JP2018126939A - Data output regulating device for three-dimensional object molding - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a data output regulating device for three-dimensional object molding capable of more appropriately determining suitability of output of a 3D polygon model.SOLUTION: A regulation model database 40 in which a two-dimensional frequency distribution expressing features of a regulation model which is a polygon model whose output is to be regulated is registered, frequency distribution calculating means 10 for calculating the two-dimensional frequency distribution where two parameters are calculated on the basis of a specific triangle specified by predetermined points of three polygons in an object model with respect to a target model which is a polygon model to be output and each of the two parameters corresponds to two coordinates, and frequency distribution collation means 20 determining whether an output should be restricted or not by collating the two-dimensional frequency distribution of the object model with the two-dimensional frequency distribution of the regulation model are provided.SELECTED DRAWING: Figure 8

Description

  In the present invention, when using a three-dimensional object forming apparatus such as a 3D printer that processes a resin or the like to form a three-dimensional object based on data representing the three-dimensional object, it is determined which is inappropriate for output from the three-dimensional object forming apparatus. It relates to technology.

  In recent years, 3D printers that process and model resin, gypsum, and the like based on data representing a three-dimensional object have become widespread as three-dimensional object modeling apparatuses. The 3D printer outputs a three-dimensional object using a polygon model that represents a three-dimensional shape of the three-dimensional object as a set of polygons. As a medical application of 3D printer, 3D printer output modeling data (polygon model) is created based on CT / MRI image (DICOM format 3D voxel data) taken by medical diagnosis. Attempts have been made to output organ models for informed consent or to create artificial organs (blood vessels, bones, joints, etc.) for implantation in the body.

  3D printers have an innovation that can propagate not only information but also things remotely to the remote location via the Internet. For this reason, there has been a problem that dangerous materials such as guns and swords that have been regulated by customs have been distributed across the border in the form of data and can be easily obtained as 3D printers. In order to cope with this, the applicant has developed a technique for determining whether or not to restrict the output when outputting a three-dimensional object from a 3D printer based on a 3D polygon model (Patent Literature). 1 and 2).

JP, 2006-107471, A JP, 2006-124241, A

  In the techniques described in Patent Literatures 1 and 2, for each of a target model that is a polygon model to be output and a restriction model that is a polygon model to be restricted, a distance distribution that is a one-dimensional frequency distribution from a relationship between predetermined polygons. Then, it is determined whether or not the output of the target model should be regulated by creating and collating the angle distribution.

  However, even when collation is performed using the techniques described in Patent Documents 1 and 2, there may be a situation in which what should be regulated is output or what may be output cannot be output. there were.

  Therefore, an object of the present invention is to provide a three-dimensional object formation data output restriction device that can more appropriately determine whether or not the output of a 3D polygon model is appropriate.

In order to solve the above problems, in the first aspect of the present invention,
A device for determining whether or not to regulate when outputting a polygon model expressed as a set of polygons to a three-dimensional object modeling apparatus as three-dimensional object modeling data,
A database in which a two-dimensional frequency distribution expressing the characteristics of a restriction model, which is a polygon model whose output should be restricted, is registered;
For the target model that is the polygon model to be output, two parameters are calculated based on a specific triangle specified by a predetermined point of the three polygons in the target model, and each of the two parameters is set to two coordinates. Frequency distribution calculating means for calculating a two-dimensional frequency distribution corresponding to
A frequency distribution matching means for collating the two-dimensional frequency distribution of the target model with the two-dimensional frequency distribution of the regulation model and determining whether or not the output should be regulated;
There is provided a three-dimensional object shaping data output regulation device characterized by comprising:

  According to the first aspect of the present invention, there is provided a database in which a two-dimensional frequency distribution expressing the characteristics of a restriction model that is a polygon model whose output is to be restricted is provided, and a predetermined point of three polygons in the target model. Two parameters are calculated based on the specific triangle to be formed, each of the two parameters corresponds to two coordinates, a two-dimensional frequency distribution is calculated, and the two-dimensional frequency distribution of the target model is converted to the two-dimensional frequency of the regulatory model. Since it is determined whether the output should be regulated by collating with the distribution, not only the distribution feature of each of the two parameters but also the degree of relevance of the two parameters can be added to the determination, and the 3D polygon It becomes possible to more appropriately determine the suitability of the model output.

In the second aspect of the present invention, the database is registered with a one-dimensional frequency distribution that is at least one frequency distribution of the two parameters in addition to the two-dimensional frequency distribution.
The frequency distribution calculating means calculates the one-dimensional frequency distribution in addition to the two-dimensional frequency distribution for the target model,
The frequency distribution collating means collates the one-dimensional frequency distribution of the target model with the one-dimensional frequency distribution of the restriction model in addition to the collation of the two-dimensional frequency distribution, and determines whether or not the output should be regulated. It is characterized by being.

  According to the second aspect of the present invention, in addition to the two-dimensional frequency distribution, a one-dimensional frequency distribution that is at least one frequency distribution of two parameters is registered. In addition, a one-dimensional frequency distribution is calculated, and in addition to collation of the two-dimensional frequency distribution, the one-dimensional frequency distribution of the target model is collated with the one-dimensional frequency distribution of the restriction model to determine whether the output should be regulated. As a result, it is possible to exclude a restriction model with low similarity before performing high-accuracy matching using a two-dimensional frequency distribution, and to check whether the output of the 3D polygon model is more efficient and more efficient. It becomes possible to determine with high accuracy.

  In the third aspect of the present invention, one of the two parameters is a circumscribed circle radius of the specific triangle, and the other is a value based on a value obtained by dividing the square of the circumscribed circle radius by the area of the specific triangle. It is characterized by a certain area ratio.

  According to the third aspect of the present invention, one of the two parameters is a circumscribed circle radius of the specific triangle, and the other is an area ratio that is a value based on a value obtained by dividing the square of the circumscribed circle radius by the area of the specific triangle. Therefore, since the parameters are low in correlation and close to linear independence, it is possible to more accurately identify a sphere, a cylinder, a figure with a pose change, and the like.

In the fourth aspect of the present invention, the coordinates of the two-dimensional frequency distribution are orthogonal coordinates,
In calculating the two-dimensional frequency distribution, the frequency distribution calculating unit divides the range of the calculated maximum value of the circumscribed circle radius into a plurality of elements, and calculates the cube of the calculated maximum value of the circumscribed circle radius. Is divided into a plurality of elements, the circumscribed circle radius and the area ratio are assigned to one of the two elements corresponding to one of two two-dimensional axes, and the two-dimensional frequency distribution is It is characterized by calculating.

  According to the fourth aspect of the present invention, when calculating the two-dimensional frequency distribution whose coordinates are orthogonal coordinates, the range of the maximum value of the calculated circumscribed circle radius is divided into a plurality of elements, and the calculated circumscribed circle radius is calculated. The range of the cube of the maximum value of 3 is divided into multiple elements, and the circumscribed circle radius and area ratio are assigned to one of the elements corresponding to one of the two two-dimensional axes. Since the distribution is calculated, the two axes are related by the circumscribed circle radius, and it is possible to efficiently calculate the two-dimensional frequency distribution that reflects sharply on the feature of the shape.

In the fifth aspect of the present invention, when calculating the one-dimensional frequency distribution, the frequency distribution calculating unit divides the range of the calculated maximum value of the circumscribed circle radius into a plurality of elements, and / or , After dividing the range of the cube of the maximum value of the calculated circumscribed circle radius into a plurality of elements,
Each circumscribed circle radius is assigned to any of the elements based on the value of the circumscribed circle radius, and / or each area ratio is assigned to any of the elements based on the value of the area ratio. Allocating and calculating the one-dimensional frequency distribution.

  According to the fifth aspect of the present invention, in calculating the one-dimensional frequency distribution, the range of the calculated maximum value of the circumscribed circle radius is divided into a plurality of elements and / or the maximum of the calculated circumscribed circle radius is calculated. The range of the cube of the value is divided into a plurality of elements, and each circumscribed circle radius is assigned to one of the elements based on the value of the circumscribed circle radius, and / or each area ratio is assigned to the area ratio. Since one-dimensional frequency distribution is calculated by assigning to one of the elements based on the value of, one of the two one-dimensional frequency distributions of area ratio and circumscribed circle distribution is associated with the circumscribed circle radius Thus, it is possible to efficiently calculate a one-dimensional frequency distribution that reacts sensitively to shape features.

  In the sixth aspect of the present invention, the frequency distribution calculating means multiplies the area of the polygon by an inner product value of a unit vector from the center of gravity of the triangle to each vertex and a normal vector of the polygon including the vertex. An average value is calculated as a weight value, and weighting is performed using the weight value.

  According to the sixth aspect of the present invention, an average value of values obtained by multiplying the area of the polygon by the inner product value of the unit vector from the center of gravity of the triangle to each vertex and the normal vector of the polygon including the vertex is used as the weight value. Since it is calculated and weighted using the weight value, it is possible to calculate a frequency distribution that takes into account the three-dimensional spatial positional relationship based on the area and normal vector of the polygons that make up the triangle, and the appropriateness of the output Can be determined.

  In the seventh aspect of the present invention, the frequency distribution calculating means uses the sum of the weight values (weight sum value SQsum) for each polygon constituting each of the target models to determine the value of each element (Hd ( md) and Ha (ma)) are divided, and if the element is a negative value, it is given as an absolute value.

  According to the seventh aspect of the present invention, in calculating the frequency distribution, the value of each element is divided by the weight value for each polygon constituting each target model, and when the element is a negative value, Since the value is changed to a positive value, the frequency distributions can be easily collated.

  In the eighth aspect of the present invention, the frequency distribution calculating means acquires three polygons in the target model in units of three for the target model, and randomly generates the first group, the second group, and the third group. The three polygons are selected by classifying them into three groups and selecting one polygon from each group.

  According to the eighth aspect of the present invention, polygons in the target model are acquired in units of three and randomly classified into three groups of the first group, the second group, and the third group, one from each group. Since polygons are selected, a combination of three polygons for forming a triangle can be created without overlapping each other, and efficient processing can be performed. In particular, grouping can be performed in a state free from peculiar defects by acquiring three units and randomly classifying them into three groups.

  Further, in the ninth aspect of the present invention, the frequency distribution matching means calculates a correlation coefficient between the frequency distributions when matching the frequency distribution of the target model with the frequency distribution of the regulatory model. It is characterized in that it is determined whether or not the output should be regulated based on the correlation coefficient.

  According to the ninth aspect of the present invention, when collating the frequency distribution of the target model with the frequency distribution of the restriction model, the correlation coefficient between the frequency distributions is calculated, and the output is regulated based on the calculated correlation coefficient. Since it is determined whether or not it should be performed, accurate collation can be easily performed.

In the tenth aspect of the present invention,
Means for outputting the target model to a connected three-dimensional object shaping apparatus;
When it is determined that the output should be regulated (output inappropriate) by the frequency distribution matching unit executed in parallel with the three-dimensional object modeling process by the three-dimensional object modeling apparatus, Means for outputting an output stop command of the target model;
It further has these.

  According to the tenth aspect of the present invention, the target model is output to the connected three-dimensional object shaping apparatus, and it is determined that the output should be restricted as a result of the collation performed by the frequency distribution collation means executed in parallel. In this case, since the output stop command for the target model is output to the three-dimensional object modeling apparatus, the output can be canceled only when the output is inappropriate without delaying the modeling of the three-dimensional object that takes time. It becomes possible.

In the eleventh aspect of the present invention,
The output control terminal and the processing server are connected via a network,
The output control terminal calculates two parameters for a target model, which is a polygon model to be output, based on a specific triangle specified by predetermined points of three polygons in the target model. A frequency distribution calculating means for calculating a two-dimensional frequency distribution by associating each of the two parameters with two coordinates,
The processing server
A database in which a two-dimensional frequency distribution expressing the characteristics of a restriction model, which is a polygon model whose output should be restricted, is registered;
Receiving means for receiving a frequency distribution of the target model from the output control terminal via a network;
A frequency distribution matching means for collating the two-dimensional frequency distribution of the target model with the two-dimensional frequency distribution of the regulation model and determining whether or not the output should be regulated;
Output suitability data transmission means for transmitting data based on whether the output should be regulated or not, determined by the frequency distribution matching means, to the output control terminal;
It is characterized by having.

  According to the eleventh aspect of the present invention, the frequency distribution of the target model is received via the network, and the determination result obtained by determining whether the output should be regulated is transmitted to the transmission source of the frequency distribution of the target model. Since it did in this way, the judgment whether an output should be controlled can be provided by a cloud type, and the process in the output side can be reduced. In addition, the database can be centrally managed on the cloud side, and there is no need to manage the database in the output control terminal connected to each 3D object shaping device such as a 3D printer, so the output is always regulated based on the latest database. It is possible to determine whether or not to do so.

In the twelfth aspect of the present invention,
The three-dimensional object shaping data output restriction device;
A three-dimensional object modeling apparatus that models a three-dimensional object using a polygon model whose output is permitted by the three-dimensional object modeling data output restriction device;
There is provided a three-dimensional object forming system.

  According to the twelfth aspect of the present invention, the three-dimensional object modeling data output regulation device and the three-dimensional object modeling device that models the three-dimensional object using the polygon model whose output is permitted by the three-dimensional object modeling data output regulation device. Since the object modeling system is realized, the three-dimensional object modeling system can be provided in the form of a 3D printer or the like incorporating a board computer.

  According to a thirteenth aspect of the present invention, there is provided a program for causing a computer to function as the three-dimensional object formation data output restriction device according to any one of the above aspects.

  According to the thirteenth aspect of the present invention, a program for causing a computer to function as a three-dimensional object shaping data output restriction device is provided. By incorporating this program, the computer becomes a three-dimensional object shaping data output restriction device. Function.

  According to the present invention, it is possible to more appropriately determine whether or not the output of the 3D polygon model is appropriate.

It is a figure which shows the relationship between a triangle and a circumscribed circle, and a triangle and an inscribed circle. It is a figure for demonstrating the relationship of the area ratio of a triangle, a circumcircle, and a triangle and a circumcircle. It is a figure which shows the relationship between 1-dimensional frequency distribution and 2-dimensional frequency distribution. It is a figure which shows the two-dimensional frequency distribution by three polygon models and an outer circle | round | yen radius and an inscribed circle radius. It is a figure which shows the two-dimensional frequency distribution by three polygon models, an outside circle radius, and an area ratio (distance). It is a figure which shows the two-dimensional frequency distribution by three polygon models, an outside circle radius, and an area ratio (non-dimensional). 1 is a hardware configuration diagram of a three-dimensional object formation system including a three-dimensional object formation data output restriction device 100 according to an embodiment of the present invention. It is a functional block diagram which shows the structure of the data output control apparatus for solid object modeling which concerns on one Embodiment of this invention. It is a flowchart which shows the process outline | summary of the data output control apparatus for solid object shaping which concerns on one Embodiment of this invention. It is a flowchart which shows the detail of the 1st method of the calculation process of the frequency distribution of step S100. It is a figure for demonstrating the group classification | category of the polygon in this embodiment. It is a figure for demonstrating the group classification | category by the remainder divided by 3 based on the order in a data arrangement | sequence. It is a flowchart which shows the detail of the 2nd method of calculation processing of the frequency distribution of step S100. It is a figure which shows the triangle for calculating | requiring a circumcircle distribution and area ratio distribution, and its circumcircle. It is a figure which shows the collation example. It is a flowchart which shows the detail of the collation process of the frequency distribution of step S200. It is a hardware block diagram of the solid object modeling system containing the data output control apparatus for solid object modeling in a modification. It is a hardware block diagram of a cloud type solid thing modeling system. It is a functional block diagram of a cloud type solid thing modeling system.

