the polygon model is repeated until the minimum evaluation value becomes larger than the allowable value). ), Data reduction is performed.

It should be noted that the grid point v _i ′ corresponds to the above-mentioned article “3.
As shown in "Hierarchical approximation of three-dimensional polygon model",
For example the grid points of the middle point or the like of the edge Ed _ij v _i, an approximation point set in place between v _j.

[0052] surface shrinkage data reduction method (hereinafter, abbreviated as a surface contraction method.) By, when the polygon model as shown in FIG. 5 is constituted by a lattice point v ₁ to v _11, for example, lattice point v ₁ is a method to reduce the number of data grid points v _1, v _2, v ₃ is gathered at the lattice point v ₁ 'to remove surface P ₁₂₃ surrounded by the grid points v ₂ and the lattice point v ₃ .

The data reduction method based on surface contraction is basically performed in the same procedure as the data reduction method based on edge contraction. That is, first, all the surfaces P _ijk (i, j, k =
1,2, ... 10. However, an evaluation value for evaluating the influence of the surface shrinkage on the shape change of the polygon model is calculated for a combination (i ≠ j ≠ k where the lattice points are adjacent to each other), and when the minimum evaluation value is equal to or smaller than the allowable value. lattice point v _i constituting the surface P _ijk corresponding to the evaluation value, v _j, v _k a reduction of gathered data in a predetermined grid point v _i 'is carried out, the same method after the surface shrinkage below Data is reduced by performing surface contraction one by one until the surface contraction of the polygon model becomes impossible.

When the three-dimensional shape data is sequentially reduced by the edge shrinkage method or the surface shrinkage method, the three-dimensional shape data constituting the DUT after the data reduction processing is the measured data actually measured by the three-dimensional shape measuring apparatus 1. Unlike the three-dimensional shape data of the object G, the three-dimensional shape data is approximated. For this reason, an error of a polygon model (hereinafter, referred to as an approximated polygon model) after data reduction with respect to a polygon model (hereinafter, referred to as an initial polygon model) composed of actually measured three-dimensional shape data is managed. It is necessary to perform data reduction processing.

In the data reduction method according to the present embodiment, for example, edge contraction is repeated, and, for example, as shown in FIG. 6, grid points a, b, and c (actually measured three-dimensional shape data) are changed to grid points a ′, _Assuming that the triangle polygon P _abc is approximated to b ′ and c ′ and the triangular polygon P _abc ′ is approximated to the triangular polygon P _abc ′, the surface including the approximated triangular polygon P _abc ′ is the first grid point involved in the approximation processing of this surface. The degree of separation from a, b, and c is managed as an error.

In the example of FIG. 6, for convenience of explanation, the lattice points involved in the approximation processing are lattice points a, b, and c. However, in the actual processing, for example, the lattice point a is gathered at the lattice point a ′. During the process, grid points other than the grid point a (measured data) are included, and thus the above-mentioned error includes the distance between these grid points and the triangular polygon P _abc ′.

Next, an error evaluation value applied to the data reduction method according to the present embodiment will be described.

Generally, the plane p in the three-dimensional space is represented by the following equation: A × x + By + Cz + D = 0 (3) where A ² + B ² + C ² = 1.

On the other hand, if the coordinates of the point v in the three-dimensional space are (v _x , v _y , v _z ), the distance d between the point v and the plane p is
Is calculated by d = A · v _x + B · v _y + C · v _z + D (4).
It looks like an expression.

[0060]

(Equation 7)

Accordingly, the square of the distance d is expressed by the following equation (6).

[0062]

(Equation 8)

The above equation (6) shows the square of the distance d between one plane p and one point v not included in this plane p. v ₁ , v ₂ , ... v _m
, The sum of squares Δ (p) of the distances to these points v _i (i = 1, 2,... M) is expressed by the following equation (7).

[0064]

(Equation 9)

In the data reduction method according to the present embodiment, for example, when data reduction is performed by edge contraction, when there are n polygon models that are affected by contraction of an edge, and when all the planes are Since the distance between each plane and a plurality of initial grid points (original three-dimensional shape data) involved in the data reduction processing for approximating the plane is evaluated, each plane is evaluated. The sum of squares Δ (p) of the distances calculated by the above equation (7) is calculated for each plane, and the sum of these is divided by the total number M of all grid points involved in the data reduction processing. Ε shown in the equation is used as the evaluation value of the error.

