JP5520804B2 - Surface mesh model generating apparatus, surface mesh model generating method and computer program for generating surface mesh model used in calculation of boundary element method - Google Patents

Description

  The present invention relates to a surface mesh model generation device, a surface mesh model generation method, and a computer program that generate a surface mesh model used in calculation of a boundary element method.

  In recent years, in order to operate robots and other devices, by detecting human brain waves (intra-brain current), a technology that controls robots and other devices to operate only by considering the operation (BMI) : Brain Machine Interface). In the field of BMI, in order to calculate an electromagnetic field generated by a brain current, a boundary element method for calculating an electromagnetic field using a three-dimensional model of a human head is generally used. In order to calculate the electromagnetic field by the boundary element method, it is necessary to model head tissues such as the scalp, skull, and brain by a surface mesh.

  By the way, since the head tissue has a particularly complicated brain shape, various methods for generating a surface mesh model have been devised. For example, Non-Patent Document 1 describes one method for generating a head surface mesh model using data obtained by MRI (Magnetic Resonance Imaging). This method performs the following seven steps to generate a surface mesh model.

[Step 1]
The outline of the cross section is extracted from data of a plurality of cross sections obtained by cutting the human head along a horizontal plane (assuming that a person is standing).
[Step 2]
A plurality of contour lines obtained are stacked to generate a three-dimensional model of the human head based on the contour lines.
[Step 3]
A surface mesh is generated by creating a node on the contour line and connecting nodes on adjacent contour lines, and a three-dimensional model of the head using the surface mesh is generated.
[Step 4]
The model obtained in step 3 is expanded and deformed into a smooth curved surface.
[Step 5]
Separately, a quasi-regular polyhedral surface mesh model is generated.
[Step 6]
The nodes of the quasi-regular polyhedron are projected onto the smooth curved surface obtained in step 4.
[Step 7]
The surface mesh model obtained by projecting in step 6 is subjected to a reverse conversion to that in the case where the surface mesh model is expanded in step 4, thereby obtaining a surface mesh model having a shape following the surface shape of the head.

  In general, in the surface mesh model, it is desirable that each element (surface mesh element) is as close to an equilateral triangle as possible and the size is uniform from the viewpoint of accuracy and efficiency of calculation by the boundary element method. Therefore, in the method of the prior art, after a three-dimensional model is generated once in step 3, an attempt is made to improve the surface mesh shape by performing deformation and projection in steps 4 to 7.

Saburo Honma, “Identification of brain potential source”, Nihon Crihonsha, p. 29-33

  However, in the method of Non-Patent Document 1 described above, the operation from the original MRI data (data having coordinates and contrast information) to the generation of the head surface mesh model once is very complicated. There was a problem that it took time and effort. Due to its complexity, it has been difficult to automate the calculation until the final head surface mesh model is generated.

  Further, in the conventional method, the inverse transformation in step 7 destroys the uniformity of the shape and size of the surface mesh, and the error is mixed when the inverse transformation in step 7 is performed. There is a problem that the shape reproducibility of the model is poor.

  Therefore, an object of the present invention is to provide a surface mesh model generation device, a surface mesh model generation method, and a computer program that can generate a surface mesh model including a surface mesh that is as uniform as possible with a small number of calculations.

The present invention that solves the above-described problems is a surface mesh model generation device that generates data of a surface mesh model used in the calculation of the boundary element method, and includes data of a point group {ri} that can specify the surface of an object. A storage device that stores object data and a projection reference model including a spherical mesh model in which surface meshes are arranged in a substantially spherical shape, and the center of the projection reference model is located inside the object surface specified by the object data in a state of being, through each node ni of the projection reference model, and a projection vector calculating means for calculating a projection vector Vi substantially perpendicular to the projection reference model of the position of the node ni, the previous SL object data having From the point group {ri}, a point ri corresponding to the surface of the object and closest to each projection vector Vi is selected, and a projection point pi is determined from the point ri. A projection point determining means, characterized in that it comprises a data generating means for generating data of the surface mesh model of the projection points pi determined in the projection point determining means as the nodal point.

  According to such an apparatus, the nodes of the spherical mesh model are projected directly onto the surface of the object consisting of point cloud data, and a surface mesh model consisting of a surface mesh of uniform size and shape is generated with a small number of man-hours. can do. That is, conventionally, a temporary surface mesh model made of a surface mesh with irregular sizes and shapes was created from the point cloud data, and the nodes of the spherical mesh model were projected onto the surface mesh model. In this apparatus, the projection point pi is determined from the point corresponding to the surface of the object at the node of the spherical mesh model without creating a provisional surface mesh model, and the target surface mesh model with the projection point pi as a node is determined. Therefore, the surface mesh model can be generated efficiently.

  When determining the projection point pi from the point ri, the point ri may be the projection point pi, or a point in the vicinity of the point ri, for example, a point obtained by projecting the point ri onto the projection vector Vi may be used as the projection point pi. .

  In the above-described apparatus, if necessary, a point on the line segment that divides the line segment connecting the projection point pi determined by the projection point determination unit and the node ni at a predetermined ratio is set as a new node ni. Update projection reference model generation means for generating a new projection reference model, wherein the projection point determination means determines the projection point pi from the projection vector Vi based on the first projection reference model, and generates the updated projection reference model It is desirable to determine the final projection point pi used by the data generation unit by executing the projection point pi by the projection vector Vi based on the projection reference model generated by the unit twice or more in total.

  According to such an apparatus, the node surface is not projected onto the surface of the object on the point cloud data from the initial projection reference model (spherical mesh model) at once, but through one or more temporary projections. A node is projected on. Therefore, when the orientation of the spherical mesh and the surface of the object is partially different, such as when there are concave or convex portions on the surface of the object, the uniformity of the shape and size of the surface mesh can be reduced by one projection. Although it may be difficult to remove, the projection direction gradually turns toward the object surface after two or more projections, and even if there are concave or convex portions on the surface of the object, it has a uniform shape and size. A surface mesh model corresponding to the surface of the object can be generated.

  In the above-described apparatus, the object data includes, as data of the point group {ri}, spatial coordinates of a plurality of points ri constituting the object, and attribute data id that is an attribute of each point ri, When the projection point determining means determines the projection point pi of the node ni on the object surface having a specific attribute, (1) the attribute data id of the point ri is a specific value, (2) the projection It is determined that the distance between the vector Vi and each point ri is within the range of the predetermined value ε, and the distance to the node ni is maximum or minimum in the point group {ri} that satisfies (1) and (2). The point ri can be selected and the projection point pi can be determined from the point ri.