<1. Basic concept of the present invention>
First, the basic concept of the present invention will be described. In the above Patent Documents 1 and 2, the distance distribution and the angle distribution are used as the frequency distribution expressing the characteristics of the polygon model. However, as an index that reflects the shape of the polygon model sensitively, an index in the polygon model (3D model) is used. A triangle formed by connecting the points of each of the three polygons is defined as a specific triangle, and the frequency distribution of the circumscribed circle radius, which is the radius of the circumscribed circle, is calculated as the circumscribed circle distribution. It is conceivable to collate this circumscribed circle distribution. Since the circumscribed circle distribution is more sensitively reflected in the shape of the polygon model than the distance distribution and the angle distribution, it is possible to perform a more accurate collation for determining the output suitability.

  Even if the circumscribed circle radius is the same, the shape of the specific triangle cannot be specified, and there are infinite variations. Therefore, it is preferable that there is at least another index in order to perform more accurate collation. As this index, it is conceivable to use an inscribed circle distribution that is a frequency distribution of the inscribed circle radius. FIG. 1 is a diagram illustrating a relationship between a triangle and a circumscribed circle, and a triangle and an inscribed circle. As shown in FIG. 1A, when the areas of the triangles are the same, the radius of the circumscribed circle is increased by changing the triangle shape from a regular triangle to a flat triangle. Specifically, the time of equilateral triangle is the minimum, and when the shape becomes flat, the radius approaches infinity. That is, the range of change of the circumscribed circle radius with respect to the triangular shape is infinite and large.

  On the other hand, as shown in FIG. 1B, when the areas of the triangles are the same, the inscribed circle radius becomes smaller by changing the triangle shape from a regular triangle to a flat triangle. Specifically, the maximum is a regular triangle, and the radius approaches 0 when the shape becomes flat. That is, the change width of the inscribed circle radius with respect to the triangular shape is finite and small.

  Consider the case of using an area ratio distribution which is a frequency distribution based on a value obtained by dividing the square of the circumscribed circle radius by the area of the triangle instead of the inscribed circle radius. FIG. 2 is a diagram for explaining the relationship between the triangle, its circumscribed circle, and the area ratio between the triangle and the circumscribed circle. FIG. 2A is the same as FIG. As described above, when the areas of the triangles are the same, the circumscribed circle radius is increased by changing the shape of the triangle from a regular triangle to a flat triangle. Specifically, when the shape is an equilateral triangle, the circumscribed circle radius approaches infinity when the shape becomes flat. That is, the range of change of the circumscribed circle radius with respect to the triangular shape is infinite and large. However, there are an infinite number of triangles having the same circumscribed circle radius, and the triangle cannot be specified only by the circumscribed circle radius.

  Therefore, as shown in FIG. 2B, when the shape of the triangle is changed from a regular triangle to a flat triangle under the same circumscribed circle radius, the square of the circumscribed circle radius is changed to the area of the triangle. The area ratio, which is a value based on the value divided by, increases. Specifically, when the regular triangle is the smallest and the shape becomes flat, the area ratio approaches infinity. That is, the range of change of the area ratio with respect to the triangular shape is infinite and large, similar to the circumscribed circle radius. Therefore, when another index is used together with the circumscribed circle distribution, the area ratio distribution is preferable to the inscribed circle distribution that reacts oppositely to the circumscribed circle radius. Therefore, in the present invention, an area ratio distribution that is a frequency distribution based on a value obtained by dividing the square of the circumscribed circle radius by the area of a triangle is used as a verification target.

In creating a two-dimensional frequency distribution, the two parameters are preferably as uncorrelated as possible and ideally linearly independent. The correlation between the two parameters can be evaluated using a normalized correlation coefficient. As the absolute value of the correlation coefficient is closer to 0, there is no correlation, so it is preferable as two parameters for creating a two-dimensional frequency distribution. Unlike the case of collation to be described later, it is not preferable that the normalized correlation coefficient has a large negative value because there is a negative correlation. The correlation coefficient between the one-dimensional frequency distributions using the two parameters needs to be in the range of −50% to 50%, practically preferably −40% to 40%, and more preferably -10% or more and 10% or less.

  For this reason, in the present embodiment, the first parameter is the circumscribed circle radius, and the second parameter is the area ratio obtained by dividing the square of the circumscribed circle radius by the area of the triangle. As a result, the circumscribed circle radius, which is the first parameter, is a dimension of length (one dimension), whereas the area ratio, which is the second parameter, is non-dimensional. There is a correlation. This is because the circumscribed circle radius is given by a value obtained by dividing the product of the three sides of the triangle by the area of the triangle (exactly ¼ of the value) and also depends on the area of the triangle. If the area ratio is defined by dividing the square of the circumscribed circle radius of the triangle by the area of the triangle, the square of the product of the three sides of the triangle is divided by the square of the area of the triangle. Insensitive to differences. Therefore, the area ratio is defined as the 1/3 power of the value obtained by dividing the square of the circumscribed circle radius of the triangle by the area of the triangle. Then, the area ratio becomes a value obtained by dividing the square of the geometric average distance of the three sides of the triangle by the area of the triangle, and becomes sensitive to the difference in shape. Eventually, the area ratio distribution may be any reflection of the ratio of the square of the circumscribed circle radius and the area of the triangle in some manner. Therefore, “a value based on the value obtained by dividing the square of the circumscribed circle radius of the triangle by the area of the triangle” further includes “a value obtained by dividing the square of the radius of the circumscribed circle by the area of the triangle”. A value raised to the third power is also included.

  However, even if a circumscribed circle distribution, an inscribed circle distribution, an area ratio distribution, or the like is used instead of the distance distribution or the angle distribution, all are one-dimensional frequency distributions. For example, a sphere and a cylinder are confused. In other words, when collating models that are basically the same type of character but only changed the pose, it was difficult to make an accurate determination because it was determined to be different. In the present invention, instead of a one-dimensional frequency distribution, a two-dimensional frequency distribution is created using two of the above indices, and collation is performed using this two-dimensional frequency distribution.

  FIG. 3 is a diagram showing the relationship between the one-dimensional frequency distribution and the two-dimensional frequency distribution. 3A shows a one-dimensional frequency distribution of a first parameter, FIG. 3B shows a one-dimensional frequency distribution of a second parameter, FIG. 3C shows a first parameter set on the X axis, This is a two-dimensional frequency distribution representing a frequency distribution of two parameters in a two-dimensional orthogonal coordinate system in which two parameters are set on the Y axis. As the first parameter and the second parameter, various frequency distributions such as the above-described distance distribution, angle distribution, circumscribed circle distribution, inscribed circle distribution, and area ratio distribution can be used. As shown in FIGS. 3A and 3B, the one-dimensional frequency distribution indicates weights (frequency, number of appearances) corresponding to individual values of the first parameter or the second parameter. As shown in FIG. 3C, the weights (frequency and number of appearances) corresponding to the values of both the first parameter and the second parameter on the two-dimensional coordinates are shown. The example of FIG. 3C shows that the weight increases when the value of the first parameter is large and the value of the second parameter is small. When the weights are integrated in the vertical axis direction with respect to the two-dimensional frequency distribution of FIG. 3C, the first parameter one-dimensional frequency distribution shown in FIG. 3A is obtained, and the two-dimensional frequency distribution of FIG. If the weights are integrated in the horizontal axis direction, the one-dimensional frequency distribution of the second parameter shown in FIG. Note that a two-dimensional frequency distribution as shown in FIG. 3C is displayed with gradation corresponding to the weight, or the first parameter is defined by the X axis, the second parameter is defined by the Y axis, and the weight is defined by the Z axis. By displaying the dimensional coordinate system in a perspective view or the like, the features of the polygon model can be grasped visually and intuitively.

  4, 5, and 6 are diagrams showing three polygon models and their two-dimensional frequency distribution. 4, 5, and 6, a sphere model A of 5040 polygons, a sphere model B of 120 polygons, and a polishing model C of 15994 polygons are used as the three polygon models. Although the sphere models A and B imitate a sphere, they are actually polyhedrons. In the example of FIG. 4, the outer circle radius and the inscribed circle radius are used as two parameters. As shown in FIGS. 4D, 4E, and 4F, when the outer circle radius and the inscribed circle radius are used as the two parameters, the distribution spreads in a fan shape around the 45 degree direction. This indicates that there is a strong positive correlation between the two parameters of the outer circle radius and the inscribed circle radius.

  In the example of FIG. 5, the outer circle radius and the area ratio (distance) are used as two parameters. The area ratio (distance) is the value obtained by dividing the area of the circumscribed circle of the triangle by the square root of the area of the triangle, and the area is divided by the different dimension of the square root of the area. The dimension is equivalent to. As shown in FIGS. 5D, 5E, and 5F, when the outer circle radius and the area ratio (distance) are used as the two parameters, the distribution is linear with the 45-degree direction as the center. This indicates that there is a positive correlation between the two parameters of the outer circle radius and the area ratio (distance).

  In the example of FIG. 6, the outer circle radius and the area ratio (non-dimensional) are used as two parameters. The area ratio (non-dimensional) is a value based on a value obtained by dividing the square of the circumscribed circle radius by the area of the specific triangle, and is divided by the same dimension, and thus is dimensionless. As shown in FIGS. 6D, 6 </ b> E, and 6 </ b> F, when the outer circle radius and the area ratio (non-dimensional) are used as the two parameters, the distribution is sharp from the 45 degree direction. This indicates that there is no significant correlation between the two parameters of the circumscribed circle radius and the area ratio (dimensionalless). As shown in FIG. 6, when the circumscribed circle radius and the area ratio (dimensionless) are used as the two parameters, the outer circle radius and the inscribed circle radius are used as shown in FIG. Compared with the case where the outer circle radius and the area ratio (distance) are used, the correlation between the two parameters is small, which is preferable.

DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, preferred embodiments of the invention will be described in detail with reference to the drawings.
<2. Device configuration>
FIG. 7 is a hardware configuration diagram of a three-dimensional object formation system including the three-dimensional object formation data output restriction device 100 according to an embodiment of the present invention. The three-dimensional object modeling data output restriction device 100 according to the present embodiment can be realized by a general-purpose computer. As shown in FIG. 7, a CPU (Central Processing Unit) 1 and a RAM (a main memory of the computer) Random Access Memory) 2, a large-capacity storage device 3 such as a hard disk or flash memory for storing programs and data executed by the CPU 1, a key input I / F (interface) 4 such as a keyboard and a mouse, and 3D A data input / output I / F (interface) 5 for data communication with an external device such as a printer or a data storage medium and a display unit 6 which is a display device such as a liquid crystal display are connected to each other via a bus. ing.

  The 3D printer 7 is a general-purpose 3D printer that processes a material such as resin, gypsum, metal, and the like based on three-dimensional object modeling data that is a polygon model expressing the three-dimensional shape of a three-dimensional object as a set of polygons. This is a three-dimensional object forming apparatus for forming an object. The 3D printer 7 includes a data processing unit 7a and an output unit 7b. The data processing unit 7a of the 3D printer 7 is connected to the data input / output I / F 5 so that the output unit 7b models the three-dimensional object based on the three-dimensional object modeling data received from the data input / output I / F 5. It has become.

  In FIG. 7, the three-dimensional object formation data output restriction device 100 and the 3D printer 7 are shown in a separated form. However, most of the currently available 3D printer products include the three-dimensional object formation data output restriction device 100. Constituent elements, such as CPU1, RAM2, storage device 3, key input I / F4 (not a keyboard / mouse for general-purpose computers, but several buttons at a numeric keypad level), data input / output I / F5, display unit 6 (several lines) A small liquid crystal panel or a touch panel capable of displaying the above characters is often used as a key input I / F 4 in an overlapping manner. Accordingly, the 3D printer 7 itself can directly receive the three-dimensional object modeling data via the external storage medium, and can be operated to model the three-dimensional object alone (particularly this is more common in a 3D printer for consumer use). ). That is, the three-dimensional object modeling system shown in FIG. 7 is often housed in one housing and distributed as a product called “3D printer”.

  FIG. 8 is a functional block diagram illustrating a configuration of the three-dimensional object formation data output restriction device according to the present embodiment. In FIG. 8, 10 is a frequency distribution calculating means, 20 is a frequency distribution matching means, 30 is a target model storage means, and 40 is a regulation model database. The frequency distribution calculating means 10 calculates a parameter that characterizes a specific triangle that is specified by a point of the center of gravity on three polygons selected from the target model for the target model that is a polygon model to be output. The frequency distribution of the parameter is calculated. In the present embodiment, two parameters, a first parameter and a second parameter, are used as parameters. More specifically, the circumscribed circle radius of a specific triangle formed by the points of the center of gravity of three polygons selected from within the target model is used as the first parameter, and is selected from within the target model as the second parameter. An area ratio that is 1/3 of the value obtained by dividing the square of the circumscribed circle radius of the specific triangle formed by the points of the center of gravity of the three polygons by the area of the specific triangle is used. Therefore, the frequency distribution calculating means 10 has a circumscribed circle distribution that is a frequency distribution of the radius of the circumscribed circle and the frequency of the area ratio that is 1/3 of the value obtained by dividing the square of the circumscribed circle radius by the area of the specific triangle. Three types of frequency distributions are calculated: an area ratio distribution, which is a distribution, and a two-dimensional frequency distribution indicating the correspondence between the circumscribed circle distribution and the area ratio distribution. In contrast to the two-dimensional frequency distribution, both the circumscribed circle distribution and the area ratio distribution are one-dimensional frequency distributions.

  The frequency distribution matching unit 20 compares the frequency distribution calculated for the target model with the frequency distribution calculated for the restriction model, and determines whether the output should be regulated, that is, whether the output is inappropriate or appropriate. To do.

  The frequency distribution calculating unit 10 and the frequency distribution matching unit 20 are realized by the CPU 1 executing a program stored in the storage device 3. The target model storage unit 30 is a storage unit that stores a target model, which is a polygon model that is a determination target of whether or not output should be restricted, and is realized by the storage device 3. The polygon model is data representing a predetermined three-dimensional shape in a three-dimensional space by a set of polygons, and is output as three-dimensional object modeling data to a three-dimensional object modeling apparatus such as a 3D printer. In this embodiment, STL (Standard Triangulated Language) is adopted as the data format of the polygon model.

  The restriction model database 40 stores a circumscribed circle distribution, an area ratio distribution, and a two-dimensional frequency distribution calculated as three kinds of frequency distributions with respect to a restriction model that is a polygon model whose output should be restricted, and is a database. And is realized by the storage device 3. The circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution, which are the three types of frequency distribution, serve as feature data representing the features of the regulatory model. That is, the difference between the original restriction models can be identified by the three types of frequency distributions, but the original restriction model cannot be restored. This is similar to the fact that individual differences can be identified by fingerprints, but the figure of the person itself cannot be restored. Therefore, the three kinds of frequency distributions do not play a role as a work, but also play a role as a so-called fingerprint that proves the identity of two works. In the regulation model database 40, not only the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution, but also the regulation model itself that is a basis for calculating the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution is registered. It is possible, but usually the regulatory model itself is not registered due to copyright issues.