[0066]

(Equation 10)

In the above equation (8), Δ (p _i )
Is the sum of squares of distances between all of the first grid point that contributed to the approximation of the plane p _i for the i-th plane p _i, m
_i is the number of terms in the sum of squares of the distance.

[0068] Further, in the calculation process of equation (8) is a matrix Kv _i because a symmetrical matrix as shown in equation (6), matrix matrix Kv _i calculated for the first grid point v _i It is preferable to store a diagonal element and an element above the diagonal element in a memory. By doing so, the memory capacity required for the arithmetic processing can be reduced. Further, equation (8) Although the elements m _i of the molecule is the number of terms of the sum of the squares of the distance in the i-th approximate surface p _i,
The elements in the lower-right corner of the matrix Kv is always "1", since the elements in the lower-right corner of the matrix ΣKv in the square sum of the calculation results of the distance is m _i, the using the value of this element (8 )
It is preferable to perform the operation of the expression. If you do this,
There is no need to re-calculate the number of terms m _i, processing becomes easy.

When the above equation (7) is applied to the evaluation of an error with respect to a certain plane p, the first grid point v involved in the process of edge contraction or plane contraction to the plane p is processed.
If _i is specified, ShigumaKv _i obtained by adding the matrix Kv _i obtained from the three-dimensional shape data of those grid points v _i is the parameter indicating the degree of error in the edge shrinkage or surface shrinkage. Therefore, in the following description referred to the ShigumaKv _i and error matrix.

Next, the procedure of the data reduction processing of the three-dimensional shape data will be described with reference to the flowchart of FIG.

The three-dimensional shape data of the measuring object G captured by the three-dimensional shape measuring device 1 is input to the shape data processing device 3, and first, a polygon model of a triangle is generated by the polygon generating unit 31 (#). 1). Further, the operator inputs an allowable value from the allowable value input unit 33 for determining whether or not the edge contraction processing is possible (# 3).

Subsequently, the evaluation value ε _j (j = 1, 2,..., N, N is the total number of edges) when all edges of the first polygon model are contracted by the evaluation value calculation unit 321 is calculated by the above equation (8). (# 5). For example, in the example of FIG. 4, the edges Ed _1r (r = 2 to 5, 9, 10), Ed
_2s (s = 5, 6,... 9), Ed _{tt + 1} (t = 3, 4 _,.
0, where t + 1 = 11 is set to t + 1 = 3. ), The evaluation value ε _j (j = 1, 2,.
9) is calculated.

At this time, for example, when the grid points v ₁ and v ₂ are gathered at the grid point v ₁ ′ and the edge Ed ₁₂ is contracted, the first surface is all deformed, and the relation between the grid point v ₁ ′ and the edge contraction is obtained. not flat surface p ₁ of eight by the lattice point v ₃ ~v _10, p _2,
... p ₁₀ (hereinafter. Referred approximate surface plane after deformation) but are formed, these approximate surface _{p k (k = 1,2, ...} 8) each square sum of distances Δ for (p _k) (K = 1, 2,
.. 8) are calculated and the sum of squares of these distances Δ
Total number M of (p _k) elements contained in the whole is calculated, the (8) the evaluation value in the shrinking of the edge Ed ₁₂ by equation epsilon (Ed ₁₂₎ is calculated. The evaluation value ε (Ed ₁₂ )
Is given by the following equation (9).

[0074]

[Equation 11]

At this time, for example, the plane p₁Is the grid point v₁’,
v_Three, V_FourIs composed of₁, V_Two,
v_Three, V_FourIs related to edge contraction when
The lattice point is v₁, V_Two, The sum of squares of the distances Δ
(P₁) Indicates these lattice points v₁, V_TwoError matrix for
(Kv₁+ Kv_Two) Is calculated by the above equation (7).
You. In this state, the grid point v₁’Is another grid point v_m(Shown
Not measured data) and grid point v₁”(Shown
) And the approximate surface p₁Is the approximate surface p₁’(Shown
), This approximation plane p₁’
The grid points involved in the edge contraction are v₁, V_Two, V_mWill be
From the sum of squares of distance Δ (p₁′) Indicates that these grid points v ₁, V
_Two, V_mError matrix (Kv₁+ Kv_Two+ Kv_m)
And is calculated by the above equation (7).