  According to such a configuration, the object data has not only the surface data but also a three-dimensional shape including internal elements, and the attribute of each point ri (for example, whether the point means skin, In the case of having an attribute such as meaning bone, a surface mesh model of the surface of an object belonging to a specific attribute can be generated. If the point ri having the maximum distance to the node ni is selected, a surface mesh model of the surface far from the projection reference model is generated, and if the point ri having the minimum distance to the node ni is selected, the projection reference model is selected. A surface mesh model of the near surface is generated.

  In the above-described apparatus, the object data includes only data of the point group {ri} corresponding to the surface of the object as the data of the point group {ri}, and the projection point determination unit is configured to output the projection vector Vi. It is also possible to calculate the distance between each point ri and determine the projection point pi from the closest point ri.

  When the object data includes only data of the point group {ri} corresponding to the surface of the object as the data of the point group {ri}, the projection point determining means can more easily perform the projection vector as in this device. A surface mesh model can be generated by calculating the distance between Vi and each point ri and determining the projection point pi from the closest point ri. Here, including only data of the point group corresponding to the surface of the object as the data of the point group {ri} means that the object represented by the point group {ri} has no thickness. However, for points other than the point group corresponding to the surface, there is a case where data indicating that the object is not an object is included. Therefore, attribute data may be included in the form, and the value of the attribute data of the point corresponding to the object surface is different from the value of the attribute data of the point corresponding to other than the object surface. As an example.

  In the above-described apparatus, the projection vector calculation means is calculated by the unit normal vector calculation means for calculating unit normal vectors of a plurality of surface meshes including each node ni as a constituent element, and the unit normal vector calculation means. By calculating the sum or average of the plurality of unit normal vectors, a vector sum calculating means for calculating the projection vector Vi of each node ni can be provided. The “unit” referred to here as a unit normal vector means that the sizes are uniform, that is, normalized, and is not necessarily limited to when the size is 1.

  When calculating the sum or average of the unit normal vectors, the vector sum calculation means multiplies the unit normal vector by a weight of the area of the surface mesh corresponding to the unit normal vector. It is desirable to calculate the sum or average of unit normal vectors. With such a configuration, an appropriate direction substantially orthogonal to the surface of the projection reference model at the node ni can be calculated as a projection vector.

  In the apparatus described above, after the projection point pi is determined by the projection point determination means, the distance between the node ni and the projection point pi corresponding to the node ni is calculated, and the node ni having the largest or smallest distance is selected. And a reference projection vector calculation means for calculating as a reference projection vector VD a vector that passes through the selected node ni and is substantially orthogonal to the projection reference model at the position of the node ni. The projection vector Vi corresponding to the node ni within the first predetermined distance from the reference projection vector VD calculated by the reference projection vector calculation means is set again in parallel with the reference projection vector VD, and the projection The point determination unit is configured to generate the data generation unit based on the projection vector Vi reset by the projection vector calculation unit. It may be configured to determine the final projected points pi used by.

  According to such an apparatus, if the projection reference model (spherical mesh model) is positioned outside the object, the distance between the node ni and the projection point pi corresponding to the node ni after the projection point pi is determined. When the node ni having the largest value is selected, the most depressed node ni is selected, and when the node ni having the smallest distance is selected, the node ni having the largest convexity is selected. Conversely, when the projection reference model (spherical mesh model) is positioned inside the object, after determining the projection point pi, the node ni having the largest distance between the node ni and the projection point pi corresponding to the node ni is determined. When the node ni is selected, the most convex node ni is selected. When the node ni having the shortest distance is selected, the most concave node ni is selected. Then, the selected node is set as the reference projection vector VD, and the projection vector Vi corresponding to the node ni within the first predetermined distance from the reference projection vector VD is set again in parallel with the reference projection vector VD. For a portion where the shape of the object is far (not copied) from the spherical shape, the projection vector Vi is directed toward the surface of the object. Thereby, even if the number of times of projection onto the object surface is small, the size and shape of the surface mesh of the generated surface mesh model can be easily aligned.

  In this apparatus, the projection vector calculation means includes a second projection that is out of the first predetermined distance range and larger than the first predetermined distance from the reference projection vector VD calculated by the reference projection vector calculation means. The projection vector Vi corresponding to the node ni within a predetermined distance range is combined with the reference projection vector VD and a vector that passes through each node ni and is substantially orthogonal to the projection reference model at the position of the node ni. It is desirable to calculate by

  By configuring in this way, it is possible to suppress a sudden change in the direction of the projection vector Vi from the node ni within the range of the second predetermined distance to the surface of the object outside the range of the first predetermined distance from the reference projection vector VD. It is possible to easily align the size and shape of the surface mesh of the surface mesh model.

  In the apparatus for generating a surface mesh model by a plurality of projections as described above, the apparatus further includes a smoothing unit that performs a smoothing process for reducing unevenness on the projection reference model generated by the updated projection reference model generation unit. desirable. As a result, a new projection reference model formed by the temporary projection points can be made a model having a gentle curved surface shape, and a sudden change in the direction of the projection vector used for the next projection (node ni within a small range). Difference in the direction of the projection vector between them) can be suppressed.

  Each of the devices described above may further include a sphere mesh generation unit that calculates the sphere mesh model and stores the sphere mesh model in the storage device. In other words, the spherical mesh model may store already prepared data in the storage device, or may be calculated by the device of the present invention and stored in the storage device.

The present invention for solving the above-described problems can also be configured as a method using a computer. That is, according to the present invention, the object data including the data of the point group {ri} that can specify the surface of the object and the projection reference model including the spherical mesh model in which the surface meshes are arranged in a substantially spherical shape are stored in the storage device. A surface mesh model generation method for generating data of a surface mesh model used in calculation of a boundary element method by a surface mesh model generation device constructed using a computer , wherein the projection vector calculation means provided in the computer includes the object data In the state where the center of the projection reference model is located inside the object surface specified in step (1), the projection reference model passes through each node ni and is substantially orthogonal to the projection reference model at the position of the node ni. and Luz step to calculate the projection vector Vi, the projection point determining unit included in the computer, the object data is Among groups {ri} points to correspond to the surface of the object, and the Luz step to determine the projection point pi, said computer comprises a closest point ri selected from the point ri in the projection vector Vi The updated projection reference model generation unit sets a point on the line segment that divides the line segment connecting the projection point pi determined by the projection point determination unit and the node ni at a predetermined ratio as a new node ni, and performs a new projection. generating a reference model, the data generation unit included in the computer, and a Luz step generates data of a surface mesh projection points pi determined in the projection point determining means as a nodal point, the projection point determination The means determines the projection point pi from the projection vector Vi based on the first projection reference model, and the projection based on the projection reference model generated by the updated projection reference model generation means. And determination of the projection point pi by vector Vi running over a total of two times, and determines the final projected point pi of the data generating means used.