  Each component shown in FIG. 8 is actually realized by mounting a dedicated program on hardware such as a computer and its peripheral devices as shown in FIG. That is, the computer executes the contents of each means according to a dedicated program. In this specification, the computer means an apparatus having an arithmetic processing unit such as a CPU and capable of data processing, and is incorporated not only in a general-purpose computer such as a personal computer but also in a “3D printer” as a product. Board computer included.

  The storage device 3 shown in FIG. 7 is mounted with a dedicated program for operating the CPU 1 and causing the computer to function as a three-dimensional object formation data output restriction device. By executing this dedicated program, the CPU 1 realizes functions as the frequency distribution calculating means 10 and the frequency distribution matching means 20. The storage device 3 not only functions as the target model storage unit 30 and the restriction model database 40 but also stores various data necessary for processing as the three-dimensional object formation data output restriction device.

  In the hardware configuration shown in FIG. 7, the frequency distribution calculating device for calculating the frequency distribution is provided by mounting only a dedicated program for causing the computer to function as the frequency distribution calculating means 10 in the storage device 3. Can also be realized. The frequency distribution calculation device calculates and outputs three types of frequency distributions based on the target model read from the target model storage unit 30. The output frequency distribution is separately input to a device provided with the frequency distribution matching means 20 and the restriction model database 40, so that the matching and the output restriction can be determined.

<3. Processing action>
<3.1. Pretreatment>
Next, the processing operation of the three-dimensional object formation data output restriction device shown in FIGS. 7 and 8 will be described. First, a circumscribed circle distribution, an area ratio distribution, and a two-dimensional frequency distribution, which are three kinds of frequency distributions, are created for a restriction model that is a polygon model to be restricted. Creation of the circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution from the polygon model can be performed in the same manner as the processing in the three-dimensional object formation data output restriction device described later. Creation of circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution from the regulation model may be performed by the three-dimensional object modeling data output regulation device or by executing the same program on another computer. Good. The created circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution are registered in the regulation model database 40.

  The target of output regulation may be not only dangerous materials such as guns and swords, but also copyrighted materials such as characters. In any case, the produced polygon model becomes a copyrighted work with a copyright holder. Therefore, in order to register a polygon model, which is a work, in the database, permission for the author is required for the act itself. As described above, the difference between the original polygon models can be identified by the format of the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution, but the original polygon model cannot be restored. This is similar to the fact that individual differences can be identified by fingerprint (fingerprint), but the figure of the person itself cannot be restored. The forms of circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution are changed to fingerprints. Corresponding, it does not fall under copyrighted work. Therefore, as in the present invention, by registering in the form of circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution, a database that records the features of the regulatory model without requiring the author's permission is constructed. Can do.

<3.2. Process Overview>
Next, the processing operation of the three-dimensional object formation data output restriction device shown in FIGS. 7 and 8 will be described. FIG. 9 is a flowchart showing a processing outline of the three-dimensional object formation data output restriction device according to the embodiment of the present invention. First, the frequency distribution calculation means 10 calculates a circumscribed circle distribution, an area ratio distribution, and a two-dimensional frequency distribution, which are three types of frequency distributions, for the target model that is a polygon model (step S100). The calculated circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution of the target model are compared with the circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution of the regulation model registered in the regulation model database 40. (Step S200).

<3.3. Frequency distribution calculation processing>
The frequency distribution calculation process (step S100) will be specifically described below. There are two types of frequency distribution calculation processing: the first method and the second method.
<3.3.1. First Method>
First, the first method will be described. FIG. 10 is a flowchart showing details of the frequency distribution calculation processing by the first method. Here, the number of polygons of the target model is N, and the variable i (i = 0,..., N−1) for specifying the polygon is used, and the vertices of each polygon i are (Xu (i), Yu (i), Zu ( i)), the normal vector of each polygon i is defined as (Xn (i), Yn (i), Zn (i)). u indicates a vertex number. In this embodiment, since the polygon is triangular, three values of u = 0, 1, and 2 are taken. Therefore, for example, Xu (i) is also expressed as X0 (i), X1 (i), and X2 (i). The polygons and normal vectors specifying the vertices are necessary for output by a 3D printer, which is a three-dimensional object forming apparatus, and the direction of the normal vectors indicates the outside of the forming surface (from the material to the air). The normal vector is normally recorded for each polygon in a polygon model for output to a 3D printer. The target model also has its output scale information Sout. The output scale information Sout is an actual dimension when the target model is output as a three-dimensional object, and is an actual dimension per unit length (length 1) of the three-dimensional coordinate system defining the vertex, expressed in mm. Has been.

  The frequency distribution calculating means 10 performs polygon normalization processing as preprocessing. Specifically, the maximum value xmax and minimum value xmin in the X direction, the maximum value ymax and minimum value ymin in the Y direction, and the maximum value zmax and minimum value zmin in the Z direction are obtained for each polygon in the target model. , (Xmax−xmin), (ymax−ymin), and (zmax−zmin), the largest one is defined as lmax. Then, the processing according to the following [Equation 1] is executed so that the coordinate values of all the polygons fall within the range of −1 to +1.

[Formula 1]
Xu ′ (i) = {Xu (i) − (xmax + xmin) / 2} × 2 / lmax
Yu ′ (i) = {Yu (i) − (ymax + ymin) / 2} × 2 / lmax
Zu ′ (i) = {Zu (i) − (zmax + zmin) / 2} × 2 / lmax

  As a result of the processing according to [Formula 1], each polygon i having vertices (Xu ′ (i), Yu ′ (i), Zu ′ (i)) has a coordinate value in the range of −1 to +1. Will fit. In the following, in order to prevent the symbols from becoming complicated, Xu ′ (i), Yu ′ (i), and Zu ′ (i) after the normalization process are changed to Xu (i), Yu (i), and Zu ( i) will be described.

  After completing the normalization process which is the pre-process, the frequency distribution calculating means 10 first executes the process according to the following [Equation 2] for the area Sp (i) of each polygon i constituting the target model. Calculate (step S501).

[Formula 2]
Vx (i) = [Y1 (i) -Y0 (i)] [Z2 (i) -Z0 (i)]-[Z1 (i) -Z0 (i)] [Y2 (i) -Y0 (i)]
Vy (i) = [Z1 (i) -Z0 (i)] [X2 (i) -X0 (i)]-[X1 (i) -X0 (i)] [Z2 (i) -Z0 (i)]
Vz (i) = [X1 (i) -X0 (i)] [Y2 (i) -Y0 (i)]-[Y1 (i) -Y0 (i)] [X2 (i) -X0 (i)]
Sp (i) = [Vx (i) ² + Vy (i) ² + Vz (i) ² ] ^1/2

  Next, for each polygon constituting the target model, the gravity center of the polygon is calculated (step S502). Specifically, by executing the processing according to the following [Equation 3], the center of gravity (Xc (i), Yc (i), Zc (i)) of the polygon having the average coordinates of the vertices of each polygon is obtained. calculate.

[Formula 3]
Xc (i) = {X0 (i) + X1 (i) + X2 (i)} / 3
Yc (i) = {Y0 (i) + Y1 (i) + Y2 (i)} / 3
Zc (i) = {Z0 (i) + Z1 (i) + Z2 (i)} / 3

  In the above [Equation 3], X0 (i), X1 (i), and X2 (i) respectively represent the cases of vertex numbers u = 0, 1, and 2 in Xu (i), and Y0 (i), Y1 ( i) and Y2 (i) respectively indicate the cases of vertex numbers u = 0, 1, and 2 in Yu (i), and Z0 (i), Z1 (i), and Z2 (i) are in Zu (i), respectively. , Vertex numbers u = 0, 1, and 2 are shown. As shown in the above [Equation 3], the polygon centroid is calculated as a point having the average coordinates of each vertex of the polygon.

  Here, the center vector of the specific triangle and the unit vector to each vertex of the specific triangle will be described. The centroid of a specific triangle formed by the polygon centroids of three polygons i1, i2, i3 (i1, i2, i3 are different integers having values 0 to N-1 as i) (Xo (i1, i2, i3), Yo (i1, i2, i3), Zo (i1, i2, i3)). That is, the center of gravity (Xo (i1, i2, i3), Yo (i1, i2, i3), Zo (i1, i2, i3)) of the specific triangle is defined by the following [Equation 4].

[Formula 4]
Xo (i1, i2, i3) = {Xc (i1) + Xc (i2) + Xc (i3)} / 3
Yo (i1, i2, i3) = {Yc (i1) + Yc (i2) + Yc (i3)} / 3
Zo (i1, i2, i3) = {Zc (i1) + Zc (i2) + Zc (i3)} / 3

  The unit vector (Ex (i2, i3, i1)) from the centroid of the specific triangle to the polygon centroid (Xc (i1), Yc (i1), Zc (i1)) of the polygon i1 by the following [Equation 5]: Ey (i2, i3, i1), Ez (i2, i3, i1)) are defined.

[Formula 5]
E (i2, i3, i1) = [{Xc (i1) −Xo (i1, i2, i3)} ² + {Yc (i1) −Yo (i1, i2, i3)} ² + {Zc (i1) − Zo (i1, i2, i3)} ² ] ^1/2
Ex (i2, i3, i1) = {Xc (i1) -Xo (i1, i2, i3)} / E (i2, i3, i1)
Ey (i2, i3, i1) = {Yc (i1) −Yo (i1, i2, i3)} / E (i2, i3, i1)
Ez (i2, i3, i1) = {Zc (i1) −Zo (i1, i2, i3)} / E (i2, i3, i1)

  The center vector of the specific triangle and the unit vector to each vertex of the specific triangle are used for calculation of the frequency distribution in step S508, which will be described later, by executing the processing according to [Formula 4] and [Formula 5].

  Next, a set of polygons constituting the polygon model is divided into three groups, and the order of the polygons in each group is changed (step S503). As a method of dividing into three groups, any method may be used as long as it can be divided into the same number. In the present embodiment, as a particularly preferable aspect, grouping is performed at random in units of three based on the order in the data arrangement of the polygon model.

  Specifically, a polygon is acquired in units of three from a set of polygons constituting a polygon model, and the first group, the second group are based on random numbers that randomly generate an integer of 0 to 2, which is the remainder of 3. And classify into any one of the third groups. Then, this process is repeatedly executed for all the polygons constituting the polygon model, thereby dividing the N polygons constituting the polygon model into N / 3 groups. The random number does not necessarily have to be 0 to 2 as long as a state that occurs with a probability of 1/3 can be realized.

  When the remainder of 3 of the original polygon number N is 2 so that the number of polygons in each group is the same, the top polygon 0 is overlapped as the last polygon N = polygon 0, and the total number of polygons is Modify to be N + 1. If the remainder of 3 of the original polygon number N is 1, the first polygon 0 and the second polygon 1 are overlapped as the second polygon N = polygon 0 from the tail and the last polygon N + 1 = polygon 1 In any case, the total number of polygons is corrected to N + 2. Even if the number of polygons is duplicated and the total number of polygons is N + 1 or N + 2 so that the number of polygons in each group is the same, the total number of polygons will be replaced with N in the following. I will explain.

  By grouping by the remainder divided by 3, three arrays G1 (h) = 3h + Q0 (q), G2 (h) = 3h + Q1 (q), G3 (h) = 3h + Q2 (q) (h = 0,. .., N / 3-1) is obtained. Here, the integer value q (q = 0,..., N / 3-1) is given the same value as the integer value h given to G1 (h), and Q0 (q), Q1 (q), Q2 (Q) takes any integer value of {0, 1, 2} based on the integer value q. That is, Q0 (q) = q mod 3, Q1 (q) = (q + 1) mod 3, and Q2 (q) = (q + 2) mod 3 (“mod 3” represents a remainder of 3). As will be described later, since the integer value q is given randomly, Q0 (q), Q1 (q), and Q2 (q) do not overlap each other, and any integer value of {0, 1, 2} is randomly assigned. Take.

  Next, the arrangement order of the polygons in each group is changed. The order is changed randomly. That is, it is shuffled. Any method may be used as long as the order of polygon arrangement can be changed. In this embodiment, the order of polygon arrangement is changed by the following method. First, three types of random number arrays R1 (k), R2 (k), and R3 (k) are created. Specifically, k = 0,..., N / 3-1 are initialized to R1 (k) = k. Subsequently, a real-valued uniform random number is generated N / 3 times within a range of 0 ≦ Rnd (k) <1, and every time it is generated, pp = Rnd (k) × N / 3 is calculated as 0 ≦ An integer value of pp ≦ N / 3-1 is calculated, and the process of exchanging the value of R1 (k) and the value of R1 (pp) is repeated N / 3 times. As a result of repetition, a random number array R1 (k) in which N / 3 consecutive integers are randomly replaced is obtained. Accordingly, for example, h = q = R1 (k) is given to the polygon array G1 (h) of the first group, and G1 (R1 (k)) = 3R1 (k) + Q0 (R1 (k)) As in (k = 0,..., N / 3-1), an array in which the order is changed can be obtained.

  The second random number array R2 (k) is given by R2 (k) = R1 (N / 3-1-k). That is, the random number array R2 (k) is obtained by reversing the order from the beginning to the end of the first random number array R1 (k). The random number array R1 (k) and the random number array R2 (k) are the other inverted random number arrays. Further, for the third random number array R3 (k), the random number array R3 (k) = k is set to a sequential value of k = 0,. In this way, by rearranging the polygon arrangement order, the polygon arrangement order of each group can be set randomly from the polygons in the target model that is a three-dimensional space, and a combination of points on the random polygons. The circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution can be obtained based on the area of the specific triangle and the circumscribed circle radius of the specific triangle. Accordingly, h = R2 (k) and q = R1 (k) are given to the polygon array G2 (h) of the second group, and G2 (R2 (k)) = 3R2 (k) + Q1 (R1 (k )), And h = R3 (k) and q = R1 (k) are given to the polygon array G3 (h) of the third group, and G3 (R3 (k)) = 3R3 (k) + Q2 (R1) (K)) and an array in which the order of the three groups is exchanged can be obtained. As will be described later, h = q = R2 (k) may be given to the polygon array G1 (h) of the first group, and G1 (R2 (k)) = 3R2 (k) + Q0 (R2 ( It is also possible to obtain an array in which the order is changed as in k)).

  The reason why the polygons are classified into the three groups in this manner is to prevent the polygons from overlapping each other when the three polygons are randomly selected to create the specific triangle. Although it is possible to sequentially form specific triangles by combining all the polygons constituting the polygon model, if the number of polygons is large, the number of combinations becomes enormous, which is not practical. Further, there is a method of forming a specific triangle by randomly selecting three polygons from all the polygons constituting the polygon model without grouping, but the same specific triangle is generated with a certain probability. If the number of samples of specific triangles extracted at random is not sufficiently large, a biased frequency distribution may be calculated. As in this embodiment, the three polygons for forming a specific triangle are overlapped with each other by classifying into three groups, selecting one polygon from each group and selecting a total of three. It becomes possible to select efficiently while giving randomness.