[0076] In this second edge shrinkage, substantially the 'error matrix Kv _1' lattice point _{v 1 (Kv 1 + Kv 2} ) as lattice points v ₁ and the lattice point v _m 'error matrix Kv ₁ of' With the error matrix Kv _m , the sum of squares of the distance Δ (p ₁ ′) according to the above equation (7)
Is calculated.

Therefore, in the process of the edge contraction processing,
In general terms, in FIG. ₁, V_Two, V_Three, V_FourTo
Data generated by edge shrinkage, not measured data
, Each grid point v₁, V_Two, V_Three, V_FourAgainst
Kv₁, Kv_Two, Kv_Three, Kv_FourToss
Then the approximate surface p₁Lattice point v₁’
Column Kv₁’To Kv₁’= Kv₁+ Kv_TwoAnd the approximate surface p₁To
Three grid points v₁’, V_Three, V_FourError matrix K
v₁’, Kv_Three, Kv_FourError matrix K obtained by adding_p1
(= Kv₁'+ Kv_Three+ Kv_Four= Kv₁+ Kv_Two+ Kv_Three+ K
v_Four) And the approximate surface p by the above equation (7).₁About distance
Sum of squares of separation Δ (p₁) Is calculated.

The formula for calculating the sum of squares of distance Δ (p ₁ ) is as follows: Δ (p ₁ ) = P ₁ ^T · K _p1 · P ₁ (10) Here, P ₁ is a column vector notation of the approximate plane p ₁ , m
₁ is the total number of error matrices Kv included in the error matrix K _p1 .

[0079] Then, approximate surface p _2, p _3, ... ₂ sum of squares of distances in the same manner as in approximate surface p ₁ described above also p ₈ delta
(P ₂ ), Δ (p ₃ ),..., Δ (p ₈ ) are calculated, and these are substituted into the above equation (9) to calculate an error evaluation value ε (Ed ₁₂ ) in contraction of the edge Ed _12. .

Then, the other edges Ed _1r ,
Error evaluation values ε (Ed _1r ), ε (Ed _2s ), and ε (Ed _{tt + 1} ) when Ed _2s and Ed _{tt + 1} are also subjected to edge contraction.
Is calculated.

Subsequently, sorting of the error evaluation values ε _j is performed by the evaluation value sorting unit 322 (# 7), and whether the minimum evaluation value Min {ε _j } is equal to or smaller than the allowable value input in step # 3. It is determined whether or not it is (# 9). Minimum evaluation value Min
If {ε _j } is larger than the permissible value (NO in # 9), the shape change when all the edges are contracted is unacceptably large, and the data reduction process by edge contraction is terminated. On the other hand, if the minimum evaluation value Min {ε _j } is equal to or smaller than the allowable value (YES in # 9), the edge / surface contraction processing unit 323 performs the contraction processing of the edge corresponding to the minimum evaluation value Min {ε _j }. (# 11). For example, in FIG. 4, if the minimum evaluation value Min {ε _j } is ε (Ed ₁₂ ), the contraction processing of the edge Ed ₁₂ is performed as shown in FIG.

Subsequently, after the error evaluation value ε _q (q = 1, 2,...) Is calculated again for the edge affected by the edge contraction processing on the polygon model after the edge contraction (# 13), Returning to step # 7, the minimum error evaluation value Min {ε _q } among these error evaluation values ε _q is calculated, and the corresponding edge contraction processing is performed (#
7 to # 11). Thereafter, the edge contraction processing is repeated one by one (loop of # 7 to # 13), and the minimum evaluation value Min
When {ε _q } becomes larger than the allowable value, the data reduction processing ends (NO in # 9).

Therefore, by performing such data reduction processing, the polygon model after data reduction is approximated to the first polygon model such that the error evaluation value ε for the first measurement data is equal to or smaller than the allowable value. Is done.

As described above, in the data reduction method according to the present embodiment, the surface of the polygon model approximated by edge contraction or surface contraction is determined with respect to the first lattice point (measured three-dimensional shape data). Since the degree of deviation is set as the evaluation value of the error, the data reduction processing can be performed in an intuitively easy-to-understand evaluation standard.

Further, since the data is reduced so that the evaluation value falls within a predetermined allowable error range, the error of the three-dimensional shape data constituting the approximated polygon model can be managed relatively accurately. In addition, the data reduction processing can be performed at high speed.