Further, the method for solving the above-described problem includes a spherical mesh model in which surface data is arranged in a substantially spherical shape and object data consisting of data of a point group {ri} capable of specifying the surface of the object in a storage device. A surface mesh model generation method for generating data of a surface mesh model used in calculation of a boundary element method by a surface mesh model generation device constructed using a computer storing a projection reference model, the projection vector provided in the computer The calculation means passes through each node ni of the projection reference model in a state where the center of the projection reference model is positioned inside the object surface specified by the object data, and the position of the node ni A step of calculating a projection vector Vi substantially orthogonal to the projection reference model, and a projection point determining unit provided in the computer Selecting a point ri corresponding to the surface of the object and closest to each projection vector Vi from the point group {ri} included in the object data, and determining a projection point pi from the point ri; After the projection point pi is determined by the projection point determination unit, the reference projection vector calculation unit included in the computer calculates the distance between the node ni and the projection point pi corresponding to the node ni, and the distance is the largest or smallest. Selecting a node ni, calculating a vector that passes through the selected node ni and is substantially orthogonal to the projection reference model at the position of the node ni as a reference projection vector VD; and data generation means provided in the computer Generating surface mesh data with the projection point pi determined in the projection point determination step as a node, The projection vector calculation means makes the projection vector Vi corresponding to the node ni within the first predetermined distance from the reference projection vector VD calculated by the reference projection vector calculation means parallel to the reference projection vector VD. The projection point determination unit is set again, and the final projection point pi used by the data generation unit is determined based on the projection vector Vi reset by the projection vector calculation unit.

Moreover, the present invention that solves the above-described problems can also be configured as a computer program. That is, according to the present invention, the object data including the data of the point group {ri} that can specify the surface of the object and the projection reference model including the spherical mesh model in which the surface meshes are arranged in a substantially spherical shape are stored in the storage device. A computer program for generating data of a surface mesh model used for calculation of a boundary element method in a computer, wherein the computer is located in a state where the center of the projection reference model is located inside an object surface specified by the object data. , through each node ni of the projection reference model, and the projection vector calculating means for calculating a projection vector Vi substantially perpendicular to the projection reference model of the position of the node ni, the point cloud with the object data {ri} Among them, a point ri that corresponds to the surface of the object and is closest to each projection vector Vi is selected from the point ri. Projection point determining means for determining a Kageten pi, a point on the line segment that divides a line segment connecting the nodes ni and projection point pi of the projection point determining means has determined at a predetermined ratio, as a new node ni, An updated projection reference model generating means for generating a new projection reference model, functioning as a data generating means for generating data of a surface mesh model with the projection point pi determined by the projection point determining means as a node , and further determining the projection point Means of determining the projection point pi from the projection vector Vi based on the first projection reference model and the determination of the projection point pi based on the projection vector Vi based on the projection reference model generated by the updated projection reference model generation unit are 2 in total. It can be configured to be executed more than once and function to determine the final projection point pi used by the data generation means.
Further, the computer program of the present invention has a projection reference model consisting of object data consisting of data of a point group {ri} capable of specifying the surface of an object and a spherical mesh model in which surface meshes are arranged in a substantially spherical shape in a storage device. A computer program for generating data of a surface mesh model used for calculation of a boundary element method in a stored computer, the computer positioning the center of the projection reference model inside an object surface specified by the object data In this state, a projection vector calculation means for calculating a projection vector Vi that passes through each node ni of the projection reference model and is substantially orthogonal to the projection reference model at the position of the node ni, a point group possessed by the object data { ri}, the point ri corresponding to the surface of the object and closest to each projection vector Vi A projection point determination unit that selects and determines the projection point pi from the point ri; after the projection point pi is determined by the projection point determination unit, the distance between the node ni and the projection point pi corresponding to the node ni is calculated; Reference projection vector calculation for selecting a node ni having a large or small distance and calculating a vector that passes through the selected node ni and is substantially orthogonal to the projection reference model at the position of the node ni as a reference projection vector VD Means for generating data of a surface mesh model with the projection point pi determined by the projection point determination means as a node, and the projection vector calculation means is a reference calculated by the reference projection vector calculation means A projection vector Vi corresponding to a node ni within the first predetermined distance from the projection vector VD is determined as the reference projection. The projection point determination unit is caused to function so as to be set again in parallel with the vector VD, and the final projection point pi used by the data generation unit based on the projection vector Vi reset by the projection vector calculation unit. Can function to determine.

  According to the surface mesh model generating apparatus, the surface mesh model generating method, and the computer program for generating the surface mesh model used in the calculation of the boundary element method of the present invention, the surface mesh model having a relatively uniform shape and size can be obtained by a small number of calculations. Can be generated.

It is the structure of the data input into the surface mesh model production | generation apparatus of this invention, and a computer. It is a figure explaining projection of the node ni to the surface of an object. It is a block diagram which shows the structure of the surface mesh model production | generation apparatus which concerns on 1st Embodiment. It is a figure which shows the example of a spherical body mesh model. It is a figure explaining the calculation method of a projection vector, (a) is a figure facing the spherical mesh model which shows the surface mesh around the node ni and the unit normal vector of each surface mesh, (b) 2 is a cross-sectional view of a spherical mesh model showing a surface mesh around a node ni and a unit normal vector of each surface mesh. It is a figure explaining projection of the node ni with respect to an object. It is a flowchart explaining operation | movement of the surface mesh model production | generation apparatus which concerns on 1st Embodiment. (A) An example of a head surface mesh model created by a conventional method, and (b) an example of a head surface mesh model created by the apparatus of the first embodiment. It is a figure explaining the projection method of the node ni in the surface mesh model production | generation apparatus which concerns on 2nd Embodiment. It is a block diagram which shows the structure of the surface mesh model production | generation apparatus which concerns on 2nd Embodiment. It is a figure explaining projection of the node node ni to an object in steps. It is a flowchart explaining operation | movement of the surface mesh model production | generation apparatus which concerns on 2nd Embodiment. It is a figure which shows an example of the model of each step of the projection in 2nd Embodiment. (A) An example of a brain and brainstem surface mesh model created by the apparatus of the first embodiment, and (b) an example of a brain and brainstem surface mesh model created by the apparatus of the second embodiment. It is a figure explaining the projection method of the node ni in the surface mesh model production | generation apparatus which concerns on 3rd Embodiment. It is a block diagram which shows the structure of the surface mesh model production | generation apparatus which concerns on 3rd Embodiment. (A) An example of a brain surface mesh model created by the apparatus of the first embodiment, and (b) an example of a brain surface mesh model created by the apparatus of the third embodiment. It is a figure explaining the projection method of the node ni in the surface mesh model production | generation apparatus which concerns on 4th Embodiment.

Next, embodiments of the present invention will be described in detail with reference to the drawings as appropriate.
[First Embodiment]
A surface mesh model generation apparatus 100 according to the first embodiment, which is a basic form of the present invention, includes a computer having a CPU 2 and storage devices such as a ROM 3, a RAM 4, and an external storage device 5. A computer program is appropriately stored in the RAM 4. This is realized by being read and executed by the CPU 2. The surface mesh model generation apparatus 100 has an interface 6 for inputting / outputting data. When the object data 181 is input from the interface 6, the boundary element method is applied to the surface of an appropriate object specified by the object data 181. This is a device for generating a surface mesh model (data of a three-dimensional model composed of a triangular surface mesh) used in calculation.

  As an example, in the present embodiment, the object data 181 is exemplified by data of head tissues such as the scalp, skull, and brain used in BMI, and these data are generated from MRI data 189 obtained by MRI. . The MRI data 189 is image data in which the water content at each point appears as contrast (brightness) in each horizontal section of the head, and in each horizontal section, each pixel has a scalp, skull, brain based on the pixel position and contrast. It can be specified which head tissue corresponds to. Therefore, by assigning to each pixel position which head tissue it belongs to as attribute data id, data having coordinates and head tissue attribute data id is obtained for each pixel of the horizontal section. If the data to which the data id is assigned is stacked, the object data 181 to which the attribute data id of the head tissue is given at the three-dimensional coordinate positions of x, y, and z is obtained. That is, the object data 181 is data in which each point ri has the content of ri = [x, y, z, id]. The object data 181 is data including a point group {ri} that is a set of the points ri.

  The surface mesh model generation apparatus 100 according to the first embodiment is an apparatus that generates a surface mesh model from a spherical mesh model by a single projection. The outline of this projection will be described. As shown in FIG. 2, the center O of the projection reference model 183 that is a spherical mesh model is positioned inside the object surface 181A, and each node ni of the projection reference model 183 is placed on the object surface 181A. Projection points pi are determined by projection, and a surface mesh model is generated using the projection points pi as nodes. In the present embodiment and the following embodiments, as shown in FIG. 2, a description will be given of a case where projection is performed such that the projection reference model 183 (spherical mesh model) is positioned outside the object. 183 (spherical mesh model) may be inside the object surface 181A.

  As shown in FIG. 3, the surface mesh model generation device 100 includes a projection vector calculation unit 110, a projection point determination unit 130, a data generation unit 150, and a storage device 180.

  The storage device 180 stores object data 181 including the above point group {ri}, a spherical mesh model 182 and a projection reference model 183. As shown in FIG. 4, the spherical mesh model 182 is a surface mesh model in which nodes are regularly arranged on the surface of the sphere. For example, 1 of each surface mesh (triangle) of the regular icosahedron surface mesh model. It can be easily generated by dividing a side into two or three equal parts to obtain a new point and projecting this point onto a spherical surface to increase the number of new nodes. In this embodiment, the spherical mesh model 182 has already created data stored in the storage device 180, but the surface mesh model generation device 100 calculates the spherical mesh model 182 and stores it in the storage device 180. You may provide the well-known spherical mesh production | generation means to memorize | store. As the projection reference model 183, a spherical mesh model 182 is stored as a default value before the generation of the surface mesh model.

  The projection vector calculation means 110 passes through each node ni of the projection reference model 183 while the center O of the projection reference model 183 is located inside the object surface 181A specified by the object data 181, and the node ni. Is a means for calculating a projection vector Vi substantially orthogonal to the projection reference model 183 at the position. For this purpose, the projection vector calculation unit 110 includes a unit normal vector calculation unit 111 and a vector sum calculation unit 112.

  The unit normal vector calculation unit 111 is a unit that calculates unit normal vectors of a plurality of surface meshes including each node ni as a constituent element. Specifically, as shown in FIG. 5A, one node ni belongs to about 4 to 6 surface meshes MEi. In FIG. 5A, the surface mesh MEi is, for example, ME1 to ME1. Let it be ME5. That is, each surface mesh ME1-ME5 has the node ni as a component. Each of the surface meshes ME1 to ME5 has two nodes as components in addition to the node ni, and unit normal vectors nv1 to nv5 of the plane specified by the three nodes can be calculated by a known calculation method. .

  The vector sum calculation means 112 is a means for calculating the projection vector Vi of each node ni by calculating the sum or average of a plurality of unit normal vectors nvi calculated by the unit normal vector calculation means 111. In the present embodiment, in particular, in order to obtain a direction vector substantially orthogonal to the surface of the projection reference model 183 at the node ni, the vector sum calculation unit 112 sets the surface corresponding to the unit normal vector nvi as the unit normal vector nvi. The average of a plurality of unit normal vectors nvi is calculated by multiplying the area of the mesh MEi as a weight. Thereby, the projection vector Vi can be calculated as shown in FIG.

Projection point determination unit 130, among the group points with the object body data 181 {ri}, corresponds to the object surface 181A, and the projection points pi closest point ri from the selected the point ri in the projection vector Vi It is a means to determine. Specifically, when the projection point determining unit 130 determines the projection point pi of the node ni for the object surface 181A having a specific attribute, the attribute data id of the next condition (1) point ri is a specific value. (2) It is determined that the distance di between the projection vector Vi and each point ri is within the range of the predetermined value ε,
This is means for selecting the point ri having the maximum or minimum distance to the node ni from the point group {ri} satisfying (1) and (2) and determining the projection point pi from the point ri. Here, as an example, the point ri having the smallest distance is selected.

  The determination of the projection point pi will be described in more detail with reference to FIG. In FIG. 6, for the sake of simplicity, the object data 181 and the projection reference model 183 are displayed in a two-dimensional section. As shown in FIG. 6, the object data 181 is arranged in a lattice point shape, and each point ri has attribute data id. In the figure, the difference in the value of the attribute data id is represented as a difference in marks. As an example, a point ri having an attribute data id value of 1 is a scalp, a point ri having an attribute data id value of 2 is a skull, and a point ri having an attribute data id value of 3 is a brain. And Here, it is assumed that a surface mesh model of the outer surface of the scalp is generated, and 1 (scalp) is input to the surface mesh model generation apparatus 100 as attribute data id of the tissue to be generated.

At this time, first, in order to satisfy the condition (1), the projection point determination unit 130 determines the value of the attribute data id for each point ri and narrows down to only the points ri having the attribute data id of 1. Next, in order to satisfy the condition of (2), the distance di with the projection vector Vi is calculated for the narrowed point ri, and only the point ri whose distance di is equal to or less than a predetermined value ε is selected. For example, a point of the foot where the point ri is lowered to the projection vector Vi is a point qi, the point qi is a vector from the origin, a node ni is a vector from the origin, a point ri is a vector from the origin, and (A, B) is a vector If the inner product of A and vector B,
The point q i can be calculated as follows, and the distance di between the point q i and the point ri is
Therefore, it is possible to determine whether di is equal to or smaller than a predetermined value ε.