  FIG. 11 is a view for explaining polygon group classification in the present embodiment. For example, as shown in FIG. 11, nine original polygon arrays (a set of polygons) P1 to P9 are classified into three groups of A group, B group, and C group. In this case, the first three polygons P1, P2, and P3 are classified into an A group, a B group, and a C group, respectively, based on a random number of [0, 1, 2], and the next three polygons P4, P5. , P6 are classified into a B group, a C group, and an A group based on a random number of [1, 2, 0], respectively, and the last three polygons P7, P8, and P9 are random numbers of [2, 0, 1]. Are classified into C group, A group, and B group, respectively. Then, the arrangement order of the polygons in each group is changed (shuffled). As a result, a specific triangle formed by the polygons P6, P9, and P3, a specific triangle formed by the polygons P1, P2, and P5 and a specific triangle formed by the polygons P8, P4, and P7 are obtained.

  FIG. 12 illustrates group classification based on whether the remainder is 0, 1 or 2 divided by 3 based on the order in the polygon model data array, rather than determining groups based on random numbers. FIG. For example, as shown in FIG. 12, it is assumed that nine original polygon arrays (a set of polygons) P1 to P9 are classified into three groups of A group, B group, and C group. In this case, the first three polygons P1, P2, and P3 are classified into an A group, a B group, and a C group based on the remainder [0, 1, 2] obtained by dividing the integer part by 3, respectively. Three polygons P4, P5, and P6 are classified into A group, B group, and C group, respectively, based on the remainder [0, 1, 2] obtained by dividing the integer part by 3, and the last three polygons P7 , P8, and P9 are classified into A group, B group, and C group, respectively, based on the remainder [0, 1, 2] obtained by dividing the integer part by 3. Then, the arrangement order of the polygons in each group is changed (shuffled). As a result, a specific triangle formed by the polygons P4, P8, and P3, a specific triangle formed by the polygons P1, P2, and P6, and a specific triangle formed by the polygons P7, P5, and P9 are obtained. As shown in FIG. 12, when grouping is performed based on the remainder divided by 3, as shown in FIG. 11, compared to the case where random grouping is performed using random numbers, the polygon array is arranged in a specific triangle to be configured. Will cause a habit.

  Next, initial setting is performed (step S504). Specifically, a circumscribed circle distribution, an area ratio distribution, a two-dimensional frequency distribution to be calculated, a loop counter, and a weight sum value are initialized. The circumscribed circle distribution calculated in the present embodiment is a circumscribed circle radius distribution of a specific triangle obtained by weighting the area of the polygon. The number of elements is MD, and each element md (md = 0,..., MD− The frequency of 1) is expressed as Hd (md). Hd (md) is a one-dimensional array composed of a predetermined number of MD elements. An arbitrary value can be set as the number of elements MD, but in this embodiment, MD = 360. After preparing such a one-dimensional array, the frequency distribution calculating means 10 sets the initial value as Hd (md) = 0. The area ratio distribution calculated in the present embodiment is an area ratio distribution obtained by weighting the area of the polygon. The number of elements is MA, and the frequency of each element ma (ma = 0,..., MA-1). Is represented as Ha (ma). Ha (ma) is a one-dimensional array composed of a predetermined number of elements. The element number MA may be the same as or different from the element number MD. Although an arbitrary value can be set as the element number MA, in the present embodiment, it is the same as the element number MD, and MA = 360. After preparing such a one-dimensional array, the frequency distribution calculating means 10 sets the initial value as Ha (ma) = 0.

The two-dimensional frequency distribution calculated in this embodiment is a two-dimensional frequency distribution of a circumscribed circle radius and an area ratio, where the number of elements is MQ ² and each element mu, mv (mu, mv = 0,... , MQ-1) is represented as Hq (mu, mv). Hq (mu, mv) is a two-dimensional array composed of a predetermined number of MQ ² elements. Although an arbitrary value can be set as the square root MQ of the number of elements, in this embodiment, MQ = MD / 3 = MA / 3 = 120. After preparing such a two-dimensional array, the frequency distribution calculating means 10 sets the initial value as Hq (mu, mv) = 0. For the loop counter LC, an initial value LC = 0 is set. Further, the weight sum value SQsum = 0, which is the sum value of the weight values SQ, is set.

  Next, the frequency distribution calculating means 10 creates a specific triangle having the centroids of the polygons among the three groups as vertices (step S505). When creating a specific triangle using three polygons, various points can be used as points on the polygon, not limited to the center of gravity of the polygon. However, since the polygon centroid is preferable as a point representing one polygon, in the present embodiment, a specific triangle is created with the polygon centroid as a vertex. The point on the polygon means a point located on a plane passing through all the vertices constituting the polygon (a point located outside the triangle like an outer center).

  In step S505, three combinations are created by changing the combinations between groups so that the number of specific triangles is equal to the total number N of polygons. Specifically, assuming that q = R1 (k), the order k (k = 0,..., N) in which the order of the polygon G1 (h) of the first group is randomly changed by the random number array R1 (k). / 3-1) the center of gravity of the polygon G1 (R1 (k)) (Xc (G1 (R1 (k))), Yc (G1 (R1 (k))), Zc (G1 (R1 (k)))) , The center of gravity (Xc (G2 (R2 (k)) of the polygon G2 (R2 (k)) in the corresponding order k obtained by randomly changing the order of the polygon G2 (h) in the second group by the random number array R2 (k). )), Yc (G2 (R2 (k))), Zc (G2 (R2 (k)))), and the third group of polygons G3 (h), the order is randomly changed by the random number array R3 (k). The center of gravity (Xc (G3 (R3 ( ))), Yc (G3 (R3 (k))), Zc (G3 (R3 (k)))) a first specific triangle N / 3 pieces created whose vertices three points.

  Similarly, as q = R2 (k), the center of gravity of the polygon G1 (R2 (k)) in the order k obtained by randomly changing the order of the first group of polygons G1 (h) by the random number array R2 (k) ( Xc (G1 (R2 (k))), Yc (G1 (R2 (k))), Zc (G1 (R2 (k)))), the second group of polygons G2 (h), a random number array R3 ( k), the center of gravity (Xc (G2 (R3 (k))), Yc (G2 (R3 (k))), Zc (G2) (R3 (k)))), the center of gravity of the polygon G3 (R1 (k)) of the corresponding order k obtained by randomly changing the order of the third group of polygons G3 (h) by the random number array R1 (k) ( Xc (G3 (R1 (k))), Yc (G3 (R1 (k))) , Zc (G3 (R1 (k)))) a second specific triangle N / 3 pieces created whose vertices three points.

  Further, assuming that q = R3 (k), the center of gravity (Xc) of the polygon G1 (R3 (k)) in the order k obtained by randomly changing the order of the polygon G1 (h) in the first group by the random number array R3 (k). (G1 (R3 (k))), Yc (G1 (R3 (k))), Zc (G1 (R3 (k)))), the second group of polygons G2 (h), a random number array R1 (k ) At the center of gravity (Xc (G2 (R1 (k))), Yc (G2 (R1 (k))), Zc (G2 () R1 (k)))), the center of gravity (Xc) of the polygon G3 (R2 (k)) of the corresponding order k, which is randomly changed in order by the random number array R2 (k) with respect to the polygon G3 (h) of the third group (G3 (R2 (k))), Yc (G3 (R2 (k)) , Zc (G3 (R2 (k)))) a third particular triangle to N / 3 pieces created whose vertices three points.

  Next, the frequency distribution calculating means 10 calculates a circumscribed circle radius of a specific triangle having the polygon centroid as a vertex (step S506). Specifically, first, by executing the processing according to the following [Formula 6], the area S (k) of the first specific triangle in the range of k = 0,..., N / 3-1. Is calculated.

[Formula 6]
As q = R1 (k),
D12 = [[Xc (G2 (R2 (k)))-Xc (G1 (R1 (k)))] ² + [Yc (G2 (R2 (k)))-Yc (G1 (R1 (k))) ] ² ] ^1/2
D23 = [[Xc (G3 (R3 (k))) − Xc (G2 (R2 (k)))] ² + [Yc (G3 (R3 (k))) − Yc (G2 (R2 (k))) ] ² ] ^1/2
D31 = [[Xc (G1 (R1 (k))) − Xc (G3 (R3 (k)))] ² + [Yc (G1 (R1 (k))) − Yc (G3 (R3 (k))) ] ² ] ^1/2
D = (D12 + D23 + D31) / 2
S (k) = [D × (D−D12) × (D−D23) × (D−D31)] ^1/2

  Then, the circumscribed circle radius D (k) of the first specific triangle is calculated in the range of k = 0,..., N / 3-1 by executing the processing according to the following [Equation 7]. .

[Formula 7]
D (k) = D12 * D23 * D31 / (4 * S (k))

  Similarly, the frequency distribution calculating means 10 executes the processing according to the following [Equation 8] to thereby obtain the area S of the second specific triangle in the range of k = 0,..., N / 3-1. (K) is calculated.

[Formula 8]
As q = R2 (k),
D23 = [[Xc (G3 (R1 (k))) − Xc (G2 (R3 (k)))] ² + [Yc (G3 (R1 (k))) − Yc (G2 (R3 (k))) ] ² ] ^1/2
D31 = [[Xe (G1 (R2 (k))) − Xc (G3 (R1 (k)))] ² + [Yc (G1 (R2 (k))) − Yc (G3 (R1 (k))) ] ² ] ^1/2
D12 = [[Xc (G2 (R3 (k))) − Xc (G1 (R2 (k)))] ² + [Yc (G2 (R3 (k))) − Yc (G1 (R2 (k))) ] ² ] ^1/2
D = (D12 + D23 + D31) / 2
S (k) = [D × (D−D12) × (D−D23) × (D−D31)] ^1/2

  The circumscribed circle radius D (k) of the second specific triangle is calculated in the range of k = 0,..., N / 3-1 by executing the process according to [Formula 7]. Similarly, the frequency distribution calculating means 10 executes the processing according to the following [Equation 9] to thereby obtain the area S of the third specific triangle in the range of k = 0,..., N / 3-1. (K) is calculated.

[Formula 9]
As q = R3 (k),
D31 = [[Xc (G1 (R3 (k))) − Xc (G3 (R2 (k)))] ² + [Yc (G1 (R3 (k))) − Yc (G3 (R2 (k))) ] ² ] ^1/2
D12 = [[Xc (G2 (R1 (k))) − Xc (G1 (R3 (k)))] ² + [Yc (G2 (R1 (k))) − Yc (G1 (R3 (k))) ] ² ] ^1/2
D23 = [[Xc (G3 (R2 (k))) − Xc (G2 (R1 (k)))] ² + [Yc (G3 (R2 (k))) − Yc (G2 (R1 (k))) ] ² ] ^1/2
D = (D12 + D23 + D31) / 2
S (k) = [D × (D−D12) × (D−D23) × (D−D31)] ^1/2

  Then, the radius D (k) of the circumscribed circle of the third specific triangle is calculated in the range of k = 0,..., N / 3-1 by executing the processing according to the above [Equation 7]. . In the above [Equation 6], [Equation 8] and [Equation 9], only the specific triangle in which the lengths D12, D23 and D31 of each side of the specific triangle satisfy all the six conditions shown in the following [Equation 10], The target of the frequency distribution of the circumscribed circle radius. Therefore, a specific triangle that does not satisfy one of the six conditions shown in [Equation 10] is not subject to the frequency distribution of the circumscribed circle radius. This is because the radius D (k) of the circumscribed circle becomes extremely large when the six conditions shown in the following [Equation 10] are not satisfied, and a highly accurate frequency distribution cannot be obtained.

[Formula 10]
D12> 0
D23> 0
D31> 0
| D12-D23-D31 | / D12> 0.1
| D23-D31-D12 | / D23> 0.1
| D31-D12-D23 | / D31> 0.1

  As shown in the above [Equation 10], the first three conditions among the six conditions mean that all sides take positive values other than 0, that is, form a triangle. Of the six conditions, the latter three conditions mean that the specific triangle to be created does not have an extremely flat shape. If the specific triangle has an extremely flat shape, the radius of the circumscribed circle approaches infinity, and an accurate frequency distribution cannot be obtained. When the six conditions shown in [Equation 10] are not satisfied, a triangle is not formed (when either side is 0), or the radius D (k) of the circumscribed circle becomes extremely large, and the frequency with high accuracy This is because the distribution cannot be obtained.

  The radius of the circumscribed circle of N / 3 first specific triangles, the radius of the circumscribed circle of N / 3 second specific triangles, and the N / 3 third specific triangles calculated by the above [Equation 7] N / 3 arrays D (k) having the radius of the circumscribed circle of N is offset by N / 3 to the N / 3 arrays of the second specific triangle, and N / The 3 arrays are offset by 2N / 3, grouped by serial number i, the range is reset to i = 0,..., N−1, and circumscribed circles of N specific triangles A radius D (i) (i = 0,..., N−1) is obtained. And the largest one among the N circumscribed circle radii D (i) of i = 0,..., N−1 is set as the maximum circumscribed circle radius Dmax.

  Next, the frequency distribution calculating means 10 calculates the area ratio between the specific triangle having the polygon centroid as a vertex and the circumscribed circle of the specific triangle (step S507). Specifically, by executing processing according to the following [Equation 11], the first specific triangle, the second specific triangle, and the third specific in the range of k = 0,..., N / 3-1. The area ratio A (k) is calculated for the triangle.

[Formula 11]
A (k) = D (k) ^2/3 / S (k) ^1/3

  As shown in [Formula 11], the area ratio A (k) is obtained by dividing the circumscribed circle radius D (k) to the 2/3 power by the 1/3 power of the area S (k) of the specific triangle. Is calculated. That is, the area ratio A (k) is a value obtained by dividing the square of the circumscribed circle radius D (k) by the area S (k) of the specific triangle to the 1/3 power (the value obtained by taking the cube root). ). This is included in the “value based on the value obtained by dividing the square of the circumscribed circle radius by the area of the specific triangle”. Therefore, the area ratio A (k) is not an accurate area ratio between the specific triangle and its circumscribed circle. However, it is a value that reflects sharply the triangle shape difference from the exact area ratio, and the horizontal axis of the frequency distribution is dimensionless, unlike the circumscribed circle distribution, and is a value that does not depend on the scale of the polygon model. It is possible to plot directly without modification. Since the area ratio distribution has a small difference depending on the shape, as described later, a method of interlocking the circumscribed circle distribution with the scale is adopted. Note that a specific triangle that does not satisfy one of the six conditions shown in [Formula 10] is not counted as a circumscribed circle distribution, an area ratio distribution, or a two-dimensional frequency distribution.

  The area ratio A (k) of N / 3 first specific triangles calculated by the above [Equation 11], the area ratio A (k) of N / 3 second specific triangles, and N / 3 pieces In contrast to the three N / 3 arrays A (k) of the area ratio A (k) of the third specific triangle, an offset of N / 3 is added to the N / 3 array for the second specific triangle, The N / 3 array for the third specific triangle is offset by 2N / 3, and the range of the serial number i is reset to i = 0,. A triangular area ratio A (i) (i = 0,..., N−1) is obtained. And the largest one among N area ratios A (i) of i = 0,..., N−1 is defined as a maximum area ratio Amax.