In particular, even when random noise data is mixed into the measured three-dimensional shape data, or when a large number of grid points are collected into one point to reduce the data, the reliability of the error evaluation value is reduced. Can be suppressed.

FIGS. 8 and 9 show a comparison of the error evaluation method in the case where random noise data is mixed with the measured three-dimensional shape data with the conventional error evaluation method.

FIG. 8 shows a case where random noise data is used.
Where the polygon model has a discontinuous surface
it's shown. FIG. 7) is a diagram showing edge contraction. In the figure
As shown, the discontinuity of the polygon model surface
Lattice point v ₁, V_TwoTo the lattice point v at the approximate center
₁’, The previous paper“ Surface Simpli
fication Using Quadric Error Metrics "
In the data reduction method, as shown in FIG.₁’
From the grid point v₁, V_FourPlane p containing₁₄And grid points
v_Two, V_FivePlane p containing_{twenty five}Distance d to₁’, D_Two’
Error, because of the perceptual approximation error
While the evaluation value is calculated for the smaller eye,
In such a data reduction method, for example, a grid point v₁, V_Twofrom
Grid point v₁’, V_Four, V_FivePlane p containing₄₅Distance d to₁, D
_TwoIs used as the basis for error evaluation, so the error
Is relatively consistent with the approximate
And not.

FIGS. 10, 11 and 12 show a comparison of the error evaluation method when a large number of grid points are gathered into one point with the conventional error evaluation method.

FIG. 10 shows eight grid points v₁, V_Two, ... v₈
And a zigzag surface (shown in cross section) is formed
Figure showing the contraction of the zigzag surface of the polygon model
is there. As shown in FIG.₁, V_Two, ... v₆Case
Child point v₇, V₈The lattice point v at the approximate center of₁’
The above-mentioned conventional paper `` Surface Simplification Using Qua
dric Error Metrics ”
Is the grid point v as shown in FIG.₁’First polygo
The zigzag faces p of the model₇₁, P₁₂, P_{twenty three}, P_{Three Four}, P
₄₅, P₅₆, P₆₈Distance d to₁’, D_Two’,… D₆’Error
Because it is the basis of the evaluation,
The evaluation value of the error is calculated to be larger,
In the data reduction method according to the embodiment, for example, each grid point v₁,
v_Two, ... v₆Grid point v from₁’, V₇, V₈Plane p containing
₇₈Distance d to₁, D_Two, ... d₆Is used as the basis for error evaluation.
Therefore, the error evaluation value relatively matches the intuitive approximation error
However, it is not calculated to the larger eye.

FIG. 13 is a flowchart showing a modification of the data reduction processing procedure for three-dimensional shape data.

In the data reduction processing procedure shown in FIG. 7, every time the edge contraction processing is performed, the evaluation value ε is calculated again for the edge affected by the edge contraction, and the next edge contraction is performed based on the evaluation value ε. Although the processing was performed, the data reduction processing procedure shown in FIG. 13 does not calculate the evaluation value ε for the edge affected by the edge contraction, but performs the edge contraction for the other edges. Things.

More specifically, the flowchart shown in FIG. 13 is different from FIG. 7 in that the processing of step # 13 is changed to step # 13 'of "prohibit contraction of edge affected by edge contraction". The processing of steps # 15 and # 17 is added between the processing of step # 9 and the processing of "end".

Therefore, in the following description, common parts of the flowchart will be briefly described, and different parts will be described in detail.

The three-dimensional shape data of the measuring object G captured by the three-dimensional shape measuring device 1 is input to the shape data processing device 3, and the polygon generating unit 31 generates a triangular polygon model (# 1). . Further, the operator inputs an allowable value from the allowable value input unit 33 for determining whether or not the edge contraction processing is possible (# 3).

Subsequently, the evaluation value ε when the edge is contracted for all edges of the polygon model by the evaluation value calculation unit 321
_j (j = 1, 2,..., N is the total number of edges) is calculated (# 5), and the evaluation value sorting unit 322 sorts the error evaluation values ε _j to obtain the minimum evaluation value Min {ε _j }. Is calculated (# 7).

Subsequently, it is determined in step # 3 whether or not the minimum evaluation value Min {ε _j } is equal to or less than the allowable value (#
9) If the minimum evaluation value Min {ε _j } is equal to or smaller than the allowable value (YES in # 9), the edge / surface contraction processing unit 323 performs the contraction processing of the edge corresponding to the minimum evaluation value Min {ε _j }. This is performed (# 11).