  For the points ri narrowed down by these two conditions (1) and (2), the point ri having the smallest distance from the node ni is selected. A point qi corresponding to this point ri is set as a projection point pi. In order to simplify this procedure, the distance between each point qi corresponding to the narrowed point ri and the node ni may be calculated, and the point qi having the smallest distance may be determined as the projection point pi.

  The data generation means 150 is means for generating surface mesh model data with the projection point pi determined by the projection point determination means 130 as a node. Specifically, since the surface mesh model is composed of data specifying the spatial coordinates of each node and which node is connected to which node, the node that the projection reference model 183 had in the data of the projection point pi By combining (applying) the combination data of ni and node ni, data of the surface mesh model is generated.

The operation (surface mesh model generation method) of the surface mesh model generation apparatus 100 configured as described above will be described with reference to the flowchart of FIG. 7. The surface mesh model generation apparatus 100 stores object data 181 in the storage device 180. The computer program is executed in a state where the projection reference model 183 is stored, the attribute data id is input, and the following steps are executed.

  First, the projection vector calculation means 110 passes through each node ni of the projection reference model 183 with the center O of the projection reference model 183 located inside the object surface 181A specified by the object data 181, and A projection vector Vi substantially orthogonal to the projection reference model 183 at the position of the node ni is calculated (S10, projection vector calculation step). In this step, as described above, in order to calculate the projection vector Vi that is substantially orthogonal to the projection reference model 183, the unit normal vector calculation unit 111 uses the surface mesh around each node ni as a constituent element. The unit normal vector nvi is calculated, and the vector sum calculation means 112 multiplies the area of the surrounding surface meshes as weights to calculate the weighted arithmetic average of the unit normal vector nvi. Thereby, the projection vector Vi at each node ni is determined.

  Next, the projection point determination unit 130 determines whether or not each point ri in the point group {ri} matches the input attribute data id, and data of the point group {ri} narrowed down to only the matching point ri. (S20, projection point determination step).

  Then, the projection point determination unit 130 calculates the distance di between the point ri and the projection vector Vi (S30, projection point determination step). Furthermore, the projection point determination means 130 selects the point ri closest to the node ni among the points ri satisfying di <ε (S40, projection point determination step). Then, the projection point determination means 130 determines a projection point pi from the selected point ri (S50, projection point determination step). Specifically, the foot point qi lowered from the selected point ri to the projection vector Vi is set as the projection point pi.

  Next, the projection point determination means 130 determines whether or not the determination of the projection points pi has been completed for all the nodes ni, and if not (S60, No), returns to step S30 to return to another When the projection point pi for the node ni is determined and the projection point pi is completed (S60, Yes), the process proceeds to step S70.

  In step S70, the data generation unit 150 generates data of the surface mesh model with the projection point pi determined by the projection point determination unit 130 as a node (S70, data generation step).

  As described above, according to the surface mesh model generation apparatus 100 of the present embodiment, the node ni of the sphere mesh model is directly projected onto the object surface 181A composed of the data of the point group {ri}, and with a small calculation, A surface mesh model composed of a surface mesh of uniform size and shape can be generated. That is, it corresponds to the object surface 181A of the node ni of the spherical mesh model without creating a temporary surface mesh model composed of a surface mesh with irregular sizes and shapes from point cloud data as in the past. Since the point to be determined is determined as the projection point pi (node of the surface mesh model), the surface mesh model can be generated efficiently.

  Then, in the conventional method, the head surface mesh model is projected after being inflated, and the head shape is inversely transformed after the projection, so as shown in FIG. However, according to the apparatus and method of the present invention, as shown in FIG. 8 (b), the shape and size of a relatively uniform surface mesh that is close to an equilateral triangle. Now, a surface mesh model can be generated.

[Second Embodiment]
Next, a second embodiment of the present invention will be described. In the present embodiment, the description will focus on the parts different from the first embodiment, and the same parts will be denoted by the same reference numerals in the drawings, and the description thereof will be omitted as appropriate.

  In the second embodiment, a description will be given of an apparatus using a method of gradually bringing a model closer to the shape of a target object surface 181A by performing a plurality of projections from a spherical mesh model. The outline of this projection will be described. As shown in FIG. 9, the node ni of the projection reference model 183 is moved from the projection reference model 183 which is a spherical mesh model 182 to a surface in front of the object surface 181A. As a new projection reference model 183, the surface mesh model composed of the new node ni ′ obtained by the above is used to perform the next projection and move to the next node ni ″. In this way, the node ni is moved a plurality of times to the object surface 181A. Finally, the projection point pi is calculated on the object surface 181A from the node ni ″ obtained by moving the lens toward. By such a method, the projection is gradually performed from the sphere toward the object surface 181A. Therefore, the projection direction gradually changes from the direction perpendicular to the spherical surface to the direction perpendicular to the object surface 181A. Even when the surface 181 </ b> A has a concave portion or a convex portion, the surface mesh that is locally collapsed is prevented.

  Specifically, as shown in FIG. 10, the surface mesh model generation device 200 according to the second embodiment includes an updated projection reference model generation unit 120 and a smoothing in addition to the surface mesh model generation device 100 according to the first embodiment. Means 140 are provided.

  The updated projection reference model generation unit 120 divides a line segment connecting the projection point pi determined by the projection point determination unit 130 and the node ni before projection (see reference numeral L1 in FIG. 11) at a predetermined ratio. This is a means for generating a new projection reference model 183 with the point as a new node ni (ni ′). Specifically, as shown in FIG. 11, the updated projection reference model generation unit 120 obtains a distance Dni ′ that is a predetermined ratio of the distance Dni between the node ni and the projection point pi when obtaining a new node ni ′ from the node ni. Then, the point of this distance Dni ′ is selected from the projection point pi and is set as a new node ni ′. The value of the predetermined ratio at this time is not particularly limited, and an appropriate value such as 90% or 70% can be selected. A new node ni ′ is obtained from each node ni, and a new projection reference model 183 having the obtained node set {ni ′} as nodes is generated.

  In the present embodiment, the projection point determination unit 130 determines the projection point pi based on the projection vector Vi based on the first projection reference model 183 and the projection reference model 183 generated by the updated projection reference model generation unit 120. The final projection point pi used by the data generation unit 150 is determined by executing the determination of the projection point pi by the projection vector Vi based on it twice or more in total.

The smoothing unit 140 is a unit that performs a smoothing process that reduces unevenness on the new projection reference model 183 generated by the updated projection reference model generation unit 120. Conventionally, a plurality of methods are known for such smoothing processing, and which method is used in the present invention is not particularly limited. In this smoothing process, if there is local unevenness in the updated projection reference model 183, the projection vectors Vi of the adjacent nodes ni may face in different directions. This is to moderate the change in the direction of Vi. In any of the smoothing methods, the shape of the surface mesh is slightly uniformed as the unevenness of the projection reference model 183 is relaxed. In the present embodiment, it is desirable to use the λ-μ smoothing technique among the conventionally known smoothing processes. In this method, the unevenness of the surface mesh is considered as noise, and noise of a certain frequency component is removed by a filter. Specifically, smoothing can be performed according to the following formula and conditions.