  Thereafter, the frequency distribution calculating means 10 calculates a circumscribed circle distribution (step S508) that is a frequency distribution of the circumscribed circle radius of the specific triangle, and the frequency of the area ratio that is the ratio of the area between each triangle and the circumscribed circle. An area ratio distribution which is a distribution is calculated (step S509). In the present embodiment, the circumscribed circle distribution and the area ratio distribution are calculated in consideration of the normal vector of the polygon. The reason will be explained. For example, in the sphere model, the normal vectors of all the polygons face outward, but in a model in which the sphere is hollow like a balloon, a polygon having a normal vector in the center direction of the sphere is also added. However, a specific triangle has no relation to the normal vector of the constructed polygon, and if the three polygon centroids are the same, they will have the same shape and the circumscribed circle radius and area ratio will be the same. In the area ratio distribution, it is impossible to distinguish between a sphere filled with material and a sphere like a balloon. Therefore, when weighting is performed in consideration of the normal vector, even if the specific triangles have the same shape, there is a difference between the circumscribed circle distribution and the area ratio distribution. Become identifiable.

  Next, the frequency distribution calculating means 10 calculates a circumscribed circle distribution that is a frequency distribution of the circumscribed circle radius of the specific triangle (step S508). Specifically, by executing the processing according to the following [Equation 12], the frequency Hd (md) of the element md is calculated for i = 0,.

[Formula 12]
If Dmax × md / MD ≦ D (i) <Dmax × (md + 1) / MD,
Hd (md) ← Hd (md) + SQ, SQsum ← SQsum + SQ
SQ = [Sp (G1 (i)) × {Ex (G2 (i), G3 (i), G1 (i)) × Xn (G1 (i)) + Ey (G2 (i), G3 (i), G1] (I)) × Yn (G1 (i)) + Ez (G2 (i), G3 (i), G1 (i)) × Zn (G1 (i))} + Sp (G2 (i)) × {Ex (G3 (I), G1 (i), G2 (i)) × Xn (G2 (i)) + Ey (G3 (i), G1 (i), G2 (i)) × Yn (G2 (i)) + Ez (G3 (I), G1 (i), G2 (i)) × Zn (G2 (i))} + Sp (G3 (i)) × {Ex (G1 (i), G2 (i), G3 (i)) × Xn (G3 (i)) + Ey (G1 (i), G2 (i), G3 (i)) × Yn (G3 (i)) + Ez (G1 (i), G2 (i), G3 (i)) × Zn (G3 (i))}] / 3
However, in the case of 0 ≦ i ≦ N / 3-1, as q = R1 (i), G1 (i) = G1 (R1 (i)), G2 (i) = G2 (R2 (i)), G3 ( i) = G3 (R3 (i))
In the case of N / 3 ≦ i ≦ 2N / 3-1, as q = R2 (i), G1 (i) = G1 (R2 (i)), G2 (i) = G2 (R3 (i)), G3 ( i) = G3 (R1 (i))
In the case of 2N / 3 ≦ i ≦ N−1, q = R3 (i) and G1 (i) = G1 (R3 (i)), G2 (i) = G2 (R1 (i)), G3 (i) = G3 (R2 (i)).

  In the above [Equation 12], SQ is the inner product value of the vector (Ex (), Ey (), Ez ()) from the center of gravity of the specific triangle to each vertex and the normal vector Xn () of each polygon. It is a weight value multiplied by the area Sp (). A vector (Ex (), Ey (), Ez ()) from the center of gravity of the specific triangle to each vertex is calculated from the center of gravity of the specific triangle calculated by using the above [Equation 4] and [Equation 5] to each vertex. Calculated using unit vectors. [Formula 12] is specified when the circumscribed circle radius D (i) of the specific triangle is equal to or larger than the value obtained by multiplying the maximum circumscribed circle radius Dmax by md / MD and smaller than the value obtained by multiplying (md + 1) / MD. This means that a weight value SQ based on three polygons having a triangle vertex as a polygon centroid is added to Hd (md).

  Similarly, the weight value SQ is added to the weight sum value SQsum. The weight value SQ becomes a small value when the direction from the center of gravity of the specific triangle to each vertex is different from the direction of the normal vector of each polygon, and may take a negative value when the direction is further reversed. If it does so, the value added to frequency Hd (md) will become small or will be subtracted. Such a phenomenon is likely to occur when a cavity exists in the polygon model, and as a result, three polygons constituting a specific triangle belonging to the polygon model of the same part are easily counted as the frequency Hd (md). . That is, the features that cross a plurality of parts are suppressed in the frequency distribution, and the characteristics of the individual parts are likely to remain.

  The circumscribed circle distribution Hd (md) (md = 0,..., MD-1) is calculated by executing the processing according to the above [Equation 12] for N specific triangles. Each element is not just a frequency, but a weight value obtained by multiplying the inner product value of the vector from the center of gravity of each specific triangle to each vertex and the normal vector of each polygon by the area of the polygon. Hd (md) represents a circumscribed circle distribution weighted by a weight value. When only 1 is added instead of the weight value, or when the area of the polygon is simply added, the normal vector of the polygon is not considered, and the cavity of the polygon model cannot be identified. Therefore, in this embodiment, the weight value SQ is added when the circumscribed circle distribution is calculated. However, if the target polygon model is composed of a single part, it is possible to maintain a certain degree of collation accuracy even when adding 1 or simply adding the area of the polygon. Since the normal vector is not taken into account, it is impossible to identify the difference whether or not the polygon model includes a cavity.

  Eventually, by executing the processing according to the above [Equation 12], the frequency distribution calculating means 10 prepares a one-dimensional array composed of elements of a predetermined number MD, and calculates the maximum value of the circumscribed circle radius After the range normalized by (maximum circumscribed circle radius Dmax) is divided equally into a predetermined number of MD elements, the radius D (i) of each circumscribed circle is set to one of the predetermined number MD based on the value. Is obtained by obtaining the number corresponding to the element md, and calculating the inner product value of the unit vector from the center of gravity of the specific triangle formed by the center of gravity of the three polygons to each vertex and the normal vector of the polygon including the vertex The circumscribed circle distribution is calculated by calculating an average value of values obtained by multiplying the area of the polygon as a weight value and performing weighting.

  Next, the frequency distribution calculating means 10 calculates an area ratio distribution that is a frequency distribution of the area ratio between each specific triangle and its circumscribed circle (step S509). Specifically, the frequency Ha (ma) of the element ma is calculated for i = 0,..., N−1 by executing processing according to the following [Equation 13].

[Formula 13]
If α × Dmax ³ × ma / MA ≦ A (i) <α × Dmax ³ × (ma + 1) / MA,
Ha (ma) ← Ha (ma) + SQ
If A (i) ≧ α × Dmax ³ , Ha (MA-1) ← Ha (MA-1) + SQ

In the above [Equation 13], the weight value SQ obtained by multiplying the inner product value of the vector from the center of gravity of the specific triangle to each vertex and the normal vector of each polygon by the area of the polygon is also processed according to the above [Equation 12]. Use the one calculated by. In the above [Equation 13], the area ratio A (i) is not less than a value obtained by multiplying the cube Dmax ³ of the maximum circumscribed circle radius by ma / MA and the correction coefficient α, and multiplying by (ma + 1) / MA and the correction coefficient α. This means that the weight value SQ using three polygons having the vertex of a specific triangle as the center of gravity is added to Ha (ma). The correction coefficient α is a scaling correction coefficient on the horizontal axis, and is set to α = 1.15, for example. The reason why the upper limit of the frequency distribution is set to the cube of the maximum circumscribed circle radius is that, as described above, the area ratio is 1/3 of the value obtained by dividing the square of the circumscribed circle radius by the area of the triangle. Therefore, the reason why α is set is that the area ratio is not an accurate area ratio, and a coefficient such as π is omitted at the time of calculation.

  Eventually, by executing the processing according to [Equation 13], the frequency distribution calculating means 10 prepares a one-dimensional array composed of elements of a predetermined number MA, and calculates the maximum value of the circumscribed circle radius. The range normalized by the value of (the maximum circumscribed circle radius Dmax) raised to the third power is equally divided into a predetermined number of MA elements, and each area ratio A (i) is determined based on the predetermined number MA. The area ratio distribution is calculated by assigning to any element ma and counting the number corresponding to element ma.

Since the circumscribed circle radius depends on the scale of the polygon model, if the distribution is created by normalizing the horizontal axis to the maximum value range, a distribution that does not depend on the scale is obtained. At this time, if a distribution normalized by the maximum value independent of the circumscribed circle radius and the area ratio is created, a distribution that does not depend on the scale between the circumscribed circle radius and the area ratio can be obtained, and the robustness to shape deformation is increased. On the other hand, shape discrimination becomes weak. In the present invention, since the distribution is normalized by the maximum value defined using the maximum circumscribed circle radius, which is the same reference value as the circumscribed circle radius, the maximum value is obtained for the circumscribed circle radius and the area ratio. Although the distribution is different, the distribution maintains the scale ratio between the two, and the spread of the distribution is narrower and sharper than when normalized with independent maximum values of the circumscribed circle radius and area ratio, and the shape discrimination Becomes higher. Actually, the area ratio can take a value equal to or greater than the cube of the maximum value of the circumscribed circle radius (maximum circumscribed circle radius), but is normalized so as to be saturated within the range of the cube of the maximum value. In the present embodiment, as shown in the last line of [Formula 13], when Dmax ³ that is the cube of the maximum circumscribed circle radius Dmax is exceeded, counting is performed with an element corresponding to the maximum value. With this setting, in the case of a sphere, the area ratio distribution has a peak at the maximum value, and has almost the same form as the circumscribed circle distribution. However, as the shape deviates from the sphere, the difference between the area ratio distribution and the circumscribed circle distribution increases.

  The area ratio distribution Ha (ma) (ma = 0,..., MA−1) is calculated by executing the processing according to the above [Equation 13] for N specific triangles. Each element is not just a frequency, but a weight value obtained by multiplying the area of the polygon by the inner product of the vector from the center of the specific triangle to each vertex and the normal vector of each polygon. Ha (ma) indicates a weight value weighted area ratio distribution. When only 1 is added instead of the weight value, or when the area of the polygon is simply added, the normal vector of the polygon is not considered, and the cavity of the polygon model cannot be identified. Therefore, in this embodiment, the weight value SQ is added when calculating the area ratio distribution. However, if the target polygon model is composed of a single part, it is possible to maintain a certain degree of collation accuracy even when adding 1 or simply adding the area of the polygon. Since the normal vector is not taken into account, it is impossible to identify the difference whether or not the polygon model includes a cavity.

Eventually, by executing the processing according to [Formula 13], the frequency distribution calculating means 10 prepares a one-dimensional array composed of elements of a predetermined number MA, and calculates the maximum radius of the circumscribed circle calculated. A range normalized by a value obtained by multiplying the value cubed (Dmax ³ ) by the correction coefficient α is equally divided into a predetermined number MA, and each area ratio A (i) is determined based on the value. Assign to any element ma of the number MA, obtain the number corresponding to the element ma, and obtain a unit vector from the center of gravity of the specific triangle formed by the predetermined points of the three polygons to each vertex and the polygon containing the vertex The area ratio distribution is calculated by calculating an average value of values obtained by multiplying the area of the polygon by the inner product value with the normal vector as a weight value, and performing weighting.

  After the circumscribed circle distribution and the area ratio distribution are calculated, the frequency distribution calculating means 10 calculates a two-dimensional frequency distribution (step S510). Specifically, by executing the processing according to the following [Equation 14], the frequency Hq (mu, mv) of the element mu × mv is calculated for i = 0,..., N−1. .

[Formula 14]
If Dmax × mu / MQ ≦ D (i) <Dmax × (mu + 1) / MQ and α × Dmax ³ × mv / MQ ≦ A (i) <α × Dmax ³ × (mv + 1) / MQ,
Hq (mu, mv) <-Hq (mu, mv) + SQ
Or
If Dmax × mu / MQ ≦ D (i) <Dmax × (mu + 1) / MQ and A (i) ≧ α × Dmax ³ ,
Hq (mu, MQ-1) ← Ha (mu, MQ-1) + SQ

In the above [Equation 14], the weight value SQ obtained by multiplying the inner product value of the vector from the center of gravity of the triangle to each vertex and the normal vector of each polygon by the area of the polygon is also obtained by the processing according to the above [Equation 12]. Use the calculated value. [Expression 14] is a case where the circumscribed circle radius D (i) of the triangle is equal to or larger than the value obtained by multiplying the maximum circumscribed circle radius Dmax by mu / MQ and smaller than the value obtained by multiplying (mu + 1) / MQ. The area ratio A (i) is not less than the value obtained by multiplying the cube Dmax ³ of the maximum circumscribed circle radius by mv / MQ and the correction coefficient α, and smaller than the value obtained by multiplying (mv + 1) / MQ and the correction coefficient α. Furthermore, it means that the weight value SQ using three polygons having the vertex of the triangle as the center of gravity is added to Hq (mu, mv). In some cases, the area ratio A (i) is greater than or equal to the value obtained by multiplying the cube Dmax ³ of the maximum circumscribed circle radius by the correction coefficient α. In this case, the circumscribed circle radius D (i) of the triangle is the maximum. When the circumscribed circle radius Dmax is greater than or equal to the value obtained by multiplying mu / MQ and smaller than the value obtained by multiplying (mu + 1) / MQ, the weight value SQ using three polygons having the vertices of the triangles as centroids is expressed as Hq (mu, MQ -1).

  The two-dimensional frequency distribution Hq (mu, mv) (mu, mv = 0,..., MQ-1) is calculated by executing the processing according to the above [Equation 14] for N triangles. . Each element is not just a frequency, but a weight value obtained by multiplying the inner product value of the vector from the center of gravity of the triangle to each vertex and the normal vector of each polygon by the area of the polygon is added. Hq (mu, mv) represents a weight value-weighted two-dimensional frequency distribution. When only 1 is added instead of the weight value, or when the area of the polygon is simply added, the normal vector of the polygon is not considered, and the cavity of the polygon model cannot be identified. Therefore, in the present embodiment, the weight value SQ is added when calculating the two-dimensional frequency distribution. However, if the target polygon model is composed of a single part, it is possible to maintain a certain degree of collation accuracy even when adding 1 or simply adding the area of the polygon. Since the normal vector is not taken into account, it is impossible to identify the difference whether or not the polygon model includes a cavity.

  Once the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution are calculated, it is next determined whether or not the loop counter LC is equal to or greater than a specified value (step S511). As a result of the determination, if the loop counter LC is less than the specified value, a process of shifting the arrangement of the two groups by 1 is performed (step S512). For example, in the case where the order of the first group is fixed, in the present embodiment, the random number array R2 (k) used for the two groups of the second group and the third group is executed by executing the process according to the following [Formula 15]. ), The order of the random number array R3 (k) is shifted.

[Formula 15]
Ro = R2 (0), Ro3 = R3 (0),
For k = 0, ..., N / 3-2,
R2 (k) ← R2 (k + 1), R3 (k) ← R3 (k + 1) are repeated,
It is assumed that R2 (N / 3-1) = Ro and R3 (N / 3-1) = Ro3.