Subsequently, the contraction processing of the edge affected by the edge contraction processing is prohibited (# 13 '), and the process returns to step # 7. This processing is for performing the next edge contraction processing on an edge that is not affected by the current edge contraction processing.

Returning to step # 7, the evaluation value ε _q (q = q
1, 2, ... Q. However, sorting is performed for Q <N), and the minimum evaluation value Min {ε _q } is calculated (#
7). Then, it is determined whether or not the minimum evaluation value Min {ε _q } is equal to or less than the allowable value (# 9), and the minimum evaluation value Min
If {ε _q } is equal to or less than the allowable value (YES in # 9), the edge / surface contraction processing unit 323 sets the minimum evaluation value Min
The contraction processing of the edge corresponding to {ε _q } is performed (# 1
1) Further, the contraction processing of the edge affected by the edge contraction processing is prohibited (# 13 '), and step # 7 is performed again.
Return to

Thereafter, the same processing is repeated, and every time the edge contraction processing is performed, the next edge processing is performed while excluding the edge affected by the edge contraction (# 7, # 9, # 11). , # 13 'lube).

On the other hand, if the minimum evaluation value Min {ε _q } is larger than the allowable value in the process of repeating the above-mentioned edge contraction processing (NO in # 9), it is determined whether or not there is an edge for which edge contraction is prohibited. (# 15), and if there are any edges for which edge contraction is prohibited (YES in # 15), the error evaluation value ε _r (r = 1, 2,...) Is calculated again for those edges (# 15). 17), returning to step # 7, among these error evaluation values ε _r , the minimum error evaluation value Min {ε _r } is calculated, and the contraction processing of the edge corresponding to the minimum error evaluation value Min {ε _r } is performed. (# 7, # 9, # 11).

Then, the above-mentioned edge contraction processing is repeated,
When the minimum evaluation value Min {ε _q } becomes larger than the allowable value and there are no edges for which edge contraction has been prohibited (NO in # 9 and # 15), the data reduction processing by edge contraction is terminated.

FIG. 14 is a diagram showing an example of a data reduction process according to the processing procedure shown in FIG.

In the figure, the polygon model M ₀ is the first polygon model. This polygon model M ₀ is 2
Eight lattice points _{v 1, v 2, ... v} 28 the number of each row (3,
4, 5, 4, 5, 4, 3) are arranged in five rows, and adjacent grid points are connected.

Edges e1, e2, e3, e4 and e5 are
When each edge ei (i = 1, 2,... 5) is contracted,
Since they are not affected by each other, for convenience of explanation, they are sequentially selected as being subjected to edge contraction by the processing procedure shown in FIG.

Therefore, the data reduction process of FIG.
13 shows a case where the polygon model M ₀ is sequentially subjected to edge contraction in the order of the edges e1, e2,... E5 according to the processing procedure of FIG. Then, the polygon models M ₁ , M ₂ ,
M ₃ , M ₄ , and M ₅ define the polygon model M ₀ as edges e 1, e
This is an approximated polygon model when contraction processing is performed in the order of 2,... E5.

[0107] According to the data reduction procedure shown in FIG. 13 described above, first, when an edge e1 is approximated is contracted to the polygon model M ₁ at the first edge shrinking, and centralized grid points v _a Grid points v ₉ , v
_{10, v 11, v 13,} v 16, v 18, v 19, v 20 for a de edge formed (lattice points in the dotted frame polygon model M ₁₎ will be affected, the next edge In the contraction processing, the evaluation value ε _q is sorted again for edges excluding these edges (edges outside the dotted frame of the polygon model M ₁ ), and the minimum evaluation value Min
Edge shrinking process is approximated to a polygon model M ₂ is performed for the edge e2 having {ε _q}.

Further, in the next edge contraction processing, the collected grid points v _b and the grid points v ₁ , v ₂ ,
v ₄ , v ₆ , v ₈ , v ₁₀ , v ₁₃ , v _a (polygon model M ₂
For lattice points) and de edge formed in the dotted line frame will be affected, again for these edges excluding the edges (edges outside the dotted frame of the polygon model M _2), evaluation value ε _s sorting is performed, the edge e3 having the minimum evaluation value Min {epsilon _s} edge shrinkage process is approximated to a polygon model M ₃ is performed.