Here, v _i ⁿ is the i-th node coordinate vector, and n is a counter for the number of smoothing times. W _ij is an arbitrary weight function. This weight function w _ij can be given by the following equation as an example.

As an example of the parameters used in this calculation formula, the following values can be used.
k _pb = 0.1
f (1) = − f (2)
λ = 0.6314
μ = −0.67395

As another method of the smoothing process, there is a smoothing process using a Laplace filter. This is because when there are N point groups (j = 1 to N) in contact with a certain point i,
xi = (x1 + x2 +... + xN) / N
Thus, a new point xi is obtained.

  A method of generating a surface mesh model by the surface mesh model generation apparatus 200 as described above will be described with reference to FIG. In the surface mesh model generation device 200, the number of projections is input as a parameter for execution. As shown in FIG. 12, Steps S10 to S60 are performed in the same manner as in the first embodiment. When the determination of the projection points pi is completed for all the nodes ni in the determination in Step S60 (S60, Yes), Smoothing processing by λ-μ smoothing is performed (S63). Then, it is determined whether or not the number of times of projection c is the upper limit value. If the upper limit value is not reached (S65, No), c is incremented (S67), and the processing from step S30 is repeated. On the other hand, if the number of times of projection c is the upper limit value (S65, Yes), it means that the final projection point pi has been obtained, so the process proceeds to step S70 to create a surface mesh model.

  By the operation as described above, according to the surface mesh model generation device 200, even when the object surface 181A has local unevenness, the surface mesh model generation device 200 is composed of a surface mesh having a relatively uniform shape and size close to an equilateral triangle. A surface mesh model can be generated.

  FIG. 13 shows an example in which the surface mesh model of the brain and brainstem is generated by the surface mesh model generation apparatus 200 of the second embodiment. After projecting and smoothing from the spherical mesh model four times, the object surface 181A is finally obtained. This is a surface mesh model obtained by projecting a node ni on the surface. As shown in FIG. 14A, a locally convex portion such as a brain stem has a shape in which the surface mesh is considerably broken from an equilateral triangle in the surface mesh model generation device 100 of the first embodiment. However, as shown in FIG. 14B, the surface mesh model generation apparatus 200 according to the second embodiment can generate a model composed of a surface mesh having a shape relatively close to an equilateral triangle.

[Third Embodiment]
Next, a third embodiment of the present invention will be described. In the present embodiment, the description will focus on parts that are different from the first embodiment, and the same parts are denoted by the same reference numerals in the drawings, and the description thereof is omitted as appropriate.

  In the third embodiment, the projection is performed only once from the spherical mesh model. Even if the object surface 181A has a concave portion or a convex portion, the surface mesh is improved by the surface mesh having an improved shape compared to the first embodiment. An attempt is made to generate a mesh model. The outline of this projection will be described. As shown in FIG. 15, with respect to a shape portion where the object surface 181A is farthest from the sphere, the reference projection vector VD is obtained from the sphere mesh model 182 for a predetermined range (distance is within A1). The projection vector Vi is a direction parallel to the projection vector Vi, and the projection vector Vi is calculated by combining the reference projection vector VD and a vector substantially orthogonal to the spherical mesh model in a predetermined range (distance is A1 to A2) further outside. I have to.

  Specifically, the surface mesh model generation apparatus 300 according to the third embodiment includes a reference projection vector calculation unit 115 in addition to the configuration of the surface mesh model generation apparatus 100 of the first embodiment, as shown in FIG. ing.

  After determining the projection point pi by the projection point determination unit 130, the reference projection vector calculation unit 115 calculates the distance between the node ni and the projection point pi corresponding to the node ni, and determines the node ni having the largest or smallest distance. A means for selecting and calculating a reference projection vector VD that is a vector that passes through the selected node ni and is substantially orthogonal to the projection reference model 183 at the position of the node ni. In the present embodiment, the node ni having the largest calculated distance is selected.

  In the present embodiment, the projection vector calculation unit 110 calculates the projection vector Vi corresponding to the node ni within the first predetermined distance A1 from the reference projection vector VD calculated by the reference projection vector calculation unit 115 as a reference. It is set again in parallel with the projection vector VD. Further, the projection vector calculation unit 110 is outside the first predetermined distance A1 from the reference projection vector VD calculated by the reference projection vector calculation unit 115, and is a second predetermined distance A2 that is larger than the first predetermined distance A1. A projection vector Vi corresponding to a node ni within the range of is calculated by combining the reference projection vector VD with a vector passing through each node ni and substantially orthogonal to the projection reference model 183 at the position of the node ni. Is configured to do.

  Further, in the present embodiment, the projection point determination unit 130 determines the final projection point pi used by the data generation unit 150 based on the projection vector Vi set again by the projection vector calculation unit 110.

  With such a configuration, as shown in FIG. 15, after the projection similar to that in the first embodiment is performed once from each node ni of the spherical mesh model 182, the distance to the object surface 181A is calculated. The largest point F is selected, and a vector from the node ni corresponding to the point F toward the point F is set as a reference projection vector VD. For the node ni that is within the first predetermined distance A1 from the reference projection vector VD, the projection vector Vi is parallel to the reference projection vector VD, and is farther from the reference projection vector VD than the first predetermined distance A1. For a node ni within a predetermined distance A2 of 2, a projection vector Vi is calculated by combining the reference projection vector VD and a vector substantially orthogonal to the spherical mesh model 182 at the node ni. This synthesis is shown as a simple average in FIG. 15, but the weight of the reference projection vector VD is reduced as the distance from the reference projection vector VD increases, and the weight of the vector substantially orthogonal to the spherical mesh model 182 at the node ni is set. It is desirable to increase and combine the two vectors with a weighted average (or sum). Thereby, it is possible to avoid a sudden change in the direction of the projection vector Vi at a position where the calculation method of the projection vector Vi is switched.

  According to the surface mesh model generation apparatus 300 configured as described above, a surface mesh model composed of a surface mesh having a relatively uniform size and shape can be generated by a single projection even on an object surface 181A having a recess or the like. can do. For example, FIG. 17A shows a surface mesh model of the surface of the brain generated by the surface mesh model generation device 100 according to the first embodiment as viewed from below. In the hollow portion, a very small mesh or a surface mesh whose shape is broken from an equilateral triangle is generated. However, as shown in FIG. 17B, according to the surface mesh model generation device 300 of the present embodiment, the lower surface of the brain is also surfaced by a surface mesh having a uniform size and shape that is relatively close to an equilateral triangle. A mesh model can be generated.

[Fourth Embodiment]
Next, a fourth embodiment of the present invention will be described. In the present embodiment, the description will focus on parts that are different from the first embodiment, and the same parts are denoted by the same reference numerals in the drawings, and the description thereof is omitted as appropriate.

  In the surface mesh model generation device according to the fourth embodiment, the object data 181 includes only data of the point group {ri} corresponding to the object surface 181A as the data of the point group {ri}, and the projection point pi Acquisition can be simplified. Therefore, in the fourth embodiment, only this projection point will be described.

Here, as shown in FIG. 18, for example, the object data 181 includes a set of only the point ri having id = 2 and only the outermost point ri in FIG. 6 of the first embodiment. And Points other than id = 2 in FIG. 6 may have data indicating that the object is not an object, for example, id = 0. On the premise of such object data 181, in the surface mesh model generation device of the fourth embodiment, the projection point determination means 130 calculates the distance di between the projection vector Vi and each point ri, and the projection point from the closest point ri. Determine pi.
In this way, when the point group {ri} shows only the surface of the object in the first place, the point ri having the closest distance from the projection vector Vi is selected and projected based on this point ri. By determining the point pi, a surface mesh model can be easily generated.

Although the embodiment of the present invention has been described above, the present invention is not limited to the above-described embodiment, and can be appropriately modified and implemented.
For example, the vector sum calculation unit 112 may calculate a projection vector Vi by calculating a simple average without weighting instead of calculating a weighted average, or may calculate a projection vector Vi by calculating a simple sum. Good.

  In the embodiment, when determining the projection point pi from the point ri selected by the projection of the node ni, the foot point qi lowered from the point ri to the projection vector Vi is set as the projection point pi. However, the selected point ri It may be the projection point pi itself.

  In the above-described embodiment, the case where the closest point from the node ni is selected when the point ri is selected by the projection of the node ni has been described. However, the farthest point may be selected. In this case, for example, if a tissue with attribute data id 1 is selected in FIG. 6 of the first embodiment, a surface mesh model corresponding to the inner surface of the scalp is generated.

  In the third embodiment, the reference projection vector VD is determined by selecting the point F farthest from the node ni of the sphere mesh model. However, the reference projection vector VD is selected by selecting the point closest to the node ni of the sphere mesh model. VD may be determined.

  In the above embodiment, the case where the surface mesh model of the surface of the human tissue is generated as an example has been described. However, the surface mesh model of the surface of another object can also be generated.

DESCRIPTION OF SYMBOLS 100 Surface mesh model production | generation apparatus 110 Projection vector calculation means 111 Unit normal vector calculation means 112 Vector sum calculation means 115 Reference projection vector calculation means 120 Update projection reference model generation means 130 Projection point determination means 140 Smoothing means 150 Data generation means 180 Storage Device 181 Object data 181A Object surface 182 Spherical mesh model 183 Projection reference model

Claims (13)

A surface mesh model generation device that generates data of a surface mesh model used in the calculation of the boundary element method,
A storage device for storing object data composed of data of a point group {ri} capable of specifying the surface of the object, and a projection reference model composed of a spherical mesh model in which surface meshes are arranged in a substantially spherical shape;
In a state where the center of the projection reference model is located inside the object surface specified by the object data, the projection reference model passes through each node ni of the projection reference model and is approximately the projection reference model at the position of the node ni. Projection vector calculating means for calculating orthogonal projection vectors Vi;
Among point group {ri} to the object data has corresponds to the surface of the object, and a projection point determining means for determining a projected point pi closest point ri from the selected the point ri in the projection vector Vi ,
An updated projection reference for generating a new projection reference model, with a point on the line segment dividing the line segment connecting the projection point pi determined by the projection point determination means and the node ni at a predetermined ratio as a new node ni. Model generation means;
Data generating means for generating data of the surface mesh model with the projection point pi determined by the projection point determining means as a node ;
The projection point determination means determines the projection point pi from the projection vector Vi based on the first projection reference model, and determines the projection point pi from the projection vector Vi based on the projection reference model generated by the updated projection reference model generation means. And a final mesh point pi used by the data generation means is determined twice or more in total . A surface mesh model generation device that generates data of a surface mesh model used in the calculation of the boundary element method,
A storage device for storing object data composed of data of a point group {ri} capable of specifying the surface of the object, and a projection reference model composed of a spherical mesh model in which surface meshes are arranged in a substantially spherical shape;
In a state where the center of the projection reference model is located inside the object surface specified by the object data, the projection reference model passes through each node ni of the projection reference model and is approximately the projection reference model at the position of the node ni. Projection vector calculating means for calculating orthogonal projection vectors Vi;
Among point group {ri} to the object data has corresponds to the surface of the object, and a projection point determining means for determining a projected point pi closest point ri from the selected the point ri in the projection vector Vi ,
After the projection point pi is determined by the projection point determination means, the distance between the node ni and the projection point pi corresponding to the node ni is calculated, the node ni having the largest or smallest distance is selected, and the selected node reference projection vector calculation means for calculating a vector passing through ni and substantially orthogonal to the projection reference model at the position of the node ni as a reference projection vector VD;
Data generating means for generating data of the surface mesh model with the projection point pi determined by the projection point determining means as a node ;
The projection vector calculation means makes a projection vector Vi corresponding to a node ni within a first predetermined distance from the reference projection vector VD calculated by the reference projection vector calculation means parallel to the reference projection vector VD. Set it again,
The surface mesh model generation apparatus, wherein the projection point determination means determines a final projection point pi used by the data generation means based on the projection vector Vi set again by the projection vector calculation means . The projection vector calculation means is outside the first predetermined distance range and within the second predetermined distance range greater than the first predetermined distance from the reference projection vector VD calculated by the reference projection vector calculation means. A projection vector Vi corresponding to the node ni is calculated by combining the reference projection vector VD with a vector passing through each node ni and substantially orthogonal to the projection reference model at the position of the node ni. The surface mesh model generation apparatus according to claim 2 . The object data includes, as data of a point group {ri}, spatial coordinates of a plurality of points ri constituting the object, and attribute data id that is an attribute of each point ri,
The projection point determining means includes
When determining the projection point pi of the node ni on the object surface with a specific attribute, the following condition (1) The attribute data id of the point ri is a specific value (2) The projection vector Vi and each point ri Determine that the distance is within the range of the predetermined value ε,
The point ri having the maximum or minimum distance to the node ni in the point group {ri} satisfying (1) and (2) is selected, and the projection point pi is determined from the point ri. The surface mesh model production | generation apparatus of any one of Claim 3 . The object data includes only data of a point group {ri} corresponding to the surface of the object as data of the point group {ri},
The projection point determining means, the distance of the projection vector Vi and each point ri calculated from claim 1, wherein the determining the projection point pi closest point ri in any one of claims 3 The surface mesh model generation device described. The projection vector calculating means includes
Unit normal vector calculating means for calculating unit normal vectors of a plurality of surface meshes including each node ni as a component;
A vector sum calculating unit for calculating a projection vector Vi of each node ni by calculating a sum or an average of the plurality of unit normal vectors calculated by the unit normal vector calculating unit. The surface mesh model production | generation apparatus of any one of Claims 1-5 . The vector sum calculation means, the unit normal vector, claim 6, characterized in that for calculating the average of a plurality of unit normal vector is multiplied by the area of the surface mesh corresponding to the unit normal vector as the weight The surface mesh model production | generation apparatus as described in. The surface mesh model generation apparatus according to claim 1 , further comprising a smoothing unit that performs a smoothing process for reducing unevenness on the projection reference model generated by the updated projection reference model generation unit. The surface mesh model generation device according to any one of claims 1 to 8 , further comprising a sphere mesh generation unit that calculates the sphere mesh model and stores the sphere mesh model in the storage device. The storage device is constructed using a computer in which object data composed of point group {ri} data capable of specifying the surface of an object and a projection reference model composed of a spherical mesh model in which surface meshes are arranged in a substantially spherical shape are stored. A surface mesh model generation method for generating data of a surface mesh model used in the calculation of the boundary element method by a surface mesh model generation device ,
The projection vector calculation means included in the computer passes through each node ni of the projection reference model in a state where the center of the projection reference model is located inside the object surface specified by the object data, and and Luz step to calculate the projection vector Vi substantially perpendicular to the projection reference model position of the node ni,
The projection point determining means provided in the computer selects a point ri corresponding to the surface of the object and closest to each projection vector Vi from the point group {ri} of the object data, and projects from the point ri. and Luz steps to determine the point pi,
The updated projection reference model generation unit included in the computer sets a point on the line segment dividing the line segment connecting the projection point pi determined by the projection point determination unit and the node ni at a predetermined ratio as a new node ni. Generating a new projection reference model;
Data generating means included in the computer, and a Luz step generates data of a surface mesh projection points pi determined in the projection point determining means as the nodal point,
The projection point determination means determines the projection point pi from the projection vector Vi based on the first projection reference model, and determines the projection point pi from the projection vector Vi based on the projection reference model generated by the updated projection reference model generation means. And a final mesh point pi used by the data generation means is determined two or more times in total . The storage device is constructed using a computer in which object data composed of point group {ri} data capable of specifying the surface of an object and a projection reference model composed of a spherical mesh model in which surface meshes are arranged in a substantially spherical shape are stored. A surface mesh model generation method for generating data of a surface mesh model used in the calculation of the boundary element method by a surface mesh model generation device ,
The projection vector calculation means included in the computer passes through each node ni of the projection reference model in a state where the center of the projection reference model is located inside the object surface specified by the object data, and and Luz step to calculate the projection vector Vi substantially perpendicular to the projection reference model position of the node ni,
The projection point determining means provided in the computer selects a point ri corresponding to the surface of the object and closest to each projection vector Vi from the point group {ri} of the object data, and projects from the point ri. and Luz steps to determine the point pi,
After the projection point pi is determined by the projection point determination unit, the reference projection vector calculation unit included in the computer calculates the distance between the node ni and the projection point pi corresponding to the node ni, and the distance is the largest or smallest. Selecting a node ni and calculating as a reference projection vector VD a vector that passes through the selected node ni and is substantially orthogonal to the projection reference model at the position of the node ni;
Data generating means included in the computer, and a Luz step generates data of a surface mesh projection points pi determined in the projection point determining step as nodes,
The projection vector calculation means makes a projection vector Vi corresponding to a node ni within a first predetermined distance from the reference projection vector VD calculated by the reference projection vector calculation means parallel to the reference projection vector VD. Set it again,
The surface mesh model generation method, wherein the projection point determination means determines a final projection point pi used by the data generation means based on the projection vector Vi set again by the projection vector calculation means . In the computer in which the object data consisting of data of point groups {ri} capable of specifying the surface of the object and the projection reference model consisting of the spherical mesh model in which the surface meshes are arranged in a substantially spherical shape are stored in the storage device A computer program for generating data of a surface mesh model used in calculation, comprising:
In a state where the center of the projection reference model is located inside the object surface specified by the object data, the projection reference model passes through each node ni of the projection reference model and is approximately the projection reference model at the position of the node ni. Projection vector calculation means for calculating orthogonal projection vectors Vi;
Wherein one of the points {ri} having the object data corresponds to the surface of the object, and the projection point determining means for determining a projected point pi closest point ri from the selected the point ri in the projection vector Vi,
An updated projection reference for generating a new projection reference model, with a point on the line segment dividing the line segment connecting the projection point pi determined by the projection point determination means and the node ni at a predetermined ratio as a new node ni. Model generation means,
Function as data generation means for generating surface mesh model data with the projection point pi determined by the projection point determination means as a node ;
Further, the projection point determining means
The determination of the projection point pi based on the projection vector Vi based on the first projection reference model and the determination of the projection point pi based on the projection vector Vi based on the projection reference model generated by the updated projection reference model generation unit are executed twice or more in total. Then , the computer program is made to function so as to determine a final projection point pi used by the data generation means . In the computer in which the object data consisting of data of point groups {ri} capable of specifying the surface of the object and the projection reference model consisting of the spherical mesh model in which the surface meshes are arranged in a substantially spherical shape are stored in the storage device A computer program for generating data of a surface mesh model used in calculation, comprising:
In a state where the center of the projection reference model is located inside the object surface specified by the object data, the projection reference model passes through each node ni of the projection reference model and is approximately the projection reference model at the position of the node ni. Projection vector calculation means for calculating orthogonal projection vectors Vi;
Wherein one of the points {ri} having the object data corresponds to the surface of the object, and the projection point determining means for determining a projected point pi closest point ri from the selected the point ri in the projection vector Vi,
After the projection point pi is determined by the projection point determination means, the distance between the node ni and the projection point pi corresponding to the node ni is calculated, the node ni having the largest or smallest distance is selected, and the selected node reference projection vector calculation means for calculating a vector that passes through ni and is substantially orthogonal to the projection reference model at the position of the node ni as a reference projection vector VD;
Function as data generation means for generating surface mesh model data with the projection point pi determined by the projection point determination means as a node ;
further,
The projection vector calculation means makes the projection vector Vi corresponding to the node ni within the first predetermined distance from the reference projection vector VD calculated by the reference projection vector calculation means parallel to the reference projection vector VD. To make it work again,
A computer program for causing the projection point determination means to function so as to determine a final projection point pi used by the data generation means based on the projection vector Vi set again by the projection vector calculation means .