JP6565494B2 - Data reduction device for 3D object modeling - Google Patents

Description

  The present invention is to reduce output data to a three-dimensional object modeling apparatus when using a three-dimensional object modeling apparatus such as a 3D printer that processes a resin or the like to model a three-dimensional object based on data representing the three-dimensional object. Regarding 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. As a medical application of 3D printers, modeling data for 3D printer output is created based on CT / MRI images (DICOM format 3D voxel data) taken by medical diagnosis, and organs for surgical simulation, medical education, and informed consent Attempts have been made to output models and create artificial organs (blood vessels, bones, joints, etc.) for implantation in the body.

  Modeling data for 3D printer output, which is data for modeling a three-dimensional object, is a polygon model expressed by a collection of polygons. As a method for creating modeling data for 3D printer output of an organ model from a CT / MRI image, as shown in Patent Document 1 and Patent Document 2, a voxel of a target organ region is extracted and the Marching Cube method (patent In general, a technique for converting the boundary surface of an organ region into a surface approximated by a polyhedron (a set of triangles) and obtaining surface data expressing the surface shape is used.

Japanese Patent No. 3690501 JP 2012-216102 A US Pat. No. 7,209,136 Japanese Patent Laid-Open No. 8-153211 Japanese Patent No. 3350473 Japanese Patent No. 4463597 Japanese Patent No. 5018721 Japanese Patent Laid-Open No. 11-232489

  In the above surface conversion method, a method of generating a triangle three-dimensionally based on a voxel of about the power of 512 is used, so the triangle polygon becomes enormous, and in the CG field, time is required for screen drawing. It has been pointed out that there is a problem that the responsiveness of the interactive operation becomes worse. This also causes a problem in 3D printer output, and it takes time for printer output preprocessing (processing for converting polygons into data for additive manufacturing), and in some cases causes a work memory overflow and disables output.

  On the other hand, in the CG field, a method is used in which polygonal division is roughened in accordance with the resolution of the screen to express a curved surface, or polygons that are not used for visualization are deleted in advance. For example, in a flat object, polygons that represent only a single surface and constitute the back surface are omitted, or polygons that are hidden from the viewpoint direction and are not used for visualization are deleted in advance, as in Patent Document 4, or Patent Document 5 As described above, a method has been proposed in which inner polygons hidden by other polygons are determined and deleted in advance to reduce the drawing target polygons. Further, as disclosed in Patent Document 6, a method of substituting texture or bump mapping instead of using polygons for a fine uneven expression has been proposed.

  However, in 3D printer output, a resolution finer than that of the screen is required, and since it is necessary to form a closed space with polygons, it is not possible to omit the polygons constituting the back surface in a flat object. In addition, since the model is viewed from various angles, there is basically no hidden surface, and another shape can be modeled inside the model, so the occlusion culling method proposed in the CG field means Does not have Even minute irregularities cannot be visually expressed by shading or the like, and must be expressed by polygonal shapes. As in Patent Document 7, there are cases where a deformed expression with extremely reduced polygons is required in an architectural model, but in medical applications, reality is required as such. Therefore, as in Patent Document 8, there is no choice but to take a technique of reducing the triangular polygons themselves to such an extent that the appearance of the shaped object is not impaired.

  In the reduction of triangular polygons, the method of Patent Document 8 is fundamental. This includes (1) processing to search for triangles and ridges that do not affect the overall shape even if they are reduced from a given polygon, and (2) search for neighboring triangles that share vertices with the target ridges while reducing them. The two types of search processing including correction processing are repeated until the data amount is reduced to a desired amount. The technique of Patent Document 8 requires processing for searching for adjacent triangles that share ridgelines and vertices that are candidates for deletion in both processes, and the processing load increases in proportion to the square of the number of polygons given. Was holding.

  As a method of reducing the processing load, it is only necessary to reduce the data amount of the input polygon model to be reduced. Therefore, the input polygon model may be divided and processed. Japanese Patent Application Laid-Open No. 2004-228620 proposes a method of performing polygon conversion at the stage of a voxel image before conversion into polygons, and performing surface conversion for each divided voxel data to reduce polygons. Although this can certainly increase the speed, a surface is formed at the boundary part divided by voxel, so when polygon data is integrated, discontinuous cracks corresponding to the divided boundary part occur on the modeled object. (However, in CG applications, the boundary portion is not noticeable due to rendering).

  Moreover, even if it looks as if it is a single closed space, it may be separated into a plurality of closed spaces in terms of data. For example, if there is a small space that is in contact with the main closed space, there is no problem if the printer outputs it as it is. However, if polygon reduction is performed according to Patent Document 8, etc., the small space is cut and the distance from the main closed space becomes longer. , May become completely liberated. If the printer is output in this state, there is a possibility that an error will be stopped in the printer output pre-processing, or that a small space instructed to float in the air may fall in the middle of output and cause an output trouble (however, for CG applications) In particular, there is no problem.)

  Therefore, the present invention can obtain data for three-dimensional object modeling by efficiently reducing polygons with a small processing load from a polygon model composed of polygons while suppressing deterioration of the quality of the output modeled object. It is an object to provide a three-dimensional object modeling data reduction device.

In order to solve the above problems, in the first aspect of the present invention,
A device for reducing polygon model data expressed as a collection of polygons for modeling a three-dimensional object,
By searching for the vertices of different polygons having the same coordinate value for each vertex of each polygon constituting the polygon model, and assigning the same vertex ID to the obtained series of vertices, each polygon Each vertex included in the vertex is expressed by a vertex ID having the same value as the vertex of the same coordinate, and recorded in association with a polygon including each vertex, and the vertex ID and the coordinate assigned to the vertex configuration table A vertex coordinate table in which values are recorded in association with each other; a polygon model structuring means for creating;
A table defining means for defining a vertex duplication table for recording a correspondence relationship between a vertex recorded in the vertex coordinate table and a duplication destination vertex having the same coordinates;
Deletion of all polygons for which all of the vertices have already been set as deletion targets for the polygons recorded in the vertex configuration table, where either the product of the area, circumference, or area is less than or equal to a predetermined threshold Polygons that are not shared with the two vertices of the target ridge line are sequentially set as deletion target polygons, and further, a deletion target polygon setting means for selecting a deletion target ridge line from each set polygon,
With reference to the vertex configuration table, the two end points of the deletion target ridge line of all the polygons set by the deletion target polygon setting means are set as deletion target vertices, and the vertex coordinate table is referenced based on the deletion target vertices. An average point of the two deletion target vertices is obtained, one of the deletion target vertices is set as a representative vertex, information on the deletion target vertices other than the representative vertex is deleted from the vertex coordinate table, and the vertex ID of the representative vertex A vertex coordinate table updating means for recording the coordinate value of the average point in association with each other,
In the vertex duplication table, vertex duplication table update means for setting the duplication destination of the deletion target vertex other than the representative vertex to the representative vertex;
When the value of each vertex ID in the vertex configuration table is changed to the duplication destination set in the vertex duplication table and, as a result of the change, if two or more vertex IDs corresponding to the same polygon overlap, Vertex configuration table updating means for deleting from the vertex configuration table;
A polygon model that updates a polygon model by replacing each vertex ID of the vertex configuration table updated by the vertex configuration table update means with a coordinate value while referring to the vertex coordinate table updated by the vertex coordinate table update means Update means;
A three-dimensional object shaping data reduction device characterized by comprising:

  According to the first aspect of the present invention, vertices of different polygons having the same coordinate value are searched for each vertex of each polygon constituting the polygon model, and the same vertex is obtained for the obtained series of vertices. By assigning an ID, each vertex included in each polygon is expressed by a vertex ID having the same value as the vertex of the same coordinate, and a vertex configuration table recorded in association with the polygon including each vertex, and a vertex configuration table Vertex duplication that creates a vertex coordinate table in which the vertex IDs assigned to and the coordinate values are recorded in association with each other and records the correspondence between the vertexes recorded in the vertex coordinate table and the vertices of the same destination Define a table, and for the polygons recorded in the vertex configuration table, either the product of the area and perimeter or the area is less than the predetermined threshold value, and all vertices are already set for deletion. Polygons that are not shared with the two vertices of the deletion target ridgelines of all the polygons are sequentially set as deletion target polygons, and the deletion target ridgelines are selected from the set polygons, and the deletion target polygon setting means is referred to the vertex configuration table. The two end points of the deletion target ridgeline of all the polygons set in step 1 are set as deletion target vertices, and the average point of a plurality of deletion target vertices is obtained by referring to the vertex coordinate table based on the deletion target vertices. In the vertex duplication table, the information on the vertices to be deleted other than the representative vertices is deleted from the vertex coordinate table and the average vertex coordinate value is recorded in association with the vertex ID of the representative vertex. The duplication destination of the deletion target vertex other than the representative vertex is set as the representative vertex, and the value of each vertex ID in the vertex configuration table is set to the updated vertex duplication table. When there are two or more vertex IDs corresponding to the same polygon as a result of the change, the polygon is deleted from the vertex configuration table, and the updated vertex configuration table The polygon model is updated by replacing each vertex ID with a coordinate value while referring to the updated vertex coordinate table, so the search load of the polygon adjacent to the set polygon to be deleted is reduced. be able to. For this reason, it is possible to efficiently reduce the polygons and obtain the three-dimensional object modeling data from the polygon model constituted by the polygons with a small processing load while suppressing the deterioration of the quality of the output modeling object. In particular, a polygon model such as surface data generated based on a medical CT / MRI image can be efficiently output to a three-dimensional object forming apparatus such as a 3D printer.