Then, edges e4 and e
5 also the edge shrinkage is performed for the first polygon model M ₀ This five edge shrinking process is approximated to a polygon model M _5, the number of data is reduced to five.

Considering the process of approximating the first polygon model M ₀ to the sixth polygon model M ₆ (not shown), the processing procedure shown in FIG. does not recalculate the evaluation value, in the example of FIG. 14, the first polygon model M ₀
When the evaluation value is calculated first for the 66 edges constituting the polygon model M ₁ , the evaluation value is not recalculated for the approximated polygon models M _{1 to} M ₄ , and the polygon model M ₅ is used for the next recalculation. This is performed for the 50 edges that make up. Therefore, the sixth polygon model M ₆
The number of recalculations of the evaluation value up to is 50.

On the other hand, in the processing procedure shown in FIG. 7, since the evaluation value is recalculated for the edge affected by the edge contraction, each of the approximated polygon models M ₁ to M _{1 is obtained} .
About 16 of the edge affected by the edge shrinkage every M ₅ will recalculate evaluation values. Therefore,
In the processing procedure shown in FIG. 7, the sixth polygon model M ₆
The number of recalculations of the evaluation value up to is 16 × 5 = 80 times,
The processing procedure shown in FIG. 13 has the advantage that the number of recalculations of evaluation values is reduced and high-speed processing is possible.

FIG. 15 is a modification of the flowchart shown in FIG.

The flowchart shown in FIG. 15 is based on the fact that the evaluation value of the affected edge after the edge contraction is replaced with a predetermined evaluation value ε _max larger than the allowable value, so that the next edge contraction substantially replaces the edge. It is designed to be excluded from contraction.

More specifically, in the flowchart of FIG. 13, step # 13 'is changed to "step # 13 of the process of setting the evaluation value of the edge affected by edge contraction to ε _max ", and A step of changing the determination target of # 15 and the target of recalculation of the evaluation value of step # 17 to "an edge having an evaluation value of ε _max ", and performing an edge contraction process on the edge after the recalculation of the evaluation value after step # 17 ' The processing of # 19 and # 21 is added.

Therefore, in the following description, portions different from the flowchart of FIG. 13 will be described in detail.

In step # 11, the edge / surface contraction processing unit 3
When the contraction processing of the edge corresponding to the minimum evaluation value Min {ε _j } is performed by 23, the evaluation value of the edge affected by the edge contraction processing is set to a predetermined evaluation value ε _max larger than the allowable value. (# 13 ″), the process returns to step # 7. This processing makes these edges out of the target in the next edge contraction processing, that is, only the edges that are not affected by the edge contraction processing. Is to be performed.

Returning to step # 7, the evaluation value ε _i again
(I = 1, 2,..., N−1) is performed, and the minimum evaluation value Min {ε _i } is calculated (# 7). Then, the minimum evaluation value Min {ε _i} is determined whether or not less than the allowable value (# 9), if the minimum evaluation value Min {ε _i} is less than the allowable value (YES at # 9), the edge The surface contraction processing unit 323 performs the contraction processing of the edge corresponding to the minimum evaluation value Min {ε _i } (# 11).

Subsequently, the evaluation value of the edge affected by the edge contraction processing is set to the evaluation value ε _max (# 1)
3 "), and returns to step # 7. The same process is repeated, and every time the edge contraction process is performed, the next evaluation value is set while setting the evaluation value of the edge affected by the edge contraction to the evaluation value ε _max . Edge processing is performed (# 7, # 9, #
11, # 13 "lube).

On the other hand, if the minimum evaluation value Min {ε _i } is larger than the allowable value in the process of repeating the edge contraction processing (NO in # 9), it is determined whether or not there is an edge having the evaluation value ε _max. (# 15 '), and if there are edges having the evaluation value ε _max (YES in # 15'), the error evaluation values ε _s (s = 1, 2,...) Are calculated again for those edges (s = 1, 2,...) # 17 ').

Then, the minimum error evaluation value Min {ε _s } among these error evaluation values ε _s is calculated by sorting (# 19), and if the minimum evaluation value Min {ε _i } is not more than the allowable value. If (YES in # 21), step # 11
Then, the contraction processing of the edge corresponding to the minimum evaluation value Min {ε _i } described above is performed.