  When the order of the second group is fixed or when the order of the third group is fixed, the relationship between the groups is changed and the process according to [Formula 15] is executed. In addition, a process of incrementing the loop counter LC (LC ← LC + 1) is also performed. When there is a frequency distribution that has already been calculated, the frequency value corresponding to each element is added to each element of the frequency distribution. In step S512, after shifting the arrangement of the two groups, the combination of the polygons of the two groups and the other group is changed from the first, and the processing of steps S505 to S510 is executed to obtain the circumscribed circle distribution, area A ratio distribution and a two-dimensional frequency distribution are calculated. The calculation process of circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution in steps S505 to S510 is repeated a predetermined number of times set as a specified value. The specified value can be set as appropriate, but is about 10 when the total number of polygons N = 10000.

  That is, every time a circumscribed circle distribution, an area ratio distribution, and a two-dimensional frequency distribution are calculated, the order of polygons in two of the three groups is changed to obtain a circumscribed circle distribution, an area ratio distribution, and a two-dimensional distribution. The process of calculating the frequency distribution anew is repeated. When the loop counter LC reaches the specified value, it is determined in step S511 that the loop counter LC is equal to or greater than the specified value, so that the three types of frequency distribution are normalized (step S513).

  Specifically, by multiplying Hd (md) calculated by the above [Equation 12] by 100 / {SQsum × LC} and replacing it with Hd (md), the unit is normalized to the rate [%]. Yes. That is, the value Hd (md) of each element is divided by the multiplication value of the weight sum value SQsum, which is the sum value of the weight values SQ, and the loop count LC. Since the weight value SQ is obtained by using the area of the polygon, even if the polygon model has a different total area area, that is, a polygon model with a different scale, it is converted to a circumscribed circle distribution of the same scale, Judgment is possible as a model. In addition, since it is divided by the loop number LC, an average value for the loop number is obtained. Since Hd (md) has a frequency distribution, it needs to be a value of 0 or more. However, since the weight value SQ calculated by [Equation 12] can take a negative value, the obtained Hd (md) may be a negative value. In this case, an absolute value is taken (that is, − 1), and Hd (md) is changed to a value of 0 or more.

  Further, the unit is normalized to the rate [%] by multiplying Ha (ma) calculated by the above [Equation 13] by 100 / {SQsum × LC} and replacing it with Ha (ma). That is, the value Ha (ma) of each element is divided by the multiplication value of the weight sum value SQsum, which is the sum value of the weight values SQ, and the loop count LC. Since the weight value SQ is obtained by using the area of the polygon, even if the polygon models have different total area values, that is, polygon models with different scales, they are converted to the same scale area ratio distribution, Judgment is possible as a model. In addition, since it is divided by the loop number LC, an average value for the loop number is obtained. Since Ha (ma) has a frequency distribution, it needs to be a value of 0 or more. However, since the weight value SQ calculated by [Equation 12] can take a negative value, Ha (ma) obtained by [Equation 13] may be a negative value. (Ie, multiply by -1), and change Ha (ma) to a value of 0 or more.

  Further, by multiplying Hq (mu, mv) calculated by the above [Equation 14] by 100 / {SQsum × LC} and replacing it with Hq (mu, mv), the unit is normalized to the rate [%]. ing. That is, the value Hq (mu, mv) of each element is divided by the multiplication value of the weight sum value SQsum, which is the sum value of the weight values SQ, and the loop count LC. Since the weight value SQ is obtained by using the area of the polygon, even if the polygon model has a different total area value of the polygon, that is, a polygon model with a different scale, it is converted into a two-dimensional frequency distribution of the same scale, Judgment is possible as a polygon model. In addition, since it is divided by the loop number LC, an average value for the loop number is obtained. Since Hq (mu, mv) has a frequency distribution, it needs to be a value of 0 or more. However, since the weight value SQ calculated by [Equation 12] can take a negative value, Hq (mu, mv) obtained by [Equation 14] may be a negative value. Take an absolute value (ie, multiply by -1) and change Hq (mu, mv) to a value greater than or equal to zero.

  In the present embodiment, when calculating the circumscribed circle radius of a specific triangle and the area ratio of the triangle, a specific triangle having three centroids as the centroids of three polygons is created. The vertex of the specific triangle is preferably the center of gravity having the average coordinates of each vertex of the polygon, but it can also be a specific triangle connecting predetermined points on the polygon other than the center of gravity. The predetermined points on the polygon include, for example, any vertex constituting the polygon, a point having a value that is exactly halfway between the maximum value and the minimum value for each xyz coordinate of the polygon, and the polygon is a specific triangle. In this case, the inner center, the outer center, the vertical center, the side center, etc. can be used.

<3.3.2. Second method>
Next, the second method will be described. FIG. 13 is a flowchart showing details of the frequency distribution calculation processing by the second method. The same processes as those in the first method are denoted by the same reference numerals and description thereof is omitted. Also in the second method, steps S501 to S509 are performed in the same manner as in the first method. Then, similar to step S513 of the first method, normalization of the three types of frequency distribution is performed (step S513). In the second method, normalization is forcibly performed after calculation of the three frequency distributions. Specifically, the unit is normalized to the rate [%] by multiplying Hd (md) calculated by the above [Equation 12] by 100 / SQsum and replacing it with Hd (md). Further, the unit is normalized to the rate [%] by multiplying Ha (ma) calculated by the above [Equation 13] by 100 / SQsum and replacing it with Ha (ma). Further, Hq (mu, mv) calculated by the above [Equation 14] is further multiplied by 100 / SQsum to replace Hq (mu, mv), thereby normalizing the unit to a rate [%]. Unlike the first method, division by the loop counter LC is not performed.

  Once the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution are normalized, it is next determined whether or not the loop counter LC is 1 or more (step S521). This determines whether or not the frequency distribution is calculated for the first time. When the loop counter LC is less than 1, it means that the frequency distribution is calculated for the first time, and therefore processing for shifting the arrangement of the two groups by 1 is performed (step S512). Specifically, as in step S512 of the first method, by executing the processing according to [Formula 15], two of the arrays R1 (k), R2 (k), and R3 (k) The order of the array is shifted.

  In step S512, after shifting the arrangement of the two groups, the combination of the polygons of the two groups and the other group is changed from the first, and the processes of steps S505 to S509, S513, and S521 are executed, Normalize circular distribution, area ratio distribution, and two-dimensional frequency distribution. That is, every time a circumscribed circle distribution, an area ratio distribution, and a two-dimensional frequency distribution are calculated, the order of polygons in two of the three groups is changed to obtain a circumscribed circle distribution, an area ratio distribution, and a two-dimensional distribution. Repeat the process of calculating the frequency distribution anew. In the second and subsequent times, in step S521, since the loop counter LC is determined to be 1 or more, the immediately preceding circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution are compared (step S522). First, a process according to the following [Equation 16] is executed to calculate the Euclidean distance DD between the calculated circumscribed circle distribution and the immediately preceding circumscribed circle distribution. The Euclidean distance is a distance in the Euclidean space given as a value obtained by squaring the absolute value of the difference between the frequencies of each element. The Euclidean distance DD is obtained as a distance between two points in the MD dimensional Euclidean space.

[Formula 16]
DD = Σ _{md = 0, MD-1} [{Hd (md) −Hdp (md)} ² / MD] ^1/2

In the above [Expression 16], the subscript “md = 0, MD-1” of Σ is the following [...] ^1/2 when md takes all integers from 0 to MD-1. The sum is calculated. Hdp (md) represents the circumscribed circle distribution just before.

  Subsequently, by executing processing according to the following [Equation 17], the Euclidean distance DA between the calculated area ratio distribution and the immediately preceding area ratio distribution is calculated. The Euclidean distance DA is obtained as a distance between two points in the MA dimensional Euclidean space.

[Formula 17]
DA = Σ _{ma = 0, MA-1} [{Ha (ma) −Hap (ma)} ² / MA] ^1/2

In the above [Equation 17], the subscript “ma = 0, MA-1” of Σ is the following [...] ^1/2 when ma takes all integers from 0 to MA-1. The sum is calculated. Hap (ma) indicates the immediately preceding area ratio distribution.

  Subsequently, by executing processing according to the following [Equation 18], the Euclidean distance DQ between the calculated two-dimensional frequency distribution and the immediately preceding two-dimensional frequency distribution is calculated. The Euclidean distance DQ is obtained as a distance between two points in the MQ dimension Euclidean space.

[Formula 18]
_{DQ = Σ mv = 0, MQ} -1 Σ mu = 0, MQ-1 [{Hq (mu, mv) -Hqp (mu, mv)} 2 / MQ 2] 1/2

In the above [Expression 18], the subscript “mu = 0, MQ-1” of Σ is the following [...] ^1/2 when mu takes all integers from 0 to MQ-1. The sum is calculated. The subscript “mv = 0, MQ-1” of Σ calculates the sum of the following Σ _... [...] ^1/2 when mv takes all integers from 0 to MQ-1. It is shown that. Hqp (mu, mv) indicates the immediately preceding two-dimensional frequency distribution.

  Next, the frequency distribution calculating means 10 compares the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution Euclidean distance calculated in step S522 with the respective determination threshold values (step S523). Specifically, when the Euclidean distances DD, DA, and DQ are both smaller than the determination threshold, it is determined that the state is saturated, and when one of the Euclidean distances DD, DA, and DQ is equal to or greater than the determination threshold. It is determined that it is in the process of generation. The determination threshold can be arbitrarily set, but here it is set to 0.05.

  When it is determined in step S523 that the state is saturated, that is, when similarity is recognized between the two, the frequency distribution calculating means 10 officially calculates the circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution calculated last. Are determined to have three frequency distributions (step S524). That is, the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution immediately after the calculation are compared with the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution obtained immediately before that, and similarities are recognized as a result of the comparison. In this case, the circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution immediately after calculation are set as the circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution to be verified. At this time, since Hd (md) has a frequency distribution, it needs to be a value of 0 or more. Therefore, when the obtained Hd (md) is a negative value, the absolute value is taken (that is, multiplied by -1), and Hd (md) is changed to a value of 0 or more. Further, since Ha (ma) has a frequency distribution, it needs to be a value of 0 or more. Therefore, when the obtained Ha (ma) is a negative value, the absolute value is taken (that is, multiplied by -1), and Ha (ma) is changed to a value of 0 or more. Moreover, since Hq (mu, mv) has a frequency distribution, it needs to be a value of 0 or more. Therefore, when the obtained Hq (mu, mv) is a negative value, the absolute value is taken (that is, multiplied by -1), and Hq (mu, mv) is changed to a value of 0 or more.

  If it is determined in step S523 that the process is in the process of being generated, the process of shifting the arrangement of the two groups by 1 is performed (step S512), and then the processes of steps S505 to S509, S513, S521, and S522 are repeatedly executed.

  FIG. 14 shows a specific triangle and its circumscribed circle for obtaining a circumscribed circle distribution, an area ratio distribution, and a two-dimensional frequency distribution obtained from the target model. FIG. 14 shows a polygon model when the polygon is triangular. For the three polygons selected from the polygon model, a specific triangle is created by connecting the centroids having the average coordinates of the vertices of each polygon. Then, a circumscribed circle of the specific triangle is obtained. FIG. 14 shows the relationship between a specific triangle and its circumscribed circle radius. In FIG. 14, the downward arrow indicates the radius of the circumscribed circle.

  In general, when the polygon model has a shape close to a sphere, the circumscribed circle of a specific triangle connecting the centers of three randomly selected polygons is a circle obtained by cutting the sphere along a plane formed by the three centers. become. That is, in the case of a sphere, the circumscribed circle radius often coincides with the radius of the sphere, and in the circumscribed circle distribution, a peak appears at one location corresponding to the radius of the sphere. However, as the polygon density gets closer to the polyhedron, the circumscribed circle distribution spreads toward the shorter circumscribed circle radius, and the circumscribed circle distribution becomes more complex as the polygon model deviates from the sphere. Therefore, the circumscribed circle distribution using the circumscribed circle radius is extremely effective for identifying the 3D shape.

  However, even in the case of a cylinder with a relatively low height, the circumscribed circle radius of a specific triangle connecting the centers of three randomly selected polygons often takes a value close to the radius of the circle on the bottom of the cylinder. The circular distribution has a form in which a peak appears at one location corresponding to the radius of the bottom surface of the cylinder, as in the case of a sphere, and may be indistinguishable from the circumscribed circle distribution of the sphere. On the other hand, when the polygon model is a sphere, most of the area ratio exceeds the cube of the maximum circumscribed circle radius set to the maximum value, and the area ratio distribution has a peak at the maximum value portion. The shape is almost the same as the circumscribed circle distribution. However, as the polygon model deviates from the sphere, the value that exceeds the cube of the maximum circumscribed circle radius decreases, and the area ratio distribution shifts to the 0 side. Equipped with shape discrimination that is equivalent to or better than However, since it has a complicated form different from the circumscribed circle distribution except for the sphere, it has a function to supplement the circumscribed circle distribution.

  FIG. 15 shows a matching example of a 3D sphere model that is a 3D polygon model that represents a sphere and a 3D cylinder model that is a 3D polygon model that represents a cylinder. 15A is a 3D spherical model, FIG. 15B is a 3D cylindrical model, FIG. 15C is a one-dimensional frequency distribution of the 3D spherical model, and FIG. 15D is a one-dimensional frequency distribution of the 3D cylindrical model. FIG. 15E shows the two-dimensional frequency distribution of the 3D spherical model, and FIG. 15F shows the two-dimensional frequency distribution of the 3D cylindrical model. As shown in FIGS. 15C and 15D, the area ratio distribution in the case of a cylinder having a relatively low height that cannot be distinguished from the circumscribed circle distribution does not generate a peak at the maximum value like a sphere. Since the peak position is shifted near the center, it is possible to distinguish between a sphere and a cylinder in the area ratio distribution. Also, since the area ratio is a dimensionless quantity, it does not depend on the scale of the polygon model like the circumscribed circle radius, so a fixed upper limit is set when plotting in a one-dimensional or two-dimensional frequency distribution. Thus, a frequency distribution that does not depend on the scale of the polygon model can be calculated. However, even if the polygon model has a complicated shape and the range that the circumscribed circle distribution can take (the maximum circumscribed circle radius) becomes wider, the frequency distribution of the area ratio does not change significantly, and the shape distinguishability is weak. Therefore, in this embodiment, the maximum value of the area ratio distribution is set to a value depending on the maximum circumscribed circle radius, and when the possible range of the circumscribed circle distribution (maximum circumscribed circle radius) becomes wider, the area ratio distribution is interlocked. Shifts greatly in the 0 direction, and responds sharply to differences in shape. By plotting the circumscribed circle distribution in the range of the maximum circumscribed circle radius, the scale of the horizontal axis of the circumscribed circle distribution and the area ratio distribution is automatically maintained at a predetermined ratio without depending on the scale of the polygon model. This made it possible to identify shapes with minute differences such as spheres, cylinders, and figures with different poses.

<3.4. Frequency distribution matching process>
Next, the frequency distribution matching process in step S200 will be described. FIG. 16 is a flowchart showing the frequency distribution matching process. First, the frequency distribution matching unit 20 acquires the frequency distribution extracted from the restriction model database 40 (step S610). As frequency distribution, circumscribed circle distribution Hdo (re, md) (md = 0,..., MD-1), area ratio distribution Hao (re, ma) (ma = 0,..., MA-1), A two-dimensional frequency distribution Hqo (re, mu, mv) (mu, mv = 0,..., MQ-1) is acquired.

  Next, the frequency distribution matching unit 20 calculates a correlation coefficient between each element between the circumscribed circle distribution of the target model and the circumscribed circle distribution of the restriction model extracted from the restriction model database 40 (step S620). The frequency distribution matching unit 20 executes the process according to the following [Equation 19], whereby the average value Ad of the circumscribed circle distribution Hd (md) of the target model, the circumscribed circle distribution Hdo (re , Md) is calculated as an average value Ado (re).

[Formula 19]
Ad = Σ _{md = 0, MD-1} Hd (md) / MD
Ado (re) = Σ _{md = 0, MD-1} Hdo (re, md) / MD

  Subsequently, by executing processing according to the following [Equation 20], the standard deviation Sd of the circumscribed circle distribution Hd (md) of the target model and the standard deviation Sdo of the circumscribed circle distribution Hdo (re, md) of the regulated model (Re) is calculated.

[Formula 20]
Sd = [Σ _{md = 0, MD-1} (Hd (md) −Ad) ² ] ^1/2
Sdo (re) = [Σ _{md = 0, MD-1} (Hdo (re, md) −Ado (re)) ² ] ^1/2

  Strictly speaking, the standard deviation needs to be further divided by a constant MD in {} of the above [Equation 20]. However, since the purpose here is to calculate the correlation coefficient, it is necessary to divide by the constant MD in n for calculating the covariance of the numerator in [Equation 21] to be described later. The operation of dividing by the constant MD is canceled (the denominator is divided twice by the square root of the constant MD).

  Next, by using the calculated average value and standard deviation, a process according to the following [Equation 21] is executed, whereby the circumscribed circle distribution of the target model and the circumscribed circle distribution of the restriction model corresponding to the record re A correlation coefficient Dd (re) is calculated.

[Formula 21]
Dd (re) = [Σ _{md = 0, MD-1} (Hd (md) −Ad) × (Hdo (re, md) −Ado (re))] / (Sdo (re) × Sd)

  In the above [Equation 21], the subscript “md = 0, MD-1” of Σ indicates that the sum is obtained when md takes all integers from 0 to MD-1. The correlation coefficient Dd (re) is obtained by dividing the covariance of the frequency distributions Hd (md) and Hdo (re, md) by their standard deviations. In general, the processing load is high when the square root of the denominator is divided twice as in the above equation [21]. For this reason, in the field of image processing, what is required only by the product-sum operation of numerators is called “correlation coefficient”, and Dd (re) shown in the above [Equation 21] is called “normalized correlation coefficient”. There are also customs. When collation is performed using the normalized correlation coefficient as in [Equation 21], the normalization phase can be obtained without normalizing the three frequency distributions in FIGS. 10 and 13 (S513). Since the value of the relation number is the same, the process of S513 can be omitted. (The absolute value of the frequency distribution is canceled by division of the standard deviation. However, normalization processing is required when plotting the frequency distribution on the screen as a graph or image.) Conversely, the three frequency distributions When normalization (S513) is performed, a “correlation coefficient” that only needs to be a product-sum operation of numerators may be calculated.

  Next, the frequency distribution matching unit 20 compares the correlation coefficient Dd (re) of the circumscribed circle distribution calculated in step S620 with the determination threshold value (step S630). When the correlation coefficient Dd (re) is greater than or equal to the determination threshold value, it is determined as conforming, and when the correlation coefficient Dd (re) is smaller than the determination threshold value, it is determined as non-conforming. The determination threshold value can be arbitrarily set as long as it is a positive value. Here, the correlation coefficient value taking a range of +20.0 (−1 to +1) is multiplied by 100 and expressed in% dimension. ).

  If it is determined in step S630 that the data is suitable, the frequency distribution matching unit 20 calculates a correlation coefficient between the elements based on the area ratio distribution of the target model and the area ratio distribution of the restriction model (step S640). First, by executing processing according to the following [Equation 22], the average value Aa of the area ratio distribution Ha (ma) of the target model, and the average value Aao () of the area ratio distribution Hao (re, ma) of the regulated model re) is calculated.

[Formula 22]
Aa = Σ _{ma = 0, MA-1} Ha (ma) / MA
Aao (re) = Σ _{ma = 0, MA-1} Hao (re, ma) / MA

  Subsequently, by executing the processing according to the following [Equation 23], the standard deviation Sa of the area ratio distribution Ha (ma) of the target model and the standard deviation Sao of the area ratio distribution Hao (re, ma) of the restriction model are performed. (Re) is calculated.

[Formula 23]
Sa = [ _{Σma = 0, MA-1} (Ha (ma) −Aa) ² ] ^1/2
Sao (re) = [Σma _{= 0, MA-1} (Hao (re, ma) −Aao (re)) ² ] ^1/2

  Strictly speaking, the standard deviation needs to be further divided by a constant MA within {} in the above [Equation 23]. However, since the purpose here is to calculate the correlation coefficient, it is necessary to divide by the constant MA even in the term for calculating the covariance of the numerator in [Equation 24], which will be described later. The operation of dividing by the constant MA is canceled (the denominator is divided by the square root of the constant MA twice).

  Next, by using the calculated average value and standard deviation, the processing according to the following [Equation 24] is executed, so that the area ratio distribution of the target model and the area ratio distribution of the regulation model corresponding to the record re A correlation coefficient Da (re) is calculated.

[Formula 24]
Da (re) = [Σma _{= 0, MA-1} (Ha (ma) −Aa) × (Hao (re, ma) −Aao (re))] / (Sao (re) × Sa)

  In the above [Equation 24], the subscript “ma = 0, MA−1” of Σ indicates that the sum is obtained when ma takes all integers from 0 to MA−1. The correlation coefficient Da (re) is obtained by dividing the covariance of the frequency distributions Ha (ma) and Hao (re, ma) by the respective standard deviations. In general, the processing load is high when dividing the square root of the denominator twice as in the calculation of [Equation 24]. For this reason, in the field of image processing, what is required only by the product-sum operation of numerators is called “correlation coefficient”, and Da (re) shown in the above [Equation 24] is called “normalized correlation coefficient”. There are also customs.

  Next, the frequency distribution matching unit 20 compares the correlation coefficient Da (re) of the area ratio distribution calculated in step S640 with the determination threshold value (step S650). If the correlation coefficient Da (re) is greater than or equal to the determination threshold value, it is determined as conforming, and if the correlation coefficient Da (re) is smaller than the determination threshold value, it is determined as non-conforming. The determination threshold value can be arbitrarily set as long as it is a positive value. Here, the correlation coefficient value taking a range of +20.0 (−1 to +1) is multiplied by 100 and expressed in% dimension. ).

  If it is determined in step S650 that the data is suitable, the frequency distribution matching unit 20 calculates a correlation coefficient between the elements using the two-dimensional frequency distribution of the target model and the two-dimensional frequency distribution of the restriction model (step S660). ). First, by executing processing according to the following [Equation 25], the average value Aq of the two-dimensional frequency distribution Hq (mu, mv) of the target model, the two-dimensional frequency distribution Hqo (re, mu, mv) of the regulated model ) Average value Aqo (re).

[Formula 25]
Aq = Σ _{mv = 0, MQ-1 Σmu = 0, MQ-1} Hq (mu, mv) / MQ ²
_{Aqo (re) = Σ mv =} 0, MQ-1 Σ mu = 0, MQ-1 Hqo (re, mu, mv) / MQ 2

  Subsequently, by executing processing according to the following [Equation 26], the standard deviation Sq of the two-dimensional frequency distribution Hq (mu, mv) of the target model, the two-dimensional frequency distribution Hqo (re, mu, The standard deviation Sqo (re) of mv) is calculated.

[Formula 26]
Sq = [Σ _{mv = 0, MQ-1} Σmu _{= 0, MQ-1} (Hq (mu, mv) −Aq) ² ] ^1/2
_{Sqo (re) = [Σ mv} = 0, MQ-1 Σ mu = 0, MQ-1 (Hqo (re, mu, mv) -Aqo (re)) 2] 1/2

Strictly speaking, the standard deviation needs to be further divided by a constant MQ ² in {} of the above [Equation 26]. However, since the purpose here is to calculate the correlation coefficient, it is necessary to divide by the constant MQ ² even in the term for calculating the covariance of the numerator in [Equation 27] described later. Then, the operation of dividing by the constant MQ ² is canceled (the denominator is divided twice by the square root of the constant MQ ² ).

  Next, using the calculated average value and standard deviation, the process according to the following [Equation 27] is executed, whereby the two-dimensional frequency distribution of the target model and the two-dimensional frequency of the restriction model corresponding to the record re A distribution correlation coefficient Dq (re) is calculated.

[Formula 27]
Dq (re) = [Σ _{mv = 0, MQ-1} Σmu _{= 0, MQ-1} (Hq (mu, mv) −Aq) × (Hqo (re, mu, mv) −Aqo (re))] / (Sqo (re) × Sq)

  In the above [Equation 27], the subscript “mv = 0, MQ-1” of Σ indicates that the sum is obtained when mv takes all integers from 0 to MQ-1. Further, the subscript “mu = 0, MQ-1” of Σ indicates that the sum is obtained when mu takes all integers from 0 to MQ-1. The correlation coefficient Dq (re) is obtained by dividing the covariance of the frequency distributions Hq (mu, mv) and Hqo (re, mu, mv) by the respective standard deviations. In general, the processing load is high when the square root of the denominator is divided twice as in the above equation [27]. For this reason, in the field of image processing, what is required only by the product-sum operation of numerators is called “correlation coefficient”, and Dq (re) shown in the above [Equation 27] is called “normalized correlation coefficient”. There are also customs.

  Next, the frequency distribution matching unit 20 compares the correlation coefficient Dq (re) of the two-dimensional frequency distribution calculated in step S660 with the determination threshold value (step S670). When the correlation coefficient Dq (re) is greater than or equal to the determination threshold, it is determined as conforming, and when the correlation coefficient Dq (re) is smaller than the determination threshold, it is determined as nonconforming. The determination threshold value can be arbitrarily set as long as it is a positive value. Here, the correlation coefficient value taking a range of +30.0 (−1 to +1) is multiplied by 100 and expressed in% dimension. ).

  If it is determined in step S630, S650, or S670 that it is non-conforming, the frequency distribution matching unit 20 finishes matching the target model with the restriction model of the record re, and performs matching with the restriction model of the next record re + 1. Transition. When the process according to the flowchart of FIG. 16 is executed for all records in the restriction model database 40 and there is at least one applicable restriction model, the output should be restricted to the target model (output) Inappropriate) ”, the collation process in step S200 is terminated.

  The three-dimensional object formation data output restriction device 100 not only determines conformity / nonconformity, but also displays the correlation coefficient calculated by the frequency distribution matching unit 20 in steps S620, S640, and S660 shown in FIG. Can also be output. Further, by visually confirming the correlation coefficient displayed and output by the display unit 6, for example, in the case of non-conformity, it is possible to determine not only the non-conformity but also the degree of non-conformity. Furthermore, when the display unit 6 outputs the two-dimensional frequency distribution as shown in FIG. 3C, the two parameters can be easily grasped intuitively.

<Data output to 4.3D printer>
In step S200, when the frequency distribution matching unit 20 determines that “the output should not be restricted (output appropriate)”, the target model is output to the 3D printer 7 which is a three-dimensional object formation apparatus. That is, the target model that is a polygon model whose output is permitted by the three-dimensional object modeling data output restriction device is output to the three-dimensional object modeling device that models the three-dimensional object. On the other hand, if the frequency distribution matching means 20 determines that “the output should be regulated (output inappropriate)”, the target model is not output to the 3D printer 7 which is a three-dimensional object forming apparatus. If it takes a long time to determine whether output is appropriate or not, whether the target model is output to the 3D printer 7 and whether the output is appropriate or inappropriate in parallel with the output process (three-dimensional object modeling process) of the 3D printer 7. If the output is unsuitable, an output stop command may be output to the 3D printer 7. At this time, from the user's point of view, it is only possible to confirm that the three-dimensional object shaping process in the 3D printer is started by issuing a single command to output the target model. I do not notice that the execution of the process for is started.

<5. Calculation and registration of regulatory model frequency distribution>
As a modified example, the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution calculated for the restriction model are separated from the three-dimensional object formation data output restriction device provided with the frequency distribution matching unit 20 in three dimensions. You may make it register and transmit to the data output control apparatus for object shaping | molding via a network.

  FIG. 17 is a hardware configuration diagram of a three-dimensional object formation system including a three-dimensional object formation data output restriction device according to a modification. In the three-dimensional object formation system shown in FIG. 17, the three-dimensional object formation data output restriction device 101 communicates with the public network such as the Internet in the configuration of the three-dimensional object formation data output restriction device 100 shown in FIG. 7. The network communication unit 8 is provided. The regulation model frequency distribution calculation device 102 can be realized by a general-purpose computer. As shown in FIG. 17, a CPU (Central Processing Unit) 1a, a RAM (Random Access Memory) 2a that is a main memory of the computer, A large-capacity storage device 3a such as a hard disk or flash memory for storing programs and data executed by the CPU 1a, a key input I / F (interface) 4a such as a keyboard and a mouse, and an external device such as a data storage medium A data input / output I / F (interface) 5a for data communication, a display unit 6a that is a display device such as a liquid crystal display, and a network communication unit 8a for communicating with a public network such as the Internet are provided. Connected through. The network communication unit 8 of the three-dimensional object formation data output restriction device 101 and the network communication unit 8a of the restriction model frequency distribution calculation device 102 communicate with each other, and the restriction model frequency distribution calculation device 102 transmits the three-dimensional object formation data output restriction device 101. In addition, it is possible to transmit three types of frequency distributions calculated for the regulatory model.

  In FIG. 17, the three-dimensional object formation data output restriction device 101 and the 3D printer 7 are shown in a separated form. However, most of the currently available 3D printer products include the three-dimensional object formation data output restriction device 101. Constituent elements, such as CPU1, RAM2, storage device 3, key input I / F4 (not a keyboard / mouse for general-purpose computers, but several buttons at a numeric keypad level), data input / output I / F5, display unit 6 (several lines) A small liquid crystal panel capable of displaying the above-mentioned characters, a touch panel is often overlapped to serve also as a key input I / F 4), and a network communication unit 8 (wireless LAN function) is also provided in a small but overlapping manner. Accordingly, the 3D printer itself can directly receive the data for modeling a three-dimensional object via an external storage medium or the Internet, and can be operated to model a three-dimensional object alone (especially in the case of a 3D printer for consumer use, this form is preferred. Many). That is, the three-dimensional object formation data output restriction device 101 and the 3D printer 7 shown in FIG. 17 are often housed in one housing and distributed as a product called “3D printer”.

  In the regulated model frequency distribution calculation device 102, the CPU 1a executes a program stored in the storage device 3a, thereby realizing a second frequency distribution calculation unit and a frequency distribution transmission unit. The second frequency distribution calculation means realized by the restriction model frequency distribution calculation device 102 has the same function as the frequency distribution calculation means 10 realized by the three-dimensional object formation data output restriction device 100, and is compatible with the restriction model. The circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution are calculated as the three types of frequency distribution. The frequency distribution transmission means transmits the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution, which are three types of frequency distributions calculated for the restriction model, to the three-dimensional object formation data output restriction device 101. In the three-dimensional object shaping data output restriction device 101, when the network communication unit 8 receives the frequency distribution from the restriction model frequency distribution calculation device 102, the CPU 1 executes a predetermined program and functions as a frequency distribution registration unit. The frequency distribution is registered in the regulation model database 40 realized by the storage device 3.

<6. Cloud-type 3D object modeling system>
The present invention can also be applied to a cloud-type three-dimensional object modeling system. “Cloud type 3D object modeling system” means that when the target model requested by the user is raised to the cloud, it will be checked for output on the cloud (including manual visual inspection and 3D printer output consistency check) Generally used in the sense of 3D printer consignment output service that outputs the 3D object modeling of the permitted target model with a 3D printer on the cloud and returns the output modeling object to the client. In this application, the former output The focus is on conducting a pass / fail examination on a remote computer on the cloud, and it is not essential to perform solid object modeling (3D printer output) on the cloud. FIG. 18 is a hardware configuration diagram of a cloud-type three-dimensional object modeling system. In the three-dimensional object formation system shown in FIG. 18, the three-dimensional object formation data output restriction device is realized by the output control terminal 201 and the processing server 202. In the three-dimensional object formation system shown in FIG. 18, the output control terminal 201 has a hardware configuration equivalent to the computer shown as the three-dimensional object formation data output restriction device 101 in FIG. 17. That is, the output control terminal 201 includes a CPU 11, a RAM 12, a storage device 13, a key input I / F 14, a data input / output I / F 15, a display unit 16, and a network communication unit 18, which are connected to each other via a bus. .

  The processing server 202 can be realized by incorporating a dedicated program into a general-purpose computer. As shown in FIG. 18, a CPU 11a, a RAM 12a, a storage device 13a, a key input I / F 14a, a data input / output I / F 15a, a display unit 16a, and a network communication unit 18a are connected to each other via a bus. The network communication unit 18 of the output control terminal 201 and the network communication unit 18a of the processing server 202 communicate with each other, and send output suitability data from the processing server 202 to the output control terminal 201 based on the judgment of output suitability. It is possible. In FIG. 18, the output control terminal 201 and the 3D printer 7 are shown in a separated form. However, as in the example of FIG. 17, the CPU 11, the RAM 12, and the constituent elements of the output control terminal 201 are added to the 3D printer product. The storage device 13, the key input I / F 14, the data input / output I / F 15, the display unit 16, and the network communication unit 18 may be provided in an overlapping manner.

  FIG. 19 is a functional block diagram of a cloud-type three-dimensional object modeling system. The processing server 202 constituting the cloud-type three-dimensional object modeling system includes a target model receiving unit 50 and an output suitability data transmitting unit 60 in addition to each unit of the three-dimensional object modeling data output restriction device shown in FIG. It has a configuration. The target model storage unit 31 stores not the target model itself but three types of frequency distributions calculated for the target model. Further, the frequency distribution calculating means 10 is configured to be provided not in the processing server 202 but in the output control terminal 201.

  Components having the same functions as those of the three-dimensional object formation data output restriction device shown in FIG. The target model receiving means 50 is means for receiving the frequency distribution of the target model transmitted from the output control terminal 201 and registering it in the target model storage means 31. The CPU 11a executes a predetermined program, and the network communication section This is realized by controlling 18a. The output suitability data transmission means 60 is means for sending the output suitability data to the output control terminal 201 based on “whether or not the output should be regulated” determined by the frequency distribution matching means 20, and the CPU 11a This is realized by executing a predetermined program and controlling the network communication unit 18a.

  The processing server 202 is a cloud computer connected to a network such as the Internet and can be accessed from a number of output control terminals. In the conventional server type computer, when the access of many users is concentrated, the responsiveness becomes slow and it often causes trouble for the user. In the cloud type, the physical configuration of the computer is dynamically changed by the virtualization technology. This makes it possible to always maintain a stable response. Generally, the processing server 202 is physically realized by a plurality of computers.

  The processing operation of the cloud-type three-dimensional object modeling system shown in FIGS. 18 and 19 will be described. In the output control terminal 201, when the user specifies a target model to be output via the key input I / F 14, the CPU 11 extracts the specified target model stored in the storage device 13 and specifies the target model. A model ID which is identification information to be assigned is assigned. Then, the CPU 11 performs processing on the target model to which the model ID is assigned according to the flowchart shown in FIG. 10 or FIG. 13, and the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution. Generate a frequency distribution consisting of Further, the CPU 11 transmits the generated frequency distribution to an address such as a URL set in advance in the storage device 13 via the network communication unit 18. By using a method of transmitting a frequency distribution with a significantly smaller amount of information than polygon data, not only the transmission time is greatly shortened, but also the polygon data that is a copyrighted work is not transmitted to the processing server 202 side. Since no copy remains on the processing server 202 side, copyright infringement can be avoided.

  In parallel, the CPU 11 transmits the target model to which the model ID is assigned to the data processing unit 7a of the 3D printer 7 via the data input / output I / F 15. The target model received from the output control terminal 201 is held in the printer queue in the data processing unit 7a, and enters a standby state as an output job. At this time, it is possible to execute only the process of converting the polygon format data, which is the pre-processing in the 3D printer output, into the data in the stack format, and to enter the standby state when the data is converted into the stack format data. . Since this data processing load is also reasonably high, if the output suitability determination is completed during this time, it is possible to prevent the user from feeling an extra waiting time.

  In the processing server 202, when the target model receiving unit 50 receives the frequency distribution of the target model transmitted from the output control terminal 201, it stores the frequency distribution in the target model storage unit 31. Here, according to the flowchart shown in FIG. 9, the frequency distribution matching means 20 performs processing, and determines whether the target model corresponding to the received frequency distribution is suitable for output. Output propriety data as a result of output propriety is passed from the frequency distribution matching unit 20 to the output propriety data transmitting unit 60. Then, the output suitability data transmission means 60 transmits the output suitability data with the model ID added to the output control terminal 201 that is the transmission source (access source) of the frequency distribution.

  In the output control terminal 201, when the network communication unit 18 receives the output suitability data from the processing server 202, the CPU 11 sends the received output suitability data to the data processing unit 7a of the 3D printer 7 via the data input / output I / F 15. Send to. The data processing unit 7a refers to the output job in the printer queue by using the model ID given to the received output suitability data. If the output suitability data is “appropriate (output proper)”, the data processing unit 7a changes the output job from the standby state to the output state, and outputs the target model to the output unit 7b. If the output suitability data is “No (output unsuitable)”, the data processing unit 7a discards the output job. That is, it is deleted from the printer queue.

<7. Modified example>
The preferred embodiments of the present invention have been described above. However, the present invention is not limited to the above embodiments, and various modifications can be made. For example, in the above embodiment, the polygon to be processed is a triangle, but it may be a polygon more than a quadrangle. In addition, the regulatory model and the target model are not polygonal models, but AMF (Additive Manufacturing File), FAV (FAbricatable Voxel, a format proposed by Fuji Xerox and Keio University), which are being considered as successor standards of the STL format, etc. Even for 3D data described in curved surface shape or voxel format, feature points are randomly selected to form a specific triangle, and circumscribed circle distribution, area ratio distribution, and two-dimensional frequency distribution are calculated. Verification can be performed.

  Further, in the above embodiment, the matching is performed using the circumscribed circle distribution, the area ratio distribution, and the two-dimensional frequency distribution as the three types of frequency distributions, but the one-dimensional circumscribed circle distribution and the area ratio distribution are not used. Matching may be performed using only the two-dimensional frequency distribution to determine whether the output is appropriate. When one or both of the circumscribed circle distribution and the area ratio distribution are used, the accuracy of matching is further increased, but the output suitability can be determined with high accuracy even with only the two-dimensional frequency distribution.

  In the above embodiment, the polygon center of gravity having the average coordinates of each vertex of the polygon is used as one point on the polygon for forming the triangle. If the center of gravity is used, the present invention is not limited to a triangular shape and can be applied to a polygon having an arbitrary number of vertices, but may be a point other than the center of gravity of the polygon as long as it is a point on the polygon. For example, as a point on a polygon, when the polygon is a triangle, an inner center / outer center / vertical / side center can be used.

  Further, in the above-described embodiment, in order to calculate the frequency distribution based on the value obtained by dividing the square of the circumscribed circle radius of the triangle by the area of the triangle, the radius of the circumscribed circle is set to 2 as shown in [Equation 11]. A pseudo area ratio obtained by dividing the square (the area of the circumscribed circle by π) by the area of the triangle and then raising to the 1/3 power was calculated. However, it is not limited to the one shown in [Formula 11] for calculating the area ratio distribution, and may be a product obtained by multiplying an appropriate coefficient, or may be a power other than 1/3. Good.

1, 1a, 11, 11a... CPU (Central Processing Unit)
2, 2a, 12, 12a ... RAM (Random Access Memory)
3, 3a, 13, 13a ... Storage device 4, 4a, 14, 14a ... Key input I / F
5, 5a, 15, 15a ... Data I / O I / F
6, 6a, 16, 16a ... display unit 7 ... 3D printer (three-dimensional object modeling apparatus)
7a: Data processing unit 7b: Output unit 8, 8a, 18, 18a: Network communication unit 10: Frequency distribution calculating means (frequency distribution calculating device)
DESCRIPTION OF SYMBOLS 20 ... Frequency distribution collating means 30, 31 ... Target model storage means 40 ... Regulatory model database 50 ... Target model receiving means 60 ... Output propriety data transmitting means 100, 101 ... Three-dimensional object Modeling data output restriction device 102 ... restriction model frequency distribution calculation device 201 ... output control terminal 202 ... processing server

Claims (13)

A device for determining whether or not to regulate when outputting a polygon model expressed as a set of polygons to a three-dimensional object modeling apparatus as three-dimensional object modeling data,
A database in which a two-dimensional frequency distribution expressing the characteristics of a restriction model, which is a polygon model whose output should be restricted, is registered;
For the target model that is the polygon model to be output, two parameters are calculated based on a specific triangle specified by a predetermined point of the three polygons in the target model, and each of the two parameters is set to two coordinates. Frequency distribution calculating means for calculating a two-dimensional frequency distribution corresponding to
A frequency distribution matching means for collating the two-dimensional frequency distribution of the target model with the two-dimensional frequency distribution of the regulation model and determining whether or not the output should be regulated;
A data output regulating device for three-dimensional object formation characterized by comprising: In the database, in addition to the two-dimensional frequency distribution, a one-dimensional frequency distribution that is at least one frequency distribution of the two parameters is registered.
The frequency distribution calculating means calculates the one-dimensional frequency distribution in addition to the two-dimensional frequency distribution for the target model,
The frequency distribution collating means collates the one-dimensional frequency distribution of the target model with the one-dimensional frequency distribution of the restriction model in addition to the collation of the two-dimensional frequency distribution, and determines whether or not the output should be regulated. The three-dimensional object formation data output restriction device according to claim 1, wherein the three-dimensional object formation data output restriction device is provided.   One of the two parameters is a circumscribed circle radius of the specific triangle, and the other is an area ratio that is a value based on a value obtained by dividing the square of the circumscribed circle radius by the area of the specific triangle. The three-dimensional object modeling data output restriction device according to claim 2. The coordinates of the two-dimensional frequency distribution are orthogonal coordinates;
In calculating the two-dimensional frequency distribution, the frequency distribution calculating unit divides the range of the calculated maximum value of the circumscribed circle radius into a plurality of elements, and calculates the cube of the calculated maximum value of the circumscribed circle radius. After dividing the range into multiple elements,
4. The two-dimensional frequency distribution is calculated by assigning the circumscribed circle radius and the area ratio to one of the two elements in correspondence with one of two two-dimensional axes. Data output restriction device for three-dimensional object modeling. In calculating the one-dimensional frequency distribution, the frequency distribution calculating unit divides the range of the calculated maximum value of the circumscribed circle radius into a plurality of elements and / or calculates the maximum of the calculated circumscribed circle radius. After dividing the cube of the value into multiple elements,
Each circumscribed circle radius is assigned to any of the elements based on the value of the circumscribed circle radius, and / or each area ratio is assigned to any of the elements based on the value of the area ratio. The three-dimensional object shaping data output restriction device according to claim 3, wherein the one-dimensional frequency distribution is calculated by assignment.   The frequency distribution calculating means calculates, as a weight value, an average value of values obtained by multiplying the area of the polygon by an inner product value of a unit vector from the center of gravity of the specific triangle to each vertex and a normal vector of the polygon including the vertex. The weight output is performed using the weight value, and the three-dimensional object formation data output restriction device according to claim 4 or 5.   The frequency distribution calculating means divides the value of each element by the sum of the weight values for each polygon constituting each target model, and gives the absolute value if the element is a negative value The three-dimensional object formation data output restriction device according to claim 6.   The frequency distribution calculating means obtains polygons in the target model in units of three for the target model, randomly classifies them into three groups, a first group, a second group, and a third group, The three-dimensional object formation data output restriction device according to any one of claims 1 to 7, wherein the three polygons are selected by selecting polygons one by one from the group.   The frequency distribution collating means calculates a correlation coefficient between the frequency distributions when collating the frequency distribution of the target model with the frequency distribution of the regulatory model, and outputs an output based on the calculated correlation coefficient. It is determined whether it should regulate or not. The data output regulation device for solid thing formation according to any one of claims 1 to 8 characterized by things. Means for outputting the target model to a connected three-dimensional object shaping apparatus;
When it is determined that the output should be regulated by the frequency distribution matching unit that is executed in parallel with the three-dimensional object modeling process by the three-dimensional object modeling apparatus, the three-dimensional object modeling apparatus includes the target model. Means for outputting an output stop command;
The data output regulation device for three-dimensional object formation according to any one of claims 1 to 9, further comprising: The output control terminal and the processing server are connected via a network,
The output control terminal is:
For the target model that is the polygon model to be output, two parameters are calculated based on a specific triangle specified by a predetermined point of the three polygons in the target model, and each of the two parameters is set to two coordinates. A frequency distribution calculating means for calculating a two-dimensional frequency distribution corresponding to
The processing server
A database in which a two-dimensional frequency distribution expressing the characteristics of a restriction model, which is a polygon model whose output should be restricted, is registered;
Receiving means for receiving a frequency distribution of the target model from the output control terminal via a network;
A frequency distribution matching means for collating the two-dimensional frequency distribution of the target model with the two-dimensional frequency distribution of the regulation model and determining whether or not the output should be regulated;
Output suitability data transmission means for transmitting data based on whether the output should be regulated or not, determined by the frequency distribution matching means, to the output control terminal;
A data output regulating device for three-dimensional object formation characterized by comprising: A three-dimensional object shaping data output restriction device according to any one of claims 1 to 11,
A three-dimensional object modeling apparatus that models a three-dimensional object using a polygon model whose output is permitted by the three-dimensional object modeling data output restriction device;
A three-dimensional object forming system characterized by comprising:   A program for causing a computer to function as the three-dimensional object formation data output restriction device according to any one of claims 1 to 12.