  In the second aspect of the present invention, when the number of polygons constituting the polygon model updated by the polygon model updating unit is larger than a predetermined target value, the deletion target polygon setting unit, the vertex coordinate table updating unit, The apparatus further comprises: a vertex duplication table update unit, the vertex configuration table update unit, and a control unit that performs control to repeatedly execute the process on the polygon model update unit.

  According to the second aspect of the present invention, when the number of polygons constituting the updated polygon model is larger than the target value, the deletion target polygon is set, the vertex coordinate table is updated, the vertex duplication table is updated, and the vertex configuration table is updated. Since the polygon model is repeatedly updated, the number of polygons constituting the polygon model can be reduced to the target value.

In the third aspect of the present invention,
Furthermore, a vertex update table update means is provided,
The table defining means further defines a vertex update table for recording that the vertex recorded in the vertex coordinate table is set as the deletion target vertex;
The deletion target polygon setting means refers to the vertex update table, and designates a polygon that is not recorded as being set as the deletion target vertex as a polygon that is not shared with two vertices of the deletion target ridge line of all the polygons. ,
The vertex update table update unit sets the vertex in the vertex update table as a deletion target vertex when the vertex in the vertex overlap table is updated.

  According to the third aspect of the present invention, the vertex update table for recording that the vertex recorded in the vertex coordinate table is set as the deletion target vertex is further defined, and when the deletion target polygon is set, the vertex update table is set. Referring to, the polygons that are not recorded as the deletion target vertices are not shared with the two vertices of the deletion target ridgeline of all polygons, and the predetermined vertex is updated in the vertex duplication table. In this case, the corresponding vertex in the vertex update table is set as the deletion target vertex, so other polygons that have vertices shared with any vertex of the polygon to be set as the deletion target are set in advance as the deletion target. You can easily confirm that it is not set, you can avoid setting multiple adjacent polygons as deletion targets at the same time, Maseru it can be prevented.

  In the fourth aspect of the present invention, the deletion target polygon setting means calculates an area for all the polygons recorded in the vertex configuration table, and sets a predetermined value of 1 or more as a minimum value of the area. The multiplied value is set to the predetermined threshold value.

  According to the fourth aspect of the present invention, an area is calculated for all polygons recorded in the vertex configuration table, and a value obtained by multiplying a minimum value of the area by a predetermined value of 1 or more is used as the predetermined threshold. Since it is set to a value, it is possible to delete polygons with priority given to those having a small polygon area.

  In the fifth aspect of the present invention, the deletion target polygon setting means calculates an area and a perimeter for all the polygons recorded in the vertex configuration table, and a minimum value of a product of the area and the perimeter A value obtained by multiplying a predetermined value of 1 or more is set as the predetermined threshold value.

  According to the fifth aspect of the present invention, the area and perimeter are calculated for all the polygons recorded in the vertex configuration table, and the minimum product of the area and perimeter is multiplied by a predetermined value of 1 or more. Since the predetermined value is set as the predetermined threshold value, polygons can be deleted by giving priority to a product having a small area and circumference.

  Further, the sixth aspect of the present invention is characterized in that the deletion target polygon setting means selects the shortest ridge line when selecting the deletion target ridge line from the polygon set as the deletion target.

  According to the sixth aspect of the present invention, the deletion target polygon setting means selects the shortest ridge line when selecting the deletion target ridge line from the polygon set as the deletion target. It becomes possible to delete polygons without giving much distortion.

In the seventh aspect of the present invention,
The three-dimensional object shaping data reduction device;
A three-dimensional object modeling apparatus that models a three-dimensional object using the polygon model output from the three-dimensional object modeling data reduction apparatus;
A three-dimensional object shaping system characterized by comprising a three-dimensional object shaping system.

  According to the seventh aspect of the present invention, the three-dimensional object modeling system includes the three-dimensional object modeling data reduction apparatus and the three-dimensional object modeling apparatus that models the three-dimensional object using the polygon model output from the three-dimensional object modeling data reduction apparatus. Since this is realized, it is possible to provide a three-dimensional object formation system in the form of a 3D printer or the like incorporating a board computer.

  According to the present invention, it is possible to obtain data for three-dimensional object modeling by efficiently reducing polygons with a small processing load from a polygon model composed of polygons while suppressing deterioration in quality of an output modeled object. Become.

It is a hardware block diagram of the data reduction apparatus for solid object shaping which concerns on one Embodiment of this invention. It is a functional block diagram which shows the structure of the data reduction apparatus for solid object shaping which concerns on one Embodiment of this invention. It is a figure which shows the mode of the conversion from a DICOM format voxel data to a polygon model. It is the figure which showed the DICOM format voxel data as several slice images. This is an example in which DICOM format voxel data is displayed in four forms. FIG. 6 is a diagram showing STL data obtained by converting the DICOM format voxel data shown in FIG. 5 by “3D-Slicer”. It is a figure which shows the polygon model (STL data) according to area | region. It is a figure which shows the rendering image of the polygon model (STL data) which synthesize | combined STL data according to area | region. It is a flowchart which shows the process outline | summary of the data reduction apparatus for solid object shaping which concerns on one Embodiment of this invention. It is a figure which shows an example of the polygon group made into a process target. It is a figure which shows the vertex coordinate arrangement | sequence data for implement | achieving the polygon group shown in FIG. It is a flowchart which shows the detail of the polygon reduction process in step S20. It is a flowchart which shows the detail of structuring of the polygon model of step S21. It is a figure which shows the relationship between a polygon group and a hash value. It is a figure which shows the state of each table at the time of initialization of polygon model structuring. It is a figure which shows the mode of a change of each table in polygon model structuring. It is a figure which shows the mode of a change of each table in polygon model structuring. It is a figure which shows the mode of a change of each table in polygon model structuring. It is a figure which shows the mode of a change of each table in polygon model structuring. It is a figure which shows the mode of a change of each table in polygon model structuring. It is a figure which shows the vertex structure table at the time of initialization, a vertex coordinate table, a vertex duplication table, and a vertex update table. It is a figure which shows the polygon group in the state in which one side of two deletion object polygons of P6 and P10 is set as a deletion object side. It is a figure which shows the mode of each table at the time of the process of the ridgeline JK. It is a figure which shows the mode of each table at the time of the process of ridgeline DE. It is a figure which shows the mode of the update of the vertex structure table by a vertex duplication table. It is a figure which shows the mode of the deletion of the polygon from a vertex structure table. It is a figure which shows the vertex coordinate arrangement | sequence data after a polygon deletion process. It is a figure which shows the state of the polygon group after a polygon deletion process. It is a figure for demonstrating the problem which arises by a polygon reduction process. It is a flowchart which shows the detail of the deletion process of the isolated small volume group. 32 is a flowchart showing details of a minimum interval calculation process in step S44 of FIG. 30.

DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, preferred embodiments of the invention will be described in detail with reference to the drawings.
<1. Device configuration>
FIG. 1 is a hardware configuration diagram of a three-dimensional object formation system including a three-dimensional object formation data reduction device 200 according to an embodiment of the present invention. The three-dimensional object modeling data reduction device 200 according to the present embodiment can be realized by a general-purpose computer. As shown in FIG. 1, a CPU (Central Processing Unit) 1 and a RAM (Random) that is a main memory of the computer. 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 a 3D printer And a data input / output I / F (interface) 5 for data communication with an external device such as a data storage medium and a display unit 6 which is a display device such as a liquid crystal display, and are connected to each other via a bus. Yes.

  The 3D printer 7 is a general-purpose 3D printer, which processes a material such as resin and gypsum on the basis of data for modeling a three-dimensional object, which is a polygon model expressing the three-dimensional shape of the three-dimensional object as a set of polygons. It is a three-dimensional object modeling apparatus to model. 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. Based on the reduced three-dimensional object modeling data received from the data input / output I / F 5, the output unit 7b generates a three-dimensional object. It is designed to be shaped.

  In FIG. 1, the three-dimensional object modeling data reduction device 200 and the 3D printer 7 are shown in a separated form, but most of the 3D printer products currently on the market are components of the three-dimensional object modeling data reduction device 200. CPU 1, RAM 2, storage device 3, key input I / F 4 (not a keyboard / mouse for general-purpose computers, but several buttons at a numeric keypad level), data input / output I / F 5, display 6 (several lines of characters) A small liquid crystal panel capable of displaying the image, and a touch panel is often superimposed to serve also as a key input I / F 4). 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. 1 is often housed in one housing and distributed as a product called “3D printer”.

  FIG. 2 is a functional block diagram illustrating a configuration of the three-dimensional object formation data reduction device according to the present embodiment. In FIG. 2, 10 is a control means, 20 is a group classification means, 30 is a polygon model structuring means, 40 is a table definition means, 50 is a deletion target polygon setting means, 60 is a vertex coordinate table update means, and 70 is a vertex overlap table. Update means 75, vertex update table update means, 80 vertex configuration table update means, 90 polygon model update means, 100 group synthesis means, 110 polygon model synthesis means, 120 polygon model storage means by area, 130 It is a synthetic polygon model storage means.

  The control means 10 controls the entire three-dimensional object formation data reduction device. The group classification means 20 makes a polygon belonging to each group share a side (two vertices) constituting the polygon with any other polygon in the group for the polygon model to be selected as the deletion target polygon. Sort into groups. The polygon model structuring means 30 expresses each vertex included in each polygon from the polygon model by a vertex ID having the same value as the vertex of the same coordinate, and each vertex constituting the polygon is expressed by a vertex ID. And a vertex coordinate table in which a vertex ID and a coordinate value assigned to the vertex configuration table are recorded in association with each other. The table definition unit 40 includes a vertex duplication table that records a correspondence relationship between a vertex ID recorded in the vertex coordinate table and a destination vertex ID that has the same coordinates, and a vertex update table that associates the vertex ID with an update flag. Define The deletion target polygon setting means 50 sets some polygons as deletion target polygons at predetermined intervals with respect to the polygons recorded in the vertex configuration table.

  The vertex coordinate table updating unit 60 refers to the vertex configuration table, identifies a plurality of vertex IDs constituting the deletion target polygon as a deletion target vertex, and refers to the vertex coordinate table based on the deletion target vertex to determine a plurality of deletion targets. Find the average point of the vertices, use one of the deletion target vertices as the representative vertex, delete information on the deletion target vertices other than the representative vertex from the vertex coordinate table, and correspond the coordinate value of the average point to the vertex ID of the representative vertex Add and record. The vertex duplication table updating unit 70 sets the duplication destination of all the deletion target vertices other than the representative vertex in the vertex duplication table as the representative vertex. The vertex update table update unit 75 sets an update flag for the updated vertex in the vertex update table. The vertex configuration table updating unit 80 changes the value of the vertex ID updated in the updated vertex duplication table in the vertex configuration table to the updated duplication destination, and the same as the result of the change, constituting the polygon If two or more vertex IDs having the value of are duplicated, the polygon is deleted from the vertex configuration table. The polygon model updating unit 90 replaces each vertex ID of the updated vertex configuration table with a coordinate value while referring to the updated vertex coordinate table, thereby obtaining a polygon model represented by the reduced polygon array. create.

  The group synthesizing unit 100 includes a polygon model structuring unit 30, a table defining unit 40, a deletion target polygon setting unit 50, a vertex coordinate table updating unit 60, a vertex duplication table updating unit 70, and a vertex updating table updating unit for each classified group. 75. The updated polygon models of a plurality of groups created by executing a series of processes by the vertex configuration table updating unit 80 and the polygon model updating unit 90 are combined into a single region-specific polygon model for each region. The polygon model synthesizing unit 110 synthesizes a plurality of sets of updated polygon models by region into a single synthesized polygon model. Control means 10, group classification means 20, polygon model structuring means 30, table definition means 40, deletion target polygon setting means 50, vertex coordinate table update means 60, vertex overlap table update means 70, vertex update table update means 75, vertex The configuration table update unit 80, the polygon model update unit 90, the group synthesis unit 100, and the polygon model synthesis unit 110 are realized by the CPU 1 executing a program stored in the storage device 3.

  The region-specific polygon model storage unit 120 is a storage unit that stores a region-specific polygon model, and is realized by the storage device 3. The area-specific polygon model is a polygon model configured with one area as one set. The synthesized polygon model storage unit 130 is a storage unit that stores a synthesized polygon model that is a single polygon model obtained by synthesizing a plurality of sets of region-specific polygon models, and is realized by the storage device 3. The synthesized polygon model stored in the synthesized polygon model storage unit 130 becomes the three-dimensional object modeling data reduced for output to the 3D printer 7. Both the polygon model for each area stored in the polygon model storage means 120 for each area and the synthesized polygon model stored in the combined polygon model storage means 130 are a collection of polygons and record the vertices of each polygon in units of polygons. It has become a format.

  Each component shown in FIG. 2 is actually realized by installing a dedicated program in 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.

  In the storage device 3 shown in FIG. 1, a dedicated program for operating the CPU 1 and causing the computer to function as a three-dimensional object formation data reduction device is mounted. By executing this dedicated program, the CPU 1 controls the control means 10, group classification means 20, polygon model structuring means 30, table definition means 40, deletion target polygon setting means 50, vertex coordinate table update means 60, vertex overlap. The functions as the table update unit 70, the vertex update table update unit 75, the vertex configuration table update unit 80, the polygon model update unit 90, the group synthesis unit 100, and the polygon model synthesis unit 110 are realized. Further, the storage device 3 not only functions as the region-specific polygon model storage unit 120 and the composite polygon model storage unit 130 but also stores various data necessary for processing as the three-dimensional object formation data reduction device.

<2. Processing action>
<2.1. Pretreatment>
Next, the processing operation of the three-dimensional object modeling data reduction device shown in FIGS. 1 and 2 will be described. First, pre-processing for creating a region-specific polygon model as surface data from medical voxel data will be described. The surface data is data representing a three-dimensional structure as a surface shape by surface modeling, and is a polygon model composed of polygons that are polygon data. Preprocessing is performed by a computer executing a known program. Here, a case where “3D-Slicer” which is open source software developed mainly by Harvard University in the United States is used as a known program will be described as an example. First, the computer extracts voxel data of a specific organ region from the whole voxel data. Next, the computer converts the voxel data of the specific organ region into surface data that is a polygon model. The region-specific polygon model obtained in this way is stored in the region-specific polygon model storage unit 120. The pre-processing may be performed by causing the computer that realizes the three-dimensional object modeling data reduction device shown in FIG. 1 to execute the program, or realize the three-dimensional object modeling data reduction device shown in FIG. It may be executed by a computer different from the computer, and the obtained polygon model for each region may be stored in the region-specific polygon model storage means 120 realized by the storage device 3.

  In the present embodiment, voxel data in DICOM format, which is an international standard for medical image data exchange, is used as medical voxel data. Further, STL (Standard Triangulated Language) data is used as the surface data that is a polygon model. STL data was originally an industry standard for modeling data exchange in the field of 3D graphics, and has recently been used as a standard in 3D printers. Three-dimensional shapes are represented by a collection of triangular polygons. Data. Then, when the computer executes “3D-Slicer”, the voxel data for each area as shown in FIG. 3B is extracted from the DICOM format voxel data as shown in FIG. Face model conversion is performed to obtain a polygon model (STL data) as shown in FIG. The Marching Cube method described in Patent Document 3 or the like is used for extraction of voxel data for each region and surface model conversion.

  4 to 8 show examples of processing screens by “3D-Slicer”. FIG. 4 is a diagram illustrating the DICOM format voxel data to be processed by “3D-Slicer” as a plurality of slice images. In the example of FIG. 4, the sagittal image of the human head is shown as 256 slice images. Each slice image is composed of 512 × 512 pixels. FIG. 5 is an example in which DICOM format voxel data is displayed in four forms. In FIG. 5, a volume rendering image is displayed at the top. The axial image, the sagittal image, and the coronal image are displayed in order from the left side.

  FIG. 6 is a diagram showing STL data of a polygon model obtained by converting the DICOM format voxel data shown in FIG. 5 using “3D-Slicer”. In FIG. 6, a surface rendering image of STL data is displayed at the top. In the example of FIG. 6, the eyeball / brain region threshold value: 626.75 or more (when the voxel value is 10 bits width in MRI imaging), the eyeball connective tissue L threshold value: 298.36-458.74, the eyeball connective tissue R threshold value: 298.36 By setting 431.32, surface-rendered STL data classified by region (organization) is shown.

  FIG. 7 is a diagram in which the STL data for each region obtained by “3D-Slicer” is represented by shading by shading. FIG. 8 is a diagram showing a surface rendering image of a polygon model (STL data) obtained by combining region-specific STL data. The Front View shown in FIG. 8 is the same as that shown in the upper part of FIG. After the preprocessing, the polygon model for each region as shown in FIG. 7 is stored in the polygon model storage unit 120 for each region.

<2.2. Process Overview>
Next, the processing operation of the three-dimensional object modeling data reduction device shown in FIGS. 1 and 2 will be described. FIG. 9 is a flowchart showing a processing outline of the three-dimensional object formation data reduction device according to the embodiment of the present invention. First, the group classification means 20 reads the area-specific polygon model for one area from the area-specific polygon model storage means 120 and classifies it into a plurality of groups (step S10). Next, for each group of polygon models, polygon model structuring means 30, table defining means 40, deletion target polygon setting means 50, vertex coordinate table updating means 60, vertex duplication table updating means 70, vertex update table updating means. 75, the vertex configuration table updating unit 80 and the polygon model updating unit 90 execute polygon reduction processing (step S20). The control means 10 determines whether or not the polygon reduction process has been completed for all groups (step S30). If the polygon reduction process has not been completed for all groups, the polygon reduction process of step S20 is executed for the unprocessed group. To do. When the polygon reduction processing for all the groups is completed, the group composition unit 100 deletes the isolated small volume group (step S40). Subsequently, the group synthesizing unit 100 synthesizes the polygon models of all groups (step S50). The control means 10 determines whether or not the processing has been completed for all the areas (step S60). If the processing has not been completed for all the areas, the processing of steps S10 to S50 is executed for the unprocessed areas. When the processing for all the areas is completed, the polygon model synthesizing unit 110 synthesizes the polygon model for each area of the entire area (step S70).

<2.3. Group classification processing>
First, in step S10, the group classification means 20 performs a group classification process. Specifically, with respect to the polygon model for each area, the polygons belonging to each group are classified into groups so as to share the sides constituting the polygon with any other polygon in the group. As a specific method of the group classification process, various known methods can be used.

<2.4. Polygon reduction processing>
Next, the polygon model structuring means 30, the table defining means 40, the deletion target polygon setting means 50, the vertex coordinate table updating means 60, the vertex duplication table updating means 70, the vertex update table updating means 75, and the vertex configuration table updating in step S20. The polygon reduction processing by means 80 and polygon model update means 90 will be described. As a method for deleting polygons in the polygon reduction process, a method is used in which a ridge line constituting a polygon is specified and the polygon is deleted by deleting the ridge line. Here, the ridge line means a side connecting two vertices of one polygon.

  FIG. 10 is a diagram illustrating an example of a polygon group to be processed. The polygon model is a polygon group having a three-dimensional value in the space as shown in FIG. 11, but in the example of FIG. 10, the polygon group projected on the two-dimensional space is shown for convenience of explanation on the paper. Yes. In the example of FIG. 10, a polygon group including 18 triangular polygons is shown before reduction. In FIG. 10, uppercase alphabets A to N are not used to belong to a specific polygon, but are used to identify shared vertices having different coordinates. Uppercase alphabets A to N are added for convenience in order to identify shared vertices in the entire polygon group. Vertex coordinate array data, vertex configuration table, vertex coordinate table, vertex duplication table, vertex update described later It is not recorded in the table (some of them are used for easy understanding). Polygon IDs P1 to P18 describe vertex IDs V1a to V18c for each polygon expressed in association with each polygon ID, and each corresponds to one of the shared vertices A to N. The polygon-specific vertex IDs V1a to V18c are provided for convenience of explanation, and are not recorded in the vertex coordinate array data, the vertex configuration table, the vertex coordinate table, the vertex overlap table, or the vertex update table.

  11 is a diagram showing vertex coordinate array data for realizing the polygon group shown in FIG. The vertex coordinate array data is data defining a polygon model, and a polygon model that is an aggregate of polygons is defined by an array structure. That is, FIG. 11 shows a structure in which normal vector information is deleted from STL data. As shown in FIG. 11, the vertex coordinate array data is associated with polygon IDs P1 to P18, which are polygon identification information for identifying polygons, and the three vertices of the first vertex, the second vertex, and the third vertex constituting the polygon. Each coordinate value is recorded in order.

  The polygonal vertex ID is identification information for identifying a polygon and a vertex in a format in which the ID of the polygon to which the vertex belongs and the vertex order of the polygon are specified. Specifically, as shown in FIG. 10, after V indicating a vertex, numbers included in the corresponding polygon ID, and a, b, and c indicating whether the first vertex, the second vertex, and the third vertex are different. Express with any lowercase alphabet. For example, as shown in the first line of FIG. 11, the vertex ID for each polygon of the first vertex of the polygon P1 is expressed as “V1a”. Since the number “1” is entered in the vertex ID “V1a” for each polygon, it is clear that it is the vertex of the polygon P1. Actually, this polygonal vertex ID is simply a sialyl number, and the coordinate value of each vertex is recorded in the vertex coordinate array data in the order of this number. The correspondence relationship with 10 and the polygon to which the vertex belongs are described so as to be clear. Further, in the vertex coordinate array data of FIG. 11, the coordinates of each vertex correspond to any one of the shared vertices A to N shown in FIG. Expressed with lower case letters. For example, as shown in the first line of FIG. 11, the coordinate value of the first vertex V1a of the polygon P1 corresponds to the shared vertex “D” in FIG. 10 and is therefore expressed as “(Xd, Yd, Zd)”. The For each polygon, the coordinate values of the three vertices are recorded in association with the three vertices configured. Since it is created according to the rules as described above, in the vertex coordinate array data, vertices with the same coordinates are recorded redundantly at a plurality of locations. For example, since the vertex D shown in FIG. 10 is shared by the six polygons P1, P2, P4, P5, P6, and P7, the coordinate value “(Xd, Yd, Zd)” is the vertex V1a, V2a, V4b. , V5c, V6c, V7c are recorded at six locations.

  FIG. 12 is a flowchart showing details of the polygon reduction process. First, the polygon model structuring means 30 prepares a vertex configuration table and a vertex coordinate table (step S21). In step S21, any method can be used as long as the vertex configuration table and the vertex coordinate table can be prepared, but the polygon model can be structured and created. Polygon model structuring refers to the vertex relationship (topology / phase information in the polygon model) by converting the vertex coordinate array data, which is the data that realizes the polygon model, into a structure consisting of a vertex configuration table and a vertex coordinate table. ) Is separated from the coordinate value (numerical data), and it becomes easy to search for the vertices of the surrounding polygons affected by the correction of the vertices of a certain polygon, and it is rearranged into a structure easy to edit.

  FIG. 13 is a flowchart showing details of the structuring of the polygon model in step S21. The polygon model structuring means 30 performs the structuring of the polygon model in step S21. The polygon model structuring unit 30 has functions as a hash value calculating unit, a coordinate value matching unit, a vertex configuration table processing unit, and a vertex coordinate table processing unit.

  First, the vertex configuration table, vertex coordinate table, and vertex ID are initialized (S101). In the vertex configuration table, each vertex included in each polygon is expressed by a vertex ID of a shared vertex having the same coordinate vertex, and each vertex constituting the polygon is expressed by a vertex ID and associated with the polygon. It is a recorded table. The vertex ID is vertex identification information for identifying the shared vertex, and any vertex can be used as long as the shared vertex can be uniquely specified. In this example, a serial integer value starting from 0 is used. The vertex coordinate table is a table in which vertex IDs and coordinate values assigned to the vertex configuration table are recorded in association with each other. Initialization of the vertex configuration table and the vertex coordinate table means that each item is not recorded. Also, the current vertex ID = 0 is set as the initialization of the vertex ID. Furthermore, the head position table in which the hash value and the link destination vertex ID are associated is also initialized. Initialization of the head position table is performed by setting all link destination vertex IDs to “−1”. A hash value-specific vertex coordinate table is realized by two tables, a vertex coordinate table and a head position table.

  Next, when extracting the vertex coordinate values from the vertex coordinate array data, the polygon ID and the vertex order are defined, the polygon ID is initialized to “P1”, and the vertex order is initialized to “0” (S101). Then, one vertex coordinate value corresponding to the current polygon ID and the vertex order is extracted (S102). For example, from the vertex coordinate array data shown in FIG. 11, the vertex coordinate value (Xd, Yd, Zd) of the first vertex having the polygon ID “P1” and the vertex order “0” is extracted.

  Subsequently, a hash value is calculated from the extracted vertex coordinate values (Xd, Yd, Zd) (S103). Specifically, first, the maximum values Xmax, Ymax, Zmax and the minimum values Xmin, Ymin, Zmin of the three-dimensional coordinate values x, y, z of all the polygons in the polygon model are obtained. This is to obtain the maximum value and the minimum value for each coordinate of the vertex array data as shown in FIG. Then, the coordinate values x, y, and z are classified into equal S stages and converted into integer values hx, hy, and hz (0 ≦ hx, hy, hz ≦ S−1). As the integer S, for example, S = 32 can be set. Specifically, hx, hy, hz are calculated by executing processing according to the following [Equation 1]. However, after the processing according to [Formula 1], values obtained by rounding down the decimal point are obtained as integer values hx, hy, hz.

[Formula 1]
hx = (x−Xmin) · S / (Xmax−Xmin)
hy = (y−Ymin) · S / (Ymax−Ymin)
hz = (z−Zmin) · S / (Zmax−Zmin)

  And the hash value h is calculated by performing the process according to the following [Formula 2].

[Formula 2]
h = hx + hy · S + hz · S ² (0 ≦ h ≦ S ³ −1)

  Next, the head position table is referred to using the calculated hash value (S104). Then, it is determined whether or not the link destination vertex ID corresponding to the hash value is registered in the head position table (S105). When the link destination vertex ID corresponding to the hash value (indicated as “link vertex ID” in the figure) is “−1”, that is, in the initial state, the link destination vertex ID corresponding to the hash value is not registered, that is, already exists. Means not registered.

  In this case, the vertex ID is recorded in the head position table (S106). Specifically, the current vertex ID (“0” in the initial state) is written in the link destination vertex ID corresponding to the hash value in the head position table. Subsequently, the coordinate value extracted in step S102 is written at the position of the current vertex ID in the vertex coordinate table. At this time, the vertex coordinate table also has a column for writing the link destination vertex ID, but the initial state is “−1”. Further, the current vertex ID is written in the vertex configuration table in association with the current polygon ID extracted in step S102 in the order of the vertexes. Here, it is recorded as a new vertex ID. Then, the current vertex ID is incremented (S107).

  On the other hand, if the link destination vertex ID corresponding to the hash value is not “−1” in step S105, it means that the link destination vertex ID corresponding to the hash value is already registered. In this case, it is determined whether the coordinate value extracted in step S102 matches the coordinate value corresponding to the registered link destination vertex ID in the vertex coordinate table (S108). If both coordinate values match as a result of the determination, the current vertex ID is recorded in the position of the current polygon ID and the vertex order in the vertex configuration table (S109). If the two coordinate values are different as a result of the determination in step S108, the link destination vertex ID in the vertex coordinate table is referenced to determine whether the link destination vertex ID is 0 or more (S110). As a result of the determination, if the link destination vertex ID is 0 or more, the value is set as the vertex ID, the process returns to step S108, and the coordinate value corresponding to the vertex ID is collated with the coordinate value extracted in step S102. If the result of determination in step S110 is that the link destination vertex ID is a negative value (eg, “−1”), the current vertex ID is recorded in the link destination vertex ID corresponding to that vertex ID in the vertex coordinate table, and step Returning to S107, the coordinate value extracted in step S102 is recorded at the position of the current vertex ID in the vertex coordinate table. At this time, the link destination vertex ID at the current vertex ID in the vertex coordinate table is left as “−1” in the initial state. The vertex ID is recorded in the vertex configuration table in association with the current polygon ID extracted in step S102 in the order of the vertexes. Then, the vertex ID is incremented.

  When the process of step S107 or S109 is completed, it is determined whether or not the process has been completed for all the polygons (S111). Specifically, first, the vertex order is incremented. When the vertex order exceeds “2”, the polygon ID is incremented to set the vertex order to “0”. For example, if the current polygon ID is “P1” and the polygon ID is incremented, the polygon ID becomes “P2”. If the polygon ID does not exceed the total number of polygons, the process returns to step S102 and is repeated. If the polygon ID exceeds the total number of polygons, it is determined that the processing has been completed for all the polygons, and the processing ends.

  A specific example of the polygon model structuring process in step S21 shown in FIG. 13 will be described. The case where the polygon group shown in FIG. 10 takes a hash value as shown in FIG. 14 based on the coordinate value of the vertex will be described as an example. In the example of FIG. 14, it is expressed in two dimensions for convenience of explanation, and when S = 2 in the above [Equation 2], h = hx + hy · 2 is obtained, and the hash values of the vertices A, B, D, and E are h = 0. , The hash values of vertices C and F are h = 1, the hash values of vertices G, H, J, L, and M are h = 2, and the hash values of vertices I, K, and N are h = 3 Yes. Actually, in the above [Equation 2], S = 32 is set, and h = hx + hy · 32 + hz · 1024, and the hash value h takes a value of 0 to 32767, but in the following, in order to simplify the explanation, The hash value will be described assuming that it takes the values 0 to 3 described above.

  FIG. 15 is a diagram showing the state of each table at the time of initialization in S101. FIG. 15A shows a vertex configuration table, FIG. 15B shows a head position table, and FIG. 15C shows a vertex coordinate table. In the head position table, a vertex ID is associated with a hash value and recorded as a link destination vertex ID. Here, since the hash value takes a value of 0 to 3 as shown in FIG. 14, “−1” is set as the link destination vertex ID in the initial position head table in association with all the hash values 0 to 3. "It has become. In the vertex coordinate table, the vertex coordinates are recorded in association with the vertex ID, and the link destination vertex ID is recorded.

  As shown in FIG. 15A, in the vertex configuration table, three vertex IDs are recorded in the vertex order in association with the polygon ID. The vertex order is 0, 1, 2 from the left. These correspond to the first vertex, the second vertex, and the third vertex shown in FIG. At the time of initialization in step S101, the vertex order is initialized to zero. It is assumed that the coordinate value (Xd, Yd, Zd) of the first vertex of the polygon P1 is extracted from the vertex coordinate array data in step S102, and the hash value “0” is calculated in step S103. When the head position table is referenced with the hash value “0” in step S104, since the vertex ID of the link destination is not registered in step S105, the head position table is associated with the hash value “0” of the head position table in step S106. The current vertex ID “0” is recorded as the link destination.

  In step S107, the coordinate value (Xd, Yd, Zd) extracted in step S102 is recorded at the position of the current vertex ID “0” in the vertex coordinate table, and “−1” is recorded as the link destination vertex ID. To do. In step S107, the current vertex ID “0” is recorded at the position of the current polygon ID “P1” in the current vertex order “0”. As a result, each table is in a state as shown in FIG. Then, the vertex ID is incremented to change the current vertex ID from “0” to “1”. Also, the vertex order is incremented to change the current vertex order from “0” to “1”. Since the current polygon ID is “P1” and does not exceed “P13”, it is determined in step S111 that processing has not been completed for all polygons, and the process returns to step S102.

  In step S102, the coordinate value (Xb, Yb, Zb) of the second vertex of the polygon P1 is extracted from the vertex coordinate array data based on the current polygon ID “P1” and the current vertex order “1”. In step S103, the hash value “0” is calculated for the coordinate values (Xb, Yb, Zb). If the head position table is referenced with the hash value “0” in step S104, “0” is already registered as the link destination vertex ID in step S105. Therefore, in step S108, the registered vertex ID “0” is set. The coordinate values (Xd, Yd, Zd) in the corresponding vertex coordinate table are collated with the coordinate values (Xb, Yb, Zb) extracted in step S102. As a result of the collation, there is a mismatch, so in step S110 it is determined whether the vertex ID of the link destination in the vertex coordinate table is 0 or more or a negative value.

  As shown in FIG. 16, since the vertex ID of the link destination is “−1”, in step S107, the coordinate value (Xb, X) extracted in step S102 is added to the position of the current vertex ID “1” in the vertex coordinate table. Yb, Zb) is recorded, and “−1” is recorded as the link destination vertex ID. Further, in step S107, the current vertex ID “1” is recorded at the position of the current polygon ID “P1” in the current vertex order “1” in the vertex configuration table. As a result, each table is in a state as shown in FIG. Then, the vertex ID is incremented to change the current vertex ID from “1” to “2”. Also, the vertex order is incremented to change the current vertex order from “1” to “2”. Since the current polygon ID is “P1” and does not exceed “P13”, it is determined in step S111 that processing has not been completed for all polygons, and the process returns to step S102.

  The polygon ID “P1”, the vertex ID “2”, and the vertex order “2” are processed in the same manner as the polygon ID “P1”, the vertex ID “1”, and the vertex order “1”. The state shown in FIG. 18 is obtained. Then, the vertex ID is incremented to change the current vertex ID from “2” to “3”. Since the vertex order takes only three values “0”, “1”, and “2” for one polygon, the polygon ID is incremented to “P1” → “P2”, and the vertex order is reset to the current The vertex order of “2” → “0”. Since the current polygon ID is “P2” and does not exceed “P18”, it is determined in step S111 that processing has not been completed for all polygons, and the process returns to step S102.

  In step S102, the coordinate value (Xd, Yd, Zd) of the first vertex of the polygon P2 is extracted from the vertex coordinate array data based on the current polygon ID “P2” and the current vertex order “0”. In step S103, the hash value “0” is calculated for the coordinate values (Xd, Yd, Zd). If the head position table is referenced with the hash value “0” in step S104, “0” is already registered as the link destination vertex ID in step S105. Therefore, in step S108, the registered vertex ID “0” is set. The coordinate values (Xd, Yd, Zd) in the corresponding vertex coordinate table are collated with the coordinate values (Xd, Yd, Zd) extracted in step S102. As a result of the collation, in step S109, the vertex ID “0” having the same coordinate value in the vertex coordinate table is set as the current vertex order “0” position of the current polygon ID “P2” in the vertex configuration table. To record. As a result, each table is in a state as shown in FIG.

  As described above, the process is performed up to the polygon P18, and the process is terminated by the determination in step S111. At this time, each table is in a state as shown in FIG. That is, a single vertex ID in which other coordinate values having the same hash value are recorded closest to the vertex ID is associated as a link destination. As described above, in the polygon model structuring process, coordinate values are collated in step S108, and if they do not match, they are additionally registered in the vertex coordinate table. If they match, the collation is repeated one after another. To go. In this process, the load increases as the vertex coordinate table increases and the number of registered coordinate values increases. In this embodiment, it is obvious that the hash value does not match different coordinate values without referring to all the coordinate values in the vertex coordinate table by referring to the hash value-specific vertex coordinate table. Therefore, it can be excluded from the verification target, and only the vertex coordinate table having the same hash value needs to be referred to. In the present embodiment, the coordinate value having the same hash value in the vertex coordinate table is about 1/4 at most. However, as described above, in many cases, in the above [Equation 2], S = 32 is often set. Then, the coordinate value having the same hash value in the vertex coordinate table is reduced to about 1/32767, and the verification time is also reduced to about 1/32767 compared with the case of matching with all cases. For this reason, the structuring process of the polygon model can be performed at an extremely high speed.

  In the example of FIG. 20, when the hash value is “0”, only the vertex IDs “0”, “1”, “2”, and “6” are collated in the vertex coordinate table of FIG. Then, it is possible to determine whether or not a new vertex coordinate should be additionally registered. By deleting the head position table shown in FIG. 20B and deleting the link destination vertex ID field from the vertex coordinate table shown in FIG. 20C, the vertex configuration table as shown in FIG. A vertex coordinate table can be obtained and the structuring of the polygon model is completed.

  FIG. 21 is a diagram showing the vertex configuration table and the vertex coordinate table prepared in step S21. The vertex configuration table shown in FIG. 21A associates each vertex constituting a polygon with a shared vertex that uniquely identifies the polygon in the polygon model, and a vertex ID that is identification information of the shared vertex is a polygon identification that identifies the polygon. It is a table recorded in association with polygon ID which is information. In the present embodiment, since the polygon is a triangle, in the example of FIG. 21A, three vertex IDs are associated with one polygon ID. The vertex coordinate table shown in FIG. 21B is a table in which vertex IDs that are identification information of shared vertices and vertex coordinates that are xyz coordinate values of vertices in the polygon model are recorded in association with each other.

  Next, the table definition means 40 initializes the vertex duplication table (step S22). The vertex duplication table is a table in which vertex IDs and duplication destination vertex IDs (shown as “duplication destination” in the figure) are associated with each other. FIG. 21C shows an example of the vertex overlap table. In the vertex duplication table, “−1” indicating that there is no duplication destination is set as an initial value. If it can be shown that there is no duplication destination, an initial value other than “−1” may be set.

  Next, the table definition means 40 initializes the vertex update table (step S23). The vertex update table is a table in which vertex IDs are associated with update flags (shown as “update” in the figure). FIG. 21D shows an example of the vertex update table. In the vertex update table, “0” indicating that the vertex has not been updated is set as an initial value. If it can be shown that it has not been updated, an initial value other than “0” may be set.

  Next, the deletion target polygon setting means 50 calculates the area and circumference of each polygon for all polygons constituting the polygon model, and calculates the minimum value of the product of the calculated area and circumference (step). S24). That is, for every polygon, the product is calculated by multiplying the area and the perimeter, and the value that minimizes the product of the area and the perimeter is specified in each polygon.

  Next, the deletion target polygon setting unit 50 sets a value obtained by multiplying the minimum value calculated in step S24 by a predetermined coefficient α as a predetermined threshold value, and the product of the area and the circumference is less than the predetermined threshold value. Then, a polygon in which one of the three vertices is not updated is set as a polygon to be deleted, and processing for integrating the two end points of the shortest ridge line (shortest side) of the deletion target polygon into the middle point is performed (step S25). . The predetermined coefficient α is preferably set to a real value that takes a value of 1 or more, and is preferably in the range of 1.5 ≦ α ≦ 2.5. In the present embodiment, α = 2.0. If one of the three vertices is not updated, it means that no other neighboring polygons that have vertices shared with any vertex of the polygon to be set as the deletion target are set in advance as the deletion target. This means that it is necessary to make sure that not only the two vertices that are the two end points of the shortest edge that are actually deleted, but also the other remaining vertices are not updated. By setting, the polygon model after deletion is prevented from being distorted. Specifically, referring to the vertex update table, for the polygon P6, it is confirmed that all the update flags corresponding to the vertex IDs “6”, “9”, and “10” are “0”, and the polygon to be deleted And In this way, by referring to the vertex update table, it can be confirmed that all the vertices of the polygon are not shared with the two vertices of the deletion target ridgeline of all the polygons already set as the deletion target. Two vertices of the deletion target ridge line are deletion target vertices.

  In the processing in step S25, it is assumed that there are two polygons, polygon P6 and polygon P10, in the polygon group shown in FIG. 10 whose product of area and circumference is less than the threshold value. As shown in FIG. 22, it is assumed that the shortest ridge line of the polygon P6 is the ridge line DE and the shortest ridge line of the polygon P10 is the ridge line JK. In this case, processing is performed from the ridge line JK which is the shortest ridge line of the two shortest ridge lines. Then, it is checked with reference to the vertex update table whether or not the three vertices of the polygon P10 having the ridge line JK have been updated. As shown in FIG. 21, in the initial state, the update flags at the three vertices of the polygon P10 are all “0”, so the polygon P10 is a deletion target polygon. In this case, the two vertices J and K are integrated into the middle point O, respectively.

  Next, the vertex coordinate table update unit 60, the vertex overlap table update unit 70, and the vertex update table update unit 75 update the vertex coordinate table, the vertex overlap table, and the vertex update table (step S26). Specifically, the middle point of the ridge line JK is O (Xo, Yo, Zo), and the vertex coordinate value (Xj, Yj, Zj) of the vertex ID “9” corresponding to the vertex J in the vertex coordinate table. Is changed to the coordinate value (Xo, Yo, Zo) of the middle point O. Also, the vertex coordinate value (Xk, Yk, Zk) of the vertex ID “10” corresponding to the vertex K is deleted from the vertex coordinate table.

  The vertex with the vertex ID “10” is the same as the coordinates (Xo, Yo, Zo) of the vertex with the vertex ID “9”, and overlaps. Therefore, in the vertex duplication table, the duplication destination of the vertex ID “10” deleted from the vertex coordinate table is set to the vertex ID “9”. Also, in the vertex update table, in order to record that a predetermined vertex has been updated in the vertex overlap table, the update flags of the vertex IDs “9” and “10” in which the vertex overlap table has been updated are set to “1”. Set to. This means that the vertex specified by the vertex ID is set as the deletion target vertex. As a result, each table is changed from the initial state shown in FIG. 21 to the state shown in FIG.

  Then, the process returns to step S25, and the ridge line DE which is the longest shortest ridge line of the two shortest ridge lines is processed. Specifically, it is checked by referring to the vertex update table whether or not the three vertices of the polygon P6 having the edge line DE have been updated. As shown in FIG. 23, even after the processing of the ridgeline JK of the polygon P10, the update flags at the three vertices of the polygon P6 are all “0”, so the polygon P6 becomes the deletion target polygon. In this case, the two vertices D and E are integrated into the middle point P, respectively.

  In step S26, the vertex coordinate table, the vertex update table, and the vertex overlap table are updated. Specifically, the middle point of the edge line DE is P (Xp, Yp, Zp), and the vertex coordinate value (Xd, Yd, Zd) of the vertex ID “0” corresponding to the vertex D in the vertex coordinate table. Is changed to the coordinate value (Xp, Yp, Zp) of the midpoint P. Further, the vertex coordinate value (Xe, Ye, Ze) of the vertex ID “6” corresponding to the vertex E is deleted from the vertex coordinate table.

  The vertex with the vertex ID “6” is the same as the coordinates (Xp, Yp, Zp) of the vertex with the vertex ID “0”, and overlaps. Therefore, in the vertex duplication table, the duplication destination of the vertex ID “6” deleted from the vertex coordinate table is set to the vertex ID “0”. Further, in the vertex update table, the update flags of the vertex IDs “0” and “6” whose vertex overlap table is updated are set to “1”. As a result, each table is changed from the state shown in FIG. 23 to the state shown in FIG.

  When the processing is completed for all the polygons to be deleted, the vertex configuration table update unit 80 updates the vertex configuration table based on the updated vertex duplication table, and deletes the polygons with overlapping vertices (step S27). First, the vertex configuration table is updated based on the vertex overlap table. Specifically, for the vertex ID for which the duplication destination is set in the vertex duplication table, the vertex ID of the vertex configuration table is replaced with the duplication destination vertex ID. For example, in the vertex duplication table shown in FIG. 25C, the duplication destination of the vertex ID “6” is “0” and the duplication destination of the vertex ID “10” is “9”. All the vertex IDs “6” are replaced with the vertex ID “0”, and all the vertex IDs “10” are replaced with the vertex ID “9”. As a result, the vertex configuration table is updated to a state where the vertex ID “6” and the vertex ID “10” do not exist, as shown in FIG.

  Next, polygons with overlapping vertices are deleted. Specifically, in the vertex configuration table, when the vertex IDs of two vertices among the three vertices corresponding to one polygon are the same, the polygon information is deleted from the vertex configuration table. In the example of FIG. 25A, the vertex ID “0” for the polygon P5, the vertex ID “0” for the polygon P6, the vertex ID “9” for the polygon P10, and the vertex ID “9” for the polygon P16 overlap. . For this reason, information on polygons P5, P6, P10, and P16 is deleted from the vertex configuration table. Also, information regarding vertices whose vertex coordinates are not recorded in the vertex coordinate table is deleted. As a result, the vertex configuration table is in a state as shown in FIG.

  When the vertex coordinate array data is updated, the control means 10 determines whether or not the total number of polygons after the reduction is equal to or less than the set target value (step S28). As the target value, an arbitrary value can be set in advance. If it is determined that the total number of polygons is not less than or equal to the target value, the process returns to step S22, the vertex duplication table is reinitialized, and the vertex update table is reinitialized in step S23. As a result, the vertex duplication table and the vertex update table are in a state as shown in FIGS. 26 (c) and 26 (d), respectively. After re-initializing the vertex duplication table and the vertex update table, in step S24, for all remaining polygons after reduction, the area and circumference based on the area and circumference of each polygon already calculated. Using the predetermined threshold value obtained by multiplying the newly calculated minimum value by the coefficient α, the deletion target polygon setting means 50 selects other polygons from the remaining polygons. Are selected as polygons to be deleted.

  If the result of determination in step S28 is that the total number of polygons is less than or equal to the target value, the polygon reduction process is terminated. By executing the processing according to the flowchart of FIG. 12, the number of polygons is reduced so as to be equal to or less than the target value set for each group. If the structuring process of the polygon model is not performed, a large processing load is required to search for a vertex having the same coordinates as the two correction target vertices of the deletion target side of the deletion target polygon. By performing the polygon model structuring process, the processing load can be significantly reduced.

  When the processing shown in FIG. 12 is completed, finally, the polygon model update unit 90 updates the vertex coordinate array data. Specifically, referring to the vertex coordinate table, each vertex ID in the vertex configuration table is replaced with the vertex coordinate. From the vertex configuration table shown in FIG. 26 (d) and the vertex coordinate table shown in FIG. 26 (b), vertex coordinate array data as shown in FIG. 27 is obtained. This is replaced with the original vertex coordinate array data shown in FIG. As a result, the polygon group shown in FIGS. 10 and 22 is changed to a polygon group as shown in FIG. It can be seen that not only the deletion target polygons P6 and P10 set in the polygon group shown in FIGS. 10 and 22, but also the polygons P5 and P16 are deleted. Thereby, the polygon reduction process of step S20 is complete | finished.

<2.5. Small volume group deletion processing>
Next, the process of deleting the isolated small volume group by the group combining unit 100 in step S40 will be described. Here, prior to the description of the processing for deleting the isolated small volume group, the reason for performing the processing for deleting the isolated small volume group will be described. FIG. 29 is a diagram for explaining a problem caused by the polygon reduction process. FIG. 29A shows two groups of polygons immediately after the group classification process in step S10 is completed. In the example of FIG. 29A, there are a left group including vertices D, E, and K and a right group including vertices D ′, E ′, and K ′. If the vertices D and D ′, the vertices E and E ′, and the vertices K and K ′ are less than the resolution of the 3D printer, respectively, when these two groups of polygons are output by the 3D printer, the vertices D and D ′, E ′, vertices K and K ′ are connected by resin or the like, and the two groups are output as connected objects. That is, the two groups are physically bonded.

  When the polygon reduction process in step S20 is executed for the right-side group of polygons shown in FIG. 29A, polygon E'FK 'is selected as the deletion target polygon as shown in FIG. 29B. The Further, as shown in FIG. 29C, the shortest edge E'F of the deletion target polygon E'FK 'is selected as the deletion target side, and the midpoint O of the side E'F is calculated. Then, as shown in FIG. 29 (d), the deletion target polygon E'FK 'and the deletion vertex sharing polygon D'E'F are deleted.

  As can be seen by comparing FIG. 29A and FIG. 29D, the two groups on the left and right sides are further separated after the polygon reduction process than before the polygon reduction process. When the distance between the two groups shown in FIG. 29D exceeds the resolution of the 3D printer, when the two groups of polygons are output by the 3D printer, the two groups are output as different objects. If the two groups are both large objects, there is no problem. However, when one becomes a very small object, for example, when one group is a main body and the other group is like a beard attached to the main body, the whiskers output separately from the main body are 3D. There is a risk that it may get into the printer and cause problems such as machine clogging. In order to eliminate such a problem, an isolated small volume group such as the above-mentioned beard is deleted.

  FIG. 30 is a flowchart showing details of the processing for deleting the isolated small volume group (step S40) by the group combining means 100. First, the group synthesizing unit 100 calculates the maximum value and the minimum value in the X, Y, and Z directions for all the vertices of all the polygons for each group (step S41). As a result, for group g, minimum value Xmin (g), maximum value Xmax (g), minimum value Ymin (g), maximum value Ymax (g), minimum value Zmin (g), maximum value Zmax (g) Is obtained. Next, the group synthesizing unit 100 calculates the volume of the circumscribed cuboid for each group (step S42). Specifically, the volume V (g) of the circumscribed cuboid of the group g is calculated by executing the processing according to the following [Equation 3].

[Formula 3]
V (g) = (Xmax (g) −Xmin (g)) × (Ymax (g) −Ymin (g)) × (Zmax (g) −Zmin (g))

  The group synthesizing unit 100 executes the processes of steps S41 and S42 for all groups. Thereby, the volume of a circumscribed rectangular parallelepiped is obtained for all groups. Next, the group synthesizing unit 100 identifies a group in which the volume of the circumscribed rectangular parallelepiped is the smallest among all the groups (Step S43). Then, the group synthesizing unit 100 calculates the minimum interval between the identified group and all other groups (step S44). Details of the minimum interval calculation process in step S44 will be described later.

  Subsequently, the group synthesizing unit 100 determines whether or not the minimum interval calculated in step S44 is greater than or equal to a predetermined threshold value (step S45). The predetermined threshold for comparison with the minimum interval is preferably a numerical value corresponding to 0.2 mm at the time of 3D printer output. As a result of the determination, when the minimum interval is equal to or greater than a predetermined threshold, the group with the smallest volume is separated from the nearest group by a predetermined distance or more. Is deleted (step S46). If the result of determination in step S45 is that the minimum interval is less than the predetermined threshold, the group with the smallest volume is close to the closest group and below the resolution of the 3D printer. Does not perform the process of deleting the smallest volume group.

  When the group is deleted in step S46, the group is processed in any case where the deletion is not performed. And it returns to step S43 and specifies the group from which the volume of a circumscribed rectangular parallelepiped becomes the smallest among unprocessed groups. When the processing of step S43 to step S46 is repeated and the processing for all the groups is completed, the processing for deleting the isolated small volume group is ended.

  Details of the minimum interval calculation processing in step S44 will be described. FIG. 31 is a flowchart showing details of the minimum interval calculation processing in step S44 of FIG. The group synthesizing unit 100 sets a predetermined value or more as a variable dmin indicating the minimum interval as an initial value. As an initial value given to dmin, a large value that cannot be set as a minimum interval between groups may be set. Then, the group synthesizing unit 100 extracts one group h having a volume larger than the group g from all the groups (Step S47). As a result, the minimum value Xmin (h), the maximum value Xmax (h), the minimum value Ymin (h), the maximum value Ymax (h), the minimum value Zmin (h), and the maximum value Zmax (h) are obtained for the group h. It is done. Next, the group synthesizing unit 100 calculates the minimum difference between the two groups for each of the X, Y, and Z directions (step S48). Specifically, the minimum value dx in the X direction difference, the minimum value dy in the Y direction difference, and the minimum value dz in the Z direction difference are calculated by executing processing according to the following [Equation 4]. .

[Formula 4]
dx = Min {| Xmax (g) -Xmin (h) |, | Xmin (g) -Xmax (h) |}
dy = Min {| Ymax (g) -Ymin (h) |, | Ymin (g) -Ymax (h) |}
dz = Min {| Zmax (g) -Zmin (h) |, | Zmin (g) -Zmax (h) |}

  Subsequently, the group synthesizing unit 100 sets the maximum one of the calculated minimum values for each direction as the minimum value between groups, and compares the minimum value between groups with the minimum value between all groups among other already processed groups. Then, the process of setting the smaller one as the minimum value between all groups is performed (step S49). Specifically, among the three direction-specific minimum values dx, dy, and dz calculated in step S48, the inter-group minimum value Max (dx, dy, dz) that takes the maximum value is compared with dmin, and Max ( When dx, dy, dz) <dmin, dmin = Max (dx, dy, dz). As a result, the minimum value between all groups, which is the minimum value among the minimum values between groups, is recorded in dmin.

  When the processes of steps S47, S48, and S49 are repeatedly executed and the processes for all the groups having a volume larger than the group g are completed, the minimum interval calculation process illustrated in FIG. 31 is terminated, and the process proceeds to step S45 of FIG. Thus, the minimum interval dmin is compared with the threshold value.

<2.6. Synthesis of polygon model>
As shown in the processing outline of FIG. 9, in step S50, the group synthesizing unit 100 synthesizes the polygon models of all groups to obtain an updated polygon model for each region. In step S70, the polygon model synthesizing unit 110 synthesizes the polygon model for each region of the entire area to obtain a synthesized polygon model. All the synthesis processes are performed by simply combining the polygon models for each area excluding the header part and recording the total number of polygons in the header part (however, this is the case of the binary STL format and ASCII). In the STL format, the polygon model for each area excluding the header is simply combined). By outputting the synthesized polygon model stored in the synthesized polygon model storage unit 130 to the 3D printer 7, the 3D printer 7 can efficiently form a three-dimensional object. For the three-dimensional object that was shaped, there was almost no deterioration.

<3. 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 processing target polygon is a triangle, but it may be a quadrilateral or more.

  Further, in the above embodiment, the area and perimeter are calculated for the polygon, and the polygon whose product of the area and perimeter is less than a predetermined threshold is selected as the polygon to be deleted. A polygon that is less than the threshold value may be selected as a deletion target polygon. In this case, a value obtained by multiplying the minimum value of the area by a predetermined coefficient can be used as the predetermined threshold value, and a coefficient α having a value of 1 or more can be used as the predetermined coefficient. The coefficient α is preferably in the range of 1.5 ≦ α ≦ 2.5.

  In the above embodiment, the polygon model whose volume is less than the predetermined threshold is deleted from the updated polygon models of a plurality of groups. However, it is possible not to delete the polygon model. It is.

1 ... CPU (Central Processing Unit)
2 ... RAM (Random Access Memory)
3 ... Storage device 4 ... Key input I / F
5. Data input / output I / F
6 ... Display unit 7 ... 3D printer (three-dimensional object modeling device)
7a ... Data processing unit 7b ... Output unit 10 ... Control unit 20 ... Group classification unit 30 ... Polygon model structuring unit 40 ... Table definition unit 50 ... Deletion target polygon setting Means 60: Vertex coordinate table update means 70: Vertex overlap table update means 75 ... Vertex update table update means 80 ... Vertex configuration table update means 90 ... Polygon model update means 100 ... Group Combining means 110... Polygon model synthesizing means 120... Polygon model storing means for each region 130... Synthetic polygon model storing means 200.

Claims (8)

A device for reducing polygon model data expressed as a collection of polygons for modeling a three-dimensional object,
By searching for the vertices of different polygons having the same coordinate value for each vertex of each polygon constituting the polygon model, and assigning the same vertex ID to the obtained series of vertices, each polygon Each vertex included in the vertex is expressed by a vertex ID having the same value as the vertex of the same coordinate, and recorded in association with a polygon including each vertex, and the vertex ID and the coordinate assigned to the vertex configuration table A vertex coordinate table in which values are recorded in association with each other; a polygon model structuring means for creating;
A table defining means for defining a vertex duplication table for recording a correspondence relationship between a vertex recorded in the vertex coordinate table and a duplication destination vertex having the same coordinates;
Deletion of all polygons for which all of the vertices have already been set as deletion targets for the polygons recorded in the vertex configuration table, where either the product of the area, circumference, or area is less than or equal to a predetermined threshold Polygons that are not shared with the two vertices of the target ridge line are sequentially set as deletion target polygons, and further, a deletion target polygon setting means for selecting a deletion target ridge line from each set polygon,
With reference to the vertex configuration table, the two end points of the deletion target ridge line of all the polygons set by the deletion target polygon setting means are set as deletion target vertices, and the vertex coordinate table is referenced based on the deletion target vertices. An average point of the two deletion target vertices is obtained, one of the deletion target vertices is set as a representative vertex, information on the deletion target vertices other than the representative vertex is deleted from the vertex coordinate table, and the vertex ID of the representative vertex A vertex coordinate table updating means for recording the coordinate value of the average point in association with each other,
In the vertex duplication table, vertex duplication table update means for setting the duplication destination of the deletion target vertex other than the representative vertex to the representative vertex;
When the value of each vertex ID in the vertex configuration table is changed to the duplication destination set in the vertex duplication table and, as a result of the change, if two or more vertex IDs corresponding to the same polygon overlap, Vertex configuration table updating means for deleting from the vertex configuration table;
A polygon model that updates a polygon model by replacing each vertex ID of the vertex configuration table updated by the vertex configuration table update means with a coordinate value while referring to the vertex coordinate table updated by the vertex coordinate table update means Update means;
A three-dimensional object shaping data reduction device characterized by comprising: When the number of polygons constituting the polygon model updated by the polygon model updating unit is larger than a predetermined target value, the deletion target polygon setting unit, the vertex coordinate table updating unit, the vertex duplication table updating unit, the vertex configuration table Update means, control means for performing control to repeatedly execute the process on the polygon model update means,
The three-dimensional object modeling data reduction device according to claim 1, further comprising: Furthermore, a vertex update table update means is provided,
The table defining means further defines a vertex update table for recording that the vertex recorded in the vertex coordinate table is set as the deletion target vertex;
The deletion target polygon setting means refers to the vertex update table, and designates a polygon that is not recorded as being set as the deletion target vertex as a polygon that is not shared with two vertices of the deletion target ridge line of all the polygons. ,
The said vertex update table update means sets the said vertex of a vertex update table to a deletion object vertex, when the update about the vertex in the said vertex duplication table is performed, The Claim 1 or Claim 2 characterized by the above-mentioned. 3D object modeling data reduction device. The deletion target polygon setting means includes:
The area is calculated for all the polygons recorded in the vertex configuration table, and a value obtained by multiplying the minimum value of the area by a predetermined value of 1 or more is set as the predetermined threshold value. The data reduction apparatus for three-dimensional object formation as described in any one of Claims 1-3 characterized by these. The deletion target polygon setting means includes:
Areas and perimeters are calculated for all polygons recorded in the vertex configuration table, and a value obtained by multiplying the minimum value of the product of the area and perimeter by a predetermined value of 1 or more is the predetermined threshold value. The data reduction apparatus for three-dimensional object formation according to any one of claims 1 to 3, wherein the three-dimensional object formation data reduction device is set.   6. The deletion target polygon setting means selects a shortest ridge line when selecting a deletion target ridge line from polygons set as a deletion target. The data reduction apparatus for three-dimensional object modeling described in the item. A three-dimensional object shaping data reduction device according to any one of claims 1 to 6,
A three-dimensional object modeling apparatus that models a three-dimensional object using the polygon model output from the three-dimensional object modeling data reduction apparatus;
A three-dimensional object forming system characterized by comprising:   A program for causing a computer to function as the three-dimensional object formation data reduction device according to any one of claims 1 to 6.