On the other hand, the above-mentioned edge contraction processing is repeated to determine whether there is no edge having the evaluation value ε _max (Y in # 15 ′).
ES) or the minimum evaluation value Min of the evaluation values ε _s recalculated for the edge having the evaluation value ε _max
When {ε _s } becomes larger than the allowable value (N in # 21, N
O), the data reduction process due to the edge contraction ends.

The processing procedure shown in FIG. 15 also sets the evaluation value of an edge affected by edge contraction to an evaluation value ε _max larger than the allowable value, thereby substantially reducing the edge shown in the processing procedure of FIG. Is prohibited, the number of recalculations of the evaluation value is reduced, and high-speed processing can be performed.

In the data reduction processing procedure shown in FIGS. 13 and 15, recalculation of the evaluation value is performed on the part affected by the edge contraction processing until all the parts for which the edge contraction processing is prohibited are gone. However, the edge contraction process is excluded from the target, but, for example, when the edge contraction process is repeated a predetermined number of times or when the difference between the minimum value of the evaluation value and the allowable value is within a predetermined range. When a predetermined condition such as time is satisfied, the prohibition of the edge contraction processing is released, the evaluation values are recalculated for all edges, and again,
Edge contraction may be enabled.

In this way, even when a portion where data reduction processing can be performed within the allowable error remains in a portion where the edge contraction processing is prohibited, the data reduction processing can be performed on that portion. Thus, data can be reduced as efficiently as possible.

The data reduction processing procedures shown in FIGS. 13 and 15 reduce the number of recalculations of the evaluation values and increase the processing speed.
The error is not limited to the error ε shown in the equation. The evaluation value changes due to edge shrinkage or surface shrinkage and needs to be recalculated after shrinkage.
ace Simplification Using Quadric Error Metric
The present invention can be widely applied to cases where the evaluation value indicated by “s” is adopted.

Further, in the above-described embodiment, an example has been described in which the data of the three-dimensional measurement data measured by the three-dimensional shape measuring apparatus 1 is reduced. However, the present invention is not limited to this. The present invention can be widely applied to three-dimensional data created in.

[0127]

As described above, according to the present invention,
Two or more grid points are gathered into one grid point and the edge or surface of the polygon model is contracted to reduce the number of data of a plurality of three-dimensional shape data constituting the polygon model. A data reduction method, wherein a predetermined evaluation is performed based on the distance between each surface and all first grid points involved in the deformation of each surface for all surfaces that are deformed by contracting edges or surfaces of the polygon model. When the evaluation value is equal to or less than a predetermined allowable value, the three-dimensional shape data is reduced by edge contraction or surface contraction. Error management can be performed based on an intuitive evaluation criterion called an approximation error.

Further, for example, even in a case where the direction of a surface suddenly changes in a zigzag manner in a polygon model, it is possible to perform data reduction processing preferably while managing errors relatively accurately.

In particular, since the evaluation value is the error ε defined by the above equation (1), the error ε can be easily calculated only by storing the error matrix calculated for the first three-dimensional shape data. Processing is possible, and efficient use of memory required for calculation of data reduction processing is also possible.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of a three-dimensional shape measurement data processing system to which a data reduction method according to the present invention is applied.

FIG. 2 is a block diagram illustrating a configuration of a shape data processing device.

FIG. 3 is a diagram illustrating an example of approximation of a polygon model by data reduction.

FIG. 4 is a conceptual diagram of a data reduction method by edge contraction.

FIG. 5 is a conceptual diagram of a data reduction method by surface shrinkage.

FIG. 6 is a diagram for explaining evaluation values applied to the data reduction method according to the embodiment.

FIG. 7 is a flowchart illustrating a procedure of a data reduction process of three-dimensional shape data.

FIG. 8 is a diagram illustrating edge contraction of a portion where a discontinuous surface occurs in a polygon model due to random noise data.

9 is a diagram for explaining a difference between an error evaluation value according to the present embodiment and a conventional error evaluation value in the data reduction processing shown in FIG. 8;

FIG. 10 is a diagram illustrating shrinkage of a zigzag surface of a polygon model having a zigzag surface.

11 is a diagram for explaining a conventional error evaluation value in the data reduction processing shown in FIG.

FIG. 12 is a diagram for explaining an error evaluation value according to the embodiment in the data reduction processing shown in FIG. 10;

FIG. 13 is a flowchart illustrating another embodiment of a data reduction processing procedure for three-dimensional shape data.

14 is a diagram for explaining an example of a data reduction process according to the processing procedure shown in FIG.

FIG. 15 is a diagram showing a modification of the flowchart shown in FIG. 13;

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 Three-dimensional shape measuring apparatus 101 Illumination part 102 Confocal optical system 103 Light receiving part 104 Beam splitter 105 Operation part 106 Measurement table 2, 4 External storage device 3 Shape data processing device (data reduction device) 31 Polygon generation part 32 Data reduction Unit 321 evaluation value calculation unit (evaluation value calculation unit) 322 evaluation value sorting unit 323 edge / surface contraction processing unit (comparison unit, data reduction unit) 33 allowable value input unit 34 data output unit 5 display device 6 external processing device

Claims (10)

[Claims] 1. The number of a plurality of three-dimensional shape data constituting a polygon model is reduced by concentrating two or more lattice points into one lattice point and contracting an edge or a surface of the polygon model. A method for reducing data of three-dimensional shape data, comprising: for all surfaces that are deformed by shrinking an edge or a surface of the polygon model, for each surface and all first grid points involved in the deformation of each surface. A first step of calculating a predetermined evaluation value based on the distance;
A second step of comparing the evaluation value with a preset allowable value; and a step of reducing the three-dimensional shape data by contracting the edge or surface when the evaluation value is equal to or less than the allowable value. A data reduction method for three-dimensional shape data including the three steps. 2. The data reduction method for three-dimensional shape data according to claim 1, wherein the evaluation value is an error ε defined by the following equation (1). (Equation 1) 3. The number of data of a plurality of three-dimensional coordinate data constituting the polygon model is reduced by concentrating two or more lattice points into one lattice point and shrinking the edge or surface of the polygon model. A data reduction device for three-dimensional shape data, comprising: for all surfaces that are deformed by contracting edges or surfaces of the polygon model, each surface and all first grid points involved in the deformation of each surface; Evaluation value calculation means for calculating a predetermined evaluation value based on the distance, comparison means for comparing the evaluation value with a predetermined allowable value, and when the evaluation value is equal to or less than the allowable value, the edge or the surface A data reduction unit for reducing the three-dimensional shape data by performing contraction; 4. The apparatus according to claim 3, wherein said evaluation value calculation means calculates an error ε defined by the following equation (1) as an evaluation value. . (Equation 2) 5. The evaluation value calculating means calculates an error matrix Kv for each of all grid points v constituting the first polygon model, and calculates two or more grid points v _p (p =
1,2, ...) when was gathered in one lattice point v _q, the grid point the sum of the error matrix Kv _p of each lattice point v _p that massed v
_q data reduction apparatus of the three-dimensional shape data according to claim 4, wherein it is intended to calculate the error ε by the equation (1) as error matrix Kv _q of. 6. The evaluation value calculating means stores only a diagonal element of the error matrix calculated for the first lattice point and an element above the diagonal element in the storage means,
The error matrix is restored using the diagonal element stored in the storage means and the element above the diagonal element, and the error ε is calculated by the above equation (1) using the error matrix. The data reduction device for three-dimensional shape data according to claim 5. 7. When the column vector V of the three-dimensional shape data of the first grid point is represented by the following equation (2), the evaluation value calculating means calculates an error matrix ΣKv _j calculated for each plane p _i. (J
= 1, 2, ... m total by adding the elements in the lower right corner of the formula (1) _{i) Σm i (i = 1,2} , ... n) according to claim 4, wherein the calculating the Data reduction device for 3D shape data. (Equation 3) 8. The evaluation value calculating means, wherein the grid point v _j
Data reduction apparatus of the three-dimensional shape data according to claim 4, wherein calculating the error ε by the equation (1) using the error matrix w _j · Kv _j weighted instead of the error matrix Kv _j of. 9. The three-dimensional shape data according to claim 1, wherein the grid points involved in edge contraction or surface contraction of the polygon model are grid points forming edges or surfaces of the triangular polygon model. Data reduction device. 10. A grid point forming a triangular surface which is deformed by assembling two or more grid points into one grid point is a grid point forming a triangular polygon model surface after data reduction. 3. The data reduction method for three-dimensional shape data according to claim 1, wherein: