JP2005259058A - Device, method, and program for creating three-dimensional model - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a technology for quickly creating an offset face model to a face model for which an offset face cannot be created at a high speed by a conventional technology. <P>SOLUTION: This three-dimensional model creation device creating the offset face offset by an offset distance from the face model is provided with a means storing the face model as a set of micro element groups. a means arranging a distance shape model positioned apart in the z-axis direction from the position on the plane by a distance from the position on the plane parallel to the xy-plane to the micro element, a distance value storage means storing a distance in the x-axis direction from the position on the plane to the nearest distance shape model, a means comparing the distance value stored in the distance value storage means with the offset distance value, and a means deciding the position on the offset face based on the comparison result by the distance value comparison means. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a computer technology that handles a three-dimensional model, and in particular, when obtaining an offset surface model that is offset by a predetermined distance from the original surface model, the original surface model is arranged in a coordinate space, and the offset surface model The present invention relates to a technique for determining a coordinate position.

A technique for creating a three-dimensional model using a computer or the like has become widespread. Such a technique for creating a three-dimensional model is actively used in the manufacturing industry and the like, and a technique for creating an offset surface model offset by a predetermined distance from the original surface model is required.
For example, numerically controlled (NC) machine tools require an offset surface model. An NC machine tool processes a workpiece into a processing surface by relatively moving the tool and the workpiece along a movement path taught in advance. FIG. 23 shows, for example, machining of a workpiece onto a machining surface D by an NC machine tool with three-axis control (which means that the tool can be moved in the three directions of the xyz axes, but the tool cannot be tilted). It shows how to do. As shown in FIG. 23, when the ball end mill 100 moves while maintaining its positional relationship in contact with the machining surface D, the workpiece W is machined into the machining surface D.
In an NC machine tool, a reference point is set for a tool, and the position of the tool is determined by the position of the reference point. As shown in FIG. 23, when the tool is the ball end mill 100, the center point of the spherical cutting edge surface 100a can be determined as the reference point T. When the tool reference point T is determined in this way, the position of the tool reference point T when the workpiece is processed into the processing surface D can be determined by the surface M. The surface M describing the path of the tool is offset from the machining surface D by the radius r of the cutting edge surface 100a, and is called an offset surface offset from the machining surface D by the offset distance value r.
The shape of the machining surface D is represented by a curved surface model created using a three-dimensional CAD (Computer Aided Design) or the like. In order to machine a workpiece into the machining surface D using an NC machine tool, it is necessary to create an offset surface model offset from the machining surface model by the radius of the cutting edge surface r.

In order to create the offset surface model, it is necessary to place the machining surface model in the coordinate space and obtain the coordinate position of the offset surface model. If the machining surface D is described by an equation, it is used in combination with an equation describing the shape of the cutting edge surface 100a of the ball end mill 100, and the position of the offset surface is obtained by solving the position of the tool reference point T when the two contact each other. Can be requested.
However, depending on the shape of the machining surface D, the position of the offset surface M may not be uniquely determined even if both equations are solved. FIG. 24 shows an example of this, and shows a state in which the z coordinate value of the tool reference point T when both are in contact with each other under the condition that the position of the tool reference point T in the xy direction is fixed. As shown in FIG. 24, there are three solutions of values z1, z2, and z3 as solutions of the z coordinate value in this case, but when the tool reference point T is at the position of the z coordinate values z2 and z3, the cutting edge The surface 100a also intersects the processed surface D. If this intersection is overlooked and, for example, z2 is adopted as the z coordinate value, the area of the hatched portion K is overcut. The problem with this method is that the number of solutions when the machining surface D and the cutting edge surface 100a contact each other is unknown, and it is not guaranteed that all existing contact solutions have been obtained.

If the machined surface D is handled as a curved surface, the number of solutions in contact with each other becomes unknown, and it cannot be guaranteed that the above-described overcutting is prevented. Therefore, it is common to treat the machining surface D as a mathematical model that is discretely approximated by a small element group such as a point, a line segment, or a plane segment, and describes the machining surface D as a set of minute element groups. Since the positional relationship between each microelement such as a point, a line segment, and a plane segment and the blade edge surface 100a can be determined uniquely, the positional relationship between all the microelements and the blade edge surface 100a is calculated, and If the maximum value is obtained, the above-mentioned problem of overcutting can be eliminated.
In the present specification and claims, a mathematical model in which a curved surface model is discretely approximated by a point group, line segment group, or plane segment group is referred to as a mathematical model that describes the curved surface model as a set of minute elements.

There are many studies to speed up the process of creating an offset surface model. For example, Patent Document 1 discloses a method of using a combination of the reverse offset method and a three-dimensional graphics display technique.
In the inverse offset method, instead of obtaining the position where the cutting edge surface of the tool comes into contact with the mathematical model, a virtual reversal tool in which the tool shape is reversed up and down is arranged so that the reference point is located on the mathematical model. Since the virtual reversal tool shape group arranged in this way indicates the position of the tool reference point when the cutting edge surface touches each approximate element, by selecting the highest position of the virtual reversal tool shape group, the cutting edge surface can be mathematically calculated. This is a method for obtaining the position in contact with the model.
In the technique of Patent Document 1, the position of the offset surface is determined by performing the process of selecting the highest position from the virtual reversal tool shape group arranged in the microelement group using the hidden surface processing of the three-dimensional graphics display technology. A method to speed up the processing is proposed.
Japanese Patent Application Laid-Open No. 2003-256012

According to the technique of Patent Document 1, the process of calculating the position of the offset surface can be performed at a higher speed than in the prior art. However, the technique of Patent Document 1 is a technique for an NC machine tool with three-axis control, and the height position z of the tool has a one-to-one relationship with the rotation axis position (x, y) of the tool. Is the premise. That is, the position of the offset plane M is limited to that which can be described by a two-dimensional map.
In recent years, NC machine tools have been increased in the number of control axes, and it has become possible to machine a machined surface that could not be machined by 3-axis control. For example, as shown in FIG. 1, when an NC machine tool that can further change the direction of the tool rotation axis is used, a machining surface D having an overhanging surface D1 can be simultaneously machined. In such an offset surface M with respect to the processed surface D, the z coordinate value is not necessarily monovalent with respect to the position in the xy direction. As shown in FIG. 1, for example, at a position (x _i , y _j ) in the xy direction, the position of the offset plane M must be determined by three z coordinate values.

When creating an offset surface model in which a plurality of z coordinate values exist with respect to a position determined by xy coordinates (hereinafter referred to as xy position), the technique of Patent Document 1 cannot be used.
Many techniques for speeding up the process of creating an offset surface in which only a monovalent z-coordinate value is defined for an xy position are provided. However, there is no technology for speeding up the process of creating an offset surface model in which a plurality of z coordinate values exist for the xy position, and much time and cost are wasted in the creation process. .
The present invention solves the above problems. The present invention is also applicable to a surface model (for example, a surface model in which an offset surface model is determined by a plurality of z coordinate values with respect to an xy position) for which an offset surface cannot be created at high speed by the conventional technology. To provide a technique for creating an offset surface model at high speed.

  The present invention can be embodied in a three-dimensional model creating apparatus that creates an offset surface model offset from a surface model by an offset distance. The apparatus includes a model storage unit that stores the plane model as a set of minute elements arranged in the xyz space, a plane setting unit that sets a plane parallel to the xy plane in the xyz space, and the setting thereof. Means for disposing in the xyz space a distance shape model located in the z-axis direction away from the set position on the plane by a distance from the position on the selected plane to the microelement, and a group of arranged distance shape models A distance value storage means for storing the distance in the z-axis direction from the position on the set plane to the nearest distance shape model in association with the position on the set plane; Means for comparing the distance value stored in the distance value storage means with the offset distance value, and offset surface position determining means for determining the position of the offset surface based on the comparison result of the distance value comparison means. There.

  When the surface model is described as a set of minute elements, the distance from the position in the xyz space to each minute element can be uniquely determined. For each position in the xyz space, find all the distances from that position to each minute element, and compare the distance to the nearest minute element and the desired offset distance value to find the position of the offset plane can do. That is, if the obtained distance value is equal to the offset distance value, the position can be determined as the position of the offset surface. However, if an attempt is made to determine the position of the offset surface by this method, the amount of calculation becomes enormous and the time required for processing becomes long.

The above processing can be simplified by using a distance shape model created by the present inventor. The distance shape model created by the present inventor is located away from the position in the z-axis direction by the distance from the position in the xyz space to the minute element. When the distance shape model is arranged in the xyz space when obtaining the distance from the position in the xyz space to the minute element, the distance from the position to the minute element is determined by the distance in the z-axis direction from the position to the distance shape model. I can know.
When the position for obtaining the distance to the minute element is determined in the xyz space, the distance shape model group for each minute element can be arranged in the xyz space with the position as a reference. Each microelement is located in various directions with respect to the position where the distance to the microelement is to be obtained. However, if the distance shape model group is used, all the distances to each microelement are expressed in the z-axis direction. Can do. By comparing the positions of the arranged distance shape model groups in the z-axis direction, the distances to the microelements positioned in various directions can be compared.
When arranging a distance shape model, if a plane parallel to the xy plane is defined, a distance shape model group effective for all positions on the plane can be arranged based on the z coordinate value of the plane. it can.

The distance shape model group is arranged in the xyz space, and the process of comparing the positions of the arranged distance shape model groups in the z-axis direction can be performed at high speed using, for example, a three-dimensional graphics display technique, and the set plane For each of the above positions, the distance in the z-axis direction to the distance shape model group closest to the z-axis direction can be obtained at high speed. That is, for each set position on the plane, the distance to the nearest minute element can be obtained at high speed. By sequentially changing the z coordinate value of the plane to be set, the distance to the nearest minute element can be obtained at high speed for each position in the xyz space.
If the distance to the nearest minute element is known for each position in the xyz space, the position of the offset surface can be specified by comparing with the desired offset distance. As for the position of the specified offset surface, for example, a plurality of height positions z may exist with respect to the position in the xy direction.
According to this apparatus, from a surface model (for example, a surface model in which an offset surface model is determined by a plurality of z coordinate values with respect to an xy position), an offset surface model could not be created at high speed by the conventional technology. An offset surface model offset by the offset distance can be created at high speed.

The distance value comparison means determines whether the position where the distance value storage means stores the distance value is outside or inside the offset surface, and the offset surface position determination means determines that the distance value comparison means is outside. It is preferable to determine the position of the offset surface on a line segment connecting the determined position and the position determined to be inside.
At a position where the distance to the nearest minute element is larger than the offset distance, it can be determined that the mathematical model is located outside the offset plane. At a position where the distance to the nearest minute element is smaller than the offset distance, it can be determined that the mathematical model is located inside the offset plane. Since the offset surface is located between the position determined to be inside and the position determined to be outside, the position of the offset surface can be determined on a line segment connecting these positions. The position of the offset surface can be determined by determining the size of the distance value stored in the distance value storage means and the offset distance value, and the offset surface position determination process can be performed at high speed.

  The present invention also provides a new three-dimensional model creation method for creating an offset surface model that is offset from the surface model by an offset distance. In this method, a model storing step of storing the surface model as a set of minute elements arranged in the xyz space, a step of setting a plane parallel to the xy plane in the xyz space, and the set plane A step of disposing a distance shape model located in the z-axis direction from the position on the set plane by a distance from the upper position to each microelement in the xyz space; and Among them, a distance value storage that stores the distance in the z-axis direction from the position on the set plane to the distance shape model closest to the z-axis direction in association with the position on the set plane. A step of comparing the distance value stored in the distance value storing step with the offset distance value, and a step of determining the position of the offset surface based on the comparison result of the distance value comparing step. .

In this method, by using the distance shape model created by the present inventor, the distance to the nearest minute element can be obtained at high speed for each position in the xyz space, and compared with the desired offset distance. The position of the offset surface can be specified. As for the position of the specified offset surface, there may be a plurality of height positions z with respect to the xy position, for example.
According to this method, an offset surface is offset from a surface model (for example, a surface model in which the offset surface model is determined by a plurality of z coordinate values with respect to the xy position) for which the offset surface could not be created at high speed by the conventional technique. An offset surface model offset by the distance can be created at high speed.

The technology created by the present invention is also embodied in a new three-dimensional model creation program for creating an offset surface model offset by an offset distance from a surface model. In this program, the computer stores the plane model as a set of small element groups arranged in the xyz space, sets the plane parallel to the xy plane in the xyz space, and sets the program. In the process of arranging the distance shape model located in the z-axis direction from the set position by the distance from the position on the plane in the z-axis direction in the xyz space, and the arranged distance shape model group, A distance value storing process for storing the distance in the z-axis direction from the position on the set plane to the distance shape model closest to the z-axis direction in association with the position on the set plane; A distance value comparison process for comparing the distance value stored in the distance value storage process with the offset distance value, a process for creating an offset surface model based on the comparison result of the distance value comparison process, and a distance value storage process In to execute a process of determining the position of the offset surfaces from the stored distance value.
According to this program, a surface model (for example, a surface in which the offset surface model is determined by a plurality of z coordinate values with respect to the xy position) cannot be created on the computer at a high speed by the conventional technique. An offset surface model offset by an offset distance from the model) can be created at high speed.

According to the present invention, from a surface model (for example, a surface model in which an offset surface model is determined by a plurality of z coordinate values with respect to a position in the xy direction), an offset surface could not be created at high speed by the conventional technique. A technique for creating an offset surface model offset by an offset distance at high speed is provided.
In particular, the surface model is represented by data described by a set of microelements arranged in xyz space, and the process of storing the data in a computer-readable manner is executed to set lattice points in a plane parallel to the xy plane. Then, a distance shape model located in the z-axis direction away from the lattice point by a distance equal to the distance from the lattice point to the minute element is calculated for each minute element, and among the distance shape model group calculated for the minute element group, The distance from the lattice point in the z-axis direction is calculated to be the shortest, and the result of comparing the calculated distance with the offset distance is stored in an electronic computer so as to be readable, and then the programmed electron Using a computer to create an offset surface model at high speed by using the calculation capability of an electronic computer when the offset surface is placed between grid points with different comparison results. It is possible.
In this case, a distance shape model located in the z-axis direction away from the lattice point by a distance equal to the distance from the lattice point to the minute element is calculated for each minute element, and the distance shape model group calculated for the minute element group is calculated. The step of calculating the distance at which the distance in the z-axis direction from the lattice point is the shortest and storing the result of comparing the calculated distance with the offset distance is executed for each lattice point. Thus, based on the shortest distance from each lattice point to the minute element, it is determined whether the lattice point is inside or outside the offset surface, and the result of the determination is stored.
The distance shape model here refers to existence indicating a distance in the z-axis direction from a lattice point, and corresponds to a point arranged on the z-axis passing through the lattice point. The z coordinate of the point indicates the distance in the z-axis direction from the lattice point.

Hereinafter, embodiments embodying the present invention will be described with reference to the drawings. First, the main features of the embodiment are listed.
(Mode 1): Data describing the shape of the processed surface can be created by an external three-dimensional CAD device.
(Mode 2): The three-dimensional model creation apparatus can create a mathematical model obtained by discretely approximating a curved surface model to a set of minute elements.
(Mode 3): The three-dimensional model creation apparatus can store two distance value maps. Two microelement maps can be stored.
(Form 4): The three-dimensional model creation apparatus divides the xyz space into a minute rectangular parallelepiped space, and arranges the element model of the offset plane inside the partitioned rectangular parallelepiped space.

In the present embodiment, a method for creating a tool path of a 5-axis controlled NC machine tool using the present invention will be described. As shown in FIG. 1, in a 5-axis control NC machine tool, the direction of the rotation axis of a tool such as the end mill 100 can be variably controlled. Thereby, the workpiece | work W can be processed into the processing surface D which has the processing surface D1 which is overhanging as shown in FIG.
As shown in FIG. 1, in a 5-axis control NC machine tool, a reference point T is set on the tool in the same manner as the 3-axis control NC machine tool shown in FIG. Tool paths can be defined. When the tool processes the workpiece W on the processing surface D, the reference point T of the tool moves at a position offset from the processing surface D by the shape of the cutting edge. For example, when the ball end mill 100 is used as a tool, the reference point T moves on a surface M that is offset from the machining surface D by a radius r of the cutting edge surface 100a. In this way, a surface that is offset from a predetermined surface (for example, the processed surface D) by a predetermined distance (for example, radius r) is referred to as an offset surface.

  The offset plane M can be described by a three-dimensional model. A three-dimensional model describing the offset surface M can be created by performing an offset process from a three-dimensional curved surface model describing the machining surface D. The three-dimensional model creation apparatus according to the present embodiment performs an offset process based on a predetermined offset distance from the taught three-dimensional model to create an offset surface model.

  FIG. 2 shows a configuration of the apparatus 10 that creates the three-dimensional model of the present embodiment. The creation device 10 includes a data storage unit 30, a program storage unit 50, and a processing unit 70. The creation device 10 can be configured by a computer or the like, and the data storage unit 30, the program storage unit 50, and the processing unit 70 are configured by computer hardware, software, or the like.

The data storage unit 30 stores data given from the outside, data created by the processing unit 70, and the like. The data storage unit 30 can store curved surface model description data 32, mathematical model description data 34, a distance value map 36, a minute element map 38, offset surface model description data 40, and the like. The data storage unit 30 can store two distance value maps 36, a first distance value map 36a and a second distance value map 36b. In addition, the data storage unit 30 can store two minute element maps 38, a first minute element map 38a and a second minute element map 38b.
The program storage unit 50 stores a program used by the processing unit 70. The program storage unit 50 stores a mathematical model creation program 52, a distance shape model arrangement program 54, a depth buffer processing program 56, an offset surface element selection program 58, and an offset point determination program 60.
The processing unit 70 processes the data and the like stored in the data storage unit 30 using the program and the like stored in the program storage unit 50, and generates the offset plane model description data 40 describing the offset plane M model. create.

FIG. 3 is a flowchart showing a flow of processing in which the creation apparatus 10 of the present embodiment creates the offset plane model description data 40. Hereinafter, the processing operation of the creation apparatus 10 will be described along the flow shown in FIG.
In step S <b> 2, the creation apparatus 10 stores the curved surface model description data 32 in the data storage unit 30. The curved surface model description data 32 is data describing a machining surface D to be machined by an NC machine tool, and is three-dimensional CAD data created by an external three-dimensional CAD (Computer Aided Design) device or the like. For example, the curved surface model description data 32 describes the machining surface D shown in FIG. The curved surface model description data 32 can be taught to the creation apparatus 10 via, for example, a recording medium.
As shown in FIG. 4, the curved surface model description data 32 describes the machining surface D by combining a plurality of basic shapes in the xyz space. The basic shape is, for example, the surface S, the ridge line C, or the vertex V. As the surface S, for example, a flat surface, a cylindrical surface, a spherical surface, a free curved surface, or the like is used. Each basic shape is described by an expression using individually set parameters. For example, the surface S has parameters (u, v) defined on the surface and is described by a curved surface expression S (u, v). The ridge line C is described by a curve expression C (t) by a parameter t.
All basic shapes are assigned identifier IDs that can identify them.

In step S4, mathematical model description data 34 is created. The processing unit 70 processes the curved surface model description data 32 using the mathematical model creation program 52 and creates mathematical model description data 34. The created mathematical model description data 34 is stored in the data storage unit 30.
FIG. 5 shows an example of a mathematical model B obtained by discretely approximating the machining surface D to a set of minute elements. The mathematical model is a model obtained by discretely approximating a machining surface D composed of basic shape groups to a set of a plurality of minute element groups. In FIG. 5, for the purpose of clarifying the drawing, a state in which discrete approximation is performed on only a part of the mathematical model B is shown, and a microelement group is enlarged and shown. As the minute elements constituting the mathematical model B, minute points A, minute line segments H, and minute triangular planes U are used.
The mathematical model creation program 52 reads the curved surface model data 32 describing the machining surface D, creates a mathematical model B by discrete approximation of the machining surface D with a group of minute elements, and describes the mathematical model description data 34 describing the mathematical model B. Is a program that creates Further, the mathematical model creation program 52 assigns an identifier id to each minute element and describes it together with the mathematical model description data 34. Many methods for discretely approximating a curved surface model to a set of small element groups are known, and these methods can be used as appropriate in the creating apparatus 10 of the present embodiment.

  In the next steps S6 to S12, the processing unit 70 creates the distance value map 36 and the minute element map 38. The processing unit 70 uses the distance shape model arrangement program 54 and the depth buffer processing program 56 to process the mathematical model description data 34 to create a distance value map 36 and a minute element map 38. The created distance value map 36 and minute element map 38 are stored in the data storage unit 30.

The distance value map 36 describes a position on a plane parallel to the xy plane where the z coordinate value is fixed and the shortest distance value from the position to the mathematical model B in association with each other. In the distance value map 36, a distance value is described for each position arranged in a lattice pattern having an interval Δx in the x direction and an interval Δy in the y direction on a plane parallel to the xy plane.
The microelement map 38 describes a position on a plane parallel to the xy plane where the z coordinate value is fixed, and an identifier id of the microelement located closest to the position. In the minute element map 38, the identifier id of the minute element is described for each position where the distance value is described in the distance value map 36.

The distance value map 36 will be described with reference to FIG. As shown in FIG. 6, the distance from the point P1 (x _i , y _j , z _k ) located in the xyz space to the minute point A, minute line segment H, or minute triangular plane U constituting the mathematical model B. d can be uniquely obtained for each minute element by solving for the point P1 and each minute element. That is, the value of the distance d is obtained as much as the number of minute elements constituting the mathematical model B. The smallest value of the obtained distance d is the shortest distance value from the point P1 to the mathematical model B. In order to create the distance value map 36, the z coordinate value is fixed and the map plane F is defined, and on the map plane F, the positions are arranged in a grid pattern with an interval Δx in the x direction and an interval Δy in the y direction. Therefore, it is necessary to obtain a distance d to each minute element for all the minute elements and select a minimum value of the distance d. In this method, the calculation process for creating the distance value map 36 becomes complicated, and the time required for the process also increases. In the creation apparatus 10 of this embodiment, the creation process of the distance value map 36 is simplified by the method described below.

In the creation apparatus 10 of this embodiment, a distance shape model is used in creating the distance value map 36 and the minute element map 38. Prior to explaining how the creation apparatus 10 creates the distance value map 36 and the minute element map 38, the distance shape model will be described with reference to FIGS.
FIG. 7 shows an example of the distance shape model Q. The distance shape model Q shown in FIG. 7 will be described. Figure F is a map plane z-coordinate value of z _k. In the figure, A1 is one of the minute points A constituting the mathematical model B and is located on the map plane F. P1 in the figure is a point located on the map plane F. Here, as shown in FIG. 7, a d-axis parallel to the z-axis is determined with the origin on the map plane F, and an xyd space is defined. As shown in FIG. 7, a point P1 of coordinates (x _i , y _j , z _k ) in the xyz space becomes coordinates (x _i , y _j , 0) in the xyd space. Further, the minute point A1 of the coordinates (x1, y1, z _k ) in the xyz space becomes the coordinates (x1, y1, 0) in the xyd space. The distance d from the point P1 to the minute point A1 is
d ² = (x _i −x1) ² + (y _j −y1) ² (1)
It is expressed. However, d ≧ 0.
The above equation (1) is an equation representing a right conical surface having a minute point A1 as the apex in the xyd space and the central axis extending in the positive direction of the d axis, and describes the right conical surface model Q shown in FIG. Yes. When the right conical surface model Q is arranged in the xyd space as shown in FIG. 7, the distance d from the point P1 to the minute point A1 is the height in the d-axis direction from the point P1 to the right conical surface model Q (up to the point R). Distance).
In this way, when the minute point A1 is located on the map plane F, when the right conical surface model Q is arranged as shown in FIG. 7, the minute point A1 is minute from the position (x _i , y _j , z _k ) on the map plane F. The distance d to the point A1 can be known from the height in the d-axis direction from the position (x _i , y _j , z _k ) to the right conical surface model Q.
A shape model that expresses the distance d from each position on the map plane F to the minute element by the height in the d-axis direction from the map plane F like the right conical surface model Q is called a distance shape model Q. As shown in FIG. 7, when the minute element is the minute point A1 located on the map plane F, the distance shape model Q corresponding thereto is a shape model of a right conical surface.

Next, the distance shape model Q shown in FIG. 8 will be described. FIG. 8 shows a distance shape model Q when the minute point A1 is positioned in the positive direction of the d-axis by the distance d1 from the map plane F. A minute point A1 at coordinates (x1, y1, z _k + d1) in the xyz space becomes coordinates (x1, y1, d1) in the xyd space. The distance d from the point P1 to the minute point A1 is
d ² = (x _i −x1) ² + (y _j −y1) ² + d1 ² (2)
It is expressed. However, d ≧ 0.
The above equation (2) is an equation representing one of the two-leaf hyperboloids in the xyd space, and the distance shape model Q shown in FIG. 8 has one shape of the two-leaf hyperboloid. In this distance shape model Q, the vertex is the minute point A1. The asymptotic plane is a right conical surface having a point Aa1 obtained by projecting the minute point A1 on the map plane F as a vertex and a central axis extending in the d-axis positive direction. The central axis extends in the positive direction of the d axis. When the distance shape model Q is arranged in the xyd space as shown in FIG. 8, the distance d from the point P1 to the minute point A1 is the height in the d-axis direction from the point P1 to the distance shape model Q (the distance to the point R). ).
As shown in FIG. 8, when the minute element is a minute point A located in the positive d-axis direction by d1 from the map plane F, the distance shape model Q corresponding to the minute point A has one shape of a biplane hyperboloid.
Here, the two-leaf hyperboloid will be described. A two-leaf hyperboloid is a curved surface formed when a hyperbola is rotated with a straight line connecting two focal points as a rotation axis. At this time, each hyperbola that forms a pair forms one curved surface, so the two-leaf hyperboloid becomes a pair of curved surfaces. The expression “one of the two-leaf hyperboloids” refers to one of the curved surfaces.

Next, the distance shape model Q shown in FIG. 9 will be described. FIG. 9 shows the distance shape model Q in the case where the minute point A1 is located in the d-axis negative direction by the distance d1 from the map plane F. The minute point A1 of the coordinates (x1, y1, z _k −d1) in the xyz space becomes the coordinates (x1, y1, −d1) in the xyd space. The distance d from the point P1 to the minute point A1 is
d ² = (x _i −x1) ² + (y _j −y1) ² + d1 ² (3)
It is expressed. However, d ≧ 0.
The above equation (3) is the same as the above equation (2) and represents one of the two-leaf hyperboloids in the xyd space. As shown in FIG. 9, when the minute point A1 is positioned in the d-axis negative direction by the distance d1 from the map plane F, the minute point A1 is positioned in the d-axis positive direction by the distance d1 from the map plane F. It can be handled in the same manner as the point A1 ′.
As described above, the distance d from the position on the map plane F to the minute point A can be expressed by the distance shape model Q. The distance shape model Q can be determined based on the positional relationship of the minute point A with respect to the map plane F. Specifically, it can be determined based on the position of the map plane F in the z-axis direction and the positional relationship of the minute point A1 in the z-axis direction.

In the case of the minute line segment H or the minute triangular plane U, the distance shape model for them can be determined using the above. By regarding the minute line segment H and the minute triangular plane U as a set of minute points A, a distance shape model for the minute line segment H and the minute triangle plane U is generated as a set of distance shape models Q group for the minute point A group. can do. By replacing the minute line segment H and the minute triangular plane U with a finite number of minute point A groups and arranging the distance shape model Q group for these minute point A groups, the minute line segment H and minute triangle plane U are arranged. The distance shape model can be arranged.
However, it is not preferable to further discretize the minute line segment H or the minute triangular plane U with the point A group as described above because the calculation process becomes complicated. Therefore, the creation apparatus 10 of this embodiment prepares a distance shape model for the minute line segment H and the minute triangle plane U, and directly arranges the distance shape model for the minute line segment H and the minute triangle plane U.

A distance shape model for the minute line segment H constituting the mathematical model B will be described with reference to FIGS. The distance shape model for the minute line segment H can be determined based on the positional relationship with the map plane F in the same manner as the distance shape model for the minute point A. As described above, since symmetry is established with respect to the vertical direction of the map plane F (see FIG. 9), the positional relationship between the minute line segment H and the map plane F can be classified as follows.
(Position relationship 1) Both ends of the line segment H are located on the map plane F.
(Position relationship 2) Only one end of the line segment H is located on the map plane F.
(Position relationship 3) Both ends of the line segment H are not located on the map plane F, and both ends are located on the same side with respect to the map plane F.
(Position relationship 4) Both ends of the line segment H are not located on the map plane F, and both ends are located on the opposite sides of the map plane F.
Hereinafter, the distance shape model for the line segment H will be described in order according to the above classification.

FIG. 10 shows a distance shape model Q when the minute line segment H is (positional relationship 1). The minute line segment H here means a portion connecting the end points A1 and A2, and does not include the end points A1 and A2. The distance shape model Q shown in FIG. 10 does not include the distance shape model for the end points A1 and A2 of the line segment H. The same applies to the distance shape model Q shown in FIGS. Note that both end points A1 and A2 of the minute line segment H are the minute points A constituting the mathematical model B. For the both end points A1 and A2, the distance shape model Q with respect to the minute point A described above is used. Can be arranged. The distance d from the point P1 on the map plane F to the minute line segment H is
d ² = {(x 1 −x 2) (y _j −y 2) − (y 1 −y ² ) (x _i −x ² )} ²
/ {(X1-x2) ² + (y1-y2) ² } (4)
It is expressed. However, d ≧ 0.
The above equation (4) holds only when the point P1 is located within the range Nh (shaded portion in the figure). For example, if the point P1 is located within the range N1, the end point A1 is closer to the point P1 than the minute line segment H. If the point P1 is located within the range N2, the end point A2 is closer to the point P1 than the minute line segment H is. The range Nh is a range on the map plane F that is positioned in a direction perpendicular to the line segment H.
The above equation (4) is an equation representing two planes orthogonal to the xyd space, and the distance shape model Q for the minute line segment H has the shape of two orthogonal planes as shown in FIG. Each plane of the distance shape model Q is perpendicular to the minute line segment H. One end q1 of the distance shape model Q is a generatrix when the distance shape model Q1 with respect to the minute point A1 is cut along a plane perpendicular to the minute line segment H passing through the minute point A1. The other end q2 of the distance shape model Q is a generatrix when the distance shape model Q2 with respect to the minute point A2 is cut along a plane perpendicular to the minute line segment H passing through the minute point A2. The ends q1 and q2 are two line segments orthogonal to each other at the minute points A1 and A2, and as shown in FIG. 10, two planes connecting the parallel line segments of the ends q1 and q2 are distance shape model Q. It becomes. As described above, when both ends of the minute line segment H are located on the map plane F, the distance shape model Q can be arranged with respect to the minute line segment H as shown in FIG.

FIG. 11 shows a distance shape model Q when the minute line segment H is (positional relationship 2). In the minute line segment H shown in FIG. 11, the end point A1 is located on the map plane F, and the end point A2 is located in the positive direction of the d-axis by a distance d2 from the map plane F. In the figure, Aa2 is a point Aa2 obtained by projecting the end point A2 vertically onto the map plane F. In the figure, Ha is a line segment Ha that is obtained by vertically projecting the line segment H onto the map plane F, and is a line segment that connects the points A1 and Aa2. Ab2 in the figure is an intersection of a plane passing through the point A2 and perpendicular to the line segment H, and an extension line of the line segment Ha. The distance d from the point P1 on the map plane F to the minute line segment H is
d ² = [{(x 1 −x 2) (y _j −y 2) − (y 1 −y ² ) (x _i −x ² )} ²
+ {(X _i −x2) ² + (y _j −y2) ² } d2 ² ]
/ {(X1-x2) ² + (y1-y2) ² + d2 ² } (5)
It is expressed. However, d ≧ 0.
The above equation (5) holds only when the point P1 is located within the range Nh (shaded portion in the figure). The range Nh is a range on the map plane F located in the direction perpendicular to the minute line segment H.
The above equation (5) represents an elliptical cone surface in the xyd space, and the distance shape model Q with respect to the minute line segment H has a shape of a part of the elliptical cone surface as shown in FIG. This distance shape model Q is a part of an elliptical conical surface having a vertex A1 and a line segment Ha direction as an elliptic axis direction. One end q1 of the distance shape model Q is a generatrix when the distance shape model Q1 with respect to the minute point A1 is cut along a plane passing through the minute point A1 and perpendicular to the line segment Ha. The other end q2 of the distance shape model Q is a cut when the distance shape model Q2 with respect to the minute point A2 is cut along a plane that passes through the point Ab2 and is perpendicular to the line segment Ha, and has one shape of a hyperbola. . The distance shape model Q is a ruled surface stretched by a generatrix between the minute point A1 and the hyperbolic end q2.
Thus, when only one end of the minute line segment H is located on the map plane F, the distance shape model Q can be arranged with respect to the minute line segment H as shown in FIG.

FIG. 12 shows a distance shape model Q when the minute line segment H is (positional relationship 3). In the minute line segment H shown in FIG. 12, the end point A1 is positioned in the d-axis positive direction by the distance d1 from the map plane F, and the end point A2 is positioned in the d-axis positive direction by the distance d2 from the map plane F. Yes. In the figure, Aa1 is a point Aa1 obtained by projecting the end point A1 vertically onto the map plane F. In the figure, Aa2 is a point Aa2 obtained by projecting the end point A2 vertically onto the map plane F. In the figure, Ha is a line segment Ha obtained by projecting the line segment H onto the map plane F perpendicularly, and is a line segment connecting the points Aa1 and Aa2. Ab1 in the figure is an intersection of a plane passing through the point A1 and perpendicular to the line segment H and an extension line of the line segment Ha. Ab2 in the drawing is an intersection of a plane passing through the point A2 and perpendicular to the line segment H and the line segment Ha. In the figure, Hb is an intersection Hb where an extension line of the line segment H intersects the map plane F. The distance d from the point P1 on the map plane F to the minute line segment H is
^{d 2 = [{(x1-} x2) (yj-y2) - (y1-y2) (xi-x2)} 2
+ {(D1-d2) (xj-x2) + (x1-x2) d2} ²
+ {(D1-d2) (yj-y2) + (y1-y2) d2} ² ]
^{/ {(X1-x2) 2} + (y1-y2) 2 + (d1-d2) 2} ·· (6)
It is expressed. However, d ≧ 0.
The above equation (6) holds only when the point P1 is located within the range Nh (shaded portion in the figure). The range Nh is a range on the map plane F located in the direction perpendicular to the minute line segment H.
The above equation (6) represents an elliptical cone surface in the xyd space, and as shown in FIG. 12, the distance shape model Q with respect to the minute line segment H has a shape of a part of the elliptical cone surface. This distance shape model Q is a part of an elliptical conical surface having a vertex as a point Hb and a line segment Ha direction as an elliptical axis direction. One end q1 of the distance shape model Q is a cut when the distance shape model Q1 with respect to the minute point A1 is cut along a plane perpendicular to the line segment Ha passing through the point Ab1, and has one shape of a hyperbola. . The other end q2 of the distance shape model Q is a cut when the distance shape model Q2 with respect to the minute point A2 is cut along a plane that passes through the point Ab2 and is perpendicular to the line segment Ha. Become. The distance shape model Q is a ruled surface in which a portion between one end q2 of the hyperbola and one end q2 of the hyperbola is stretched with a generatrix of an elliptical cone surface.
When both ends of the minute line segment H are not positioned on the map plane F and both ends are positioned on the same side with respect to the map plane F, as shown in FIG. A distance shape model Q can be arranged.

  A case where the minute line segment H is (positional relationship 4) will be described with reference to FIG. As shown in FIG. 13, when the end points A1 and A2 of the line segment H are located across the map plane F, the line segment H is separated from the line segment H1 by the intersection A3 of the line segment H and the map plane F. It can be handled by dividing into two line segments H2. As a result, the line segment H1 and the line segment H2 are both in the above (positional relationship 2), and the distance shape model Q in the case of (positional relationship 2) shown in FIG. 11 is obtained for each of the line segments H1 and H2. Can be arranged. Note that a point A1 'in the figure is a point that is symmetrical to the point A with respect to the map plane F. The line segment H <b> 1 ′ is a line segment located symmetrically with the line segment H <b> 1 with respect to the map plane F. Due to the symmetry with respect to the map plane F, for the line segment H1 positioned in the negative d-axis direction with respect to the map plane F, the distance shape model Q is set with respect to the line segment H1 ′ positioned symmetrically with respect to the map plane F. What is necessary is just to arrange.

Next, a distance shape model for the minute triangular plane U will be described with reference to FIG. FIG. 14 shows a distance shape model Q with respect to a minute triangular plane U. The minute triangular plane U is a triangular plane having three vertices as A1, A2, and A3 and three sides as line segments H12, H23, and H31. The triangular plane U here means a plane portion surrounded by the three vertices A1, A2, A3 and the three sides H12, H23, H31, and the three vertices A1, A2, A3 and the three sides H12, H23, Does not include H31. That is, the distance shape model Q shown in FIG. 14 does not include the distance shape model for the three vertices A1, A2, A3 and the three sides H12, H23, H31. Three vertices A 1, A 2, A 3 of the minute triangular plane U are minute points A constituting the mathematical model B. Three sides H12, H23, and H31 of the minute triangular plane U are minute line segments H constituting the mathematical model B.
Ab1 in FIG. 14 is an intersection of a straight line passing through the minute point A1 and perpendicular to the minute triangular plane U and the map plane F. Ab2 in the figure is an intersection of a straight line passing through the minute point A2 and perpendicular to the minute triangular plane U and the map plane F. Ab3 in the figure is an intersection of a straight line passing through the minute point A3 and perpendicular to the minute triangular plane U and the map plane F. Further, q1 in the figure is an intersection point where a straight line passing through the point Ab1 and perpendicular to the map plane F intersects the distance shape model Q1 with respect to the minute point A1. In the figure, q2 is an intersection where a straight line passing through the point Ab2 and perpendicular to the map plane F intersects the distance shape model Q2 with respect to the minute point A2. In the figure, q3 is an intersection where a straight line passing through the point Ab3 and perpendicular to the map plane F intersects the distance shape model Q3 with respect to the minute point A3. As shown in FIG. 14, the distance shape model Q with respect to the minute triangular plane U is a triangular plane having three vertices as a point q1, a point q2, and a point q3.

As shown in FIG. 14, the distance shape model Q with respect to the minute triangular plane U is arranged only for the range Nu. The range Nu is a range surrounded by a triangle having the points Ab1, Ab2, and Ab3 as three vertices. From the point located in the range other than the range Nu on the map plane F, the minute points A1, A2, A3 and the minute line segments H12, H23, H31 are closer than the distance to the minute triangular plane U. .
For the small triangular plane U, a distance shape model Q can be arranged as shown in FIG.
As described above, the distance shape model Q can be determined for each minute element constituting the mathematical model B. If the map plane F is determined when the mathematical model B is arranged in the xyz space, the distance shape model Q corresponding to the minute elements constituting the mathematical model B can be arranged in the xyz space. The distance d from each position on the map plane F to the minute element can be expressed by the height in the d-axis direction from each position on the map plane F to the distance shape model Q.
In the process of arranging the distance shape model Q in the xyz space, the shape model (curved surface model) described above may be placed as it is, or the distance shape model Q is discretely approximated by a set of microelement groups, You may arrange | position a microelement group in xyz space. When the distance shape model Q is arranged as a group of minute elements, all the minute element groups constituting the distance shape model Q may be arranged, or only the minute element group necessary for processing may be arranged.

Hereinafter, the processing operation of the creating apparatus 10 according to the present embodiment will be described along the flow shown in FIG. 3 again.
In steps S6 to S14, the distance value map 36 and the minute element map 38 are created using the distance shape model Q described above. Processing in steps S6 to S14 will be described with reference to FIG.
In step S6, the processing of the distance geometry model placement program 54 is defined a z-coordinate value of the map plane F to the initial value z = z _0. Thereby, the distance value map 36 and the minute element map 38 are created with respect to a plane whose z coordinate is z = z ₀ . As shown in FIG. 15, when the z-coordinate value of the map plane F is determined, the d-coordinate axis described above is defined and the xyd space is defined.
In step S8, the depth buffer processing program 56 gives initial values to the first distance value map 36a and the first minute element map 38a. A sufficiently large distance value is given as an initial value to the first distance value map 36a. A dummy identifier id is given to the second minute element map 38a.
In step S10, the distance shape model Q is placed in the xyd space for one of the microelement groups constituting the mathematical model B by the processing of the distance shape model placement program 54. As shown in FIG. 15, for example, a minute point A1 is selected, and a distance shape model Q1 for the point A1 is arranged.
In step S12, the depth buffer processing program 56 compares the d coordinate value of the distance shape model Q1 with the distance value held in the first distance value map 36a for each position (x, y) on the map plane F. To do. At the position (x, y) where the d coordinate value of the distance shape model Q1 is smaller, the distance value held in the first distance value map 36a is rewritten to the d coordinate value of the distance shape model Q1. For example, at the position (x _i , y _j , z ₀ ) of the point P1, it is rewritten to the d coordinate value of the point R1. The point R1 is located on the distance shape model Q1 and is located in the positive d-axis direction from the point P1. In the flow of this explanation, since the first distance value map 36a holds a sufficiently large initial value, all the distance values (initial values) held in the first distance value map 36a are the distance shape model Q1. To the d coordinate value.
When the distance value held in the first distance value map 36a is rewritten by the depth buffer processing program 56, the position (x, y, z ₀ ) where the distance value is rewritten is stored in the first approximate element map 38a. The retained identifier id is rewritten to the identifier id of the minute point A1. Here, since all the distance values (initial values) held in the first distance value map 36a are rewritten to the d coordinate values of the distance shape model Q1, dummy identifiers held in the first approximate element map 38a All ids are rewritten to the identifier id of the minute point A1.

In step S14, it is determined whether or not the processing in steps S10 and S12 has been performed for all the microelements constituting the mathematical model B, and S10 to S14 are repeated until the processes are performed for all the microelements.
Returning to step S10, the distance shape model arrangement program 54 arranges the distance shape model Q in the xyd space for the other one of the microelement groups constituting the mathematical model B. As shown in FIG. 15, for example, a distance shape model Q2 for the minute point A2 is arranged. When the distance shape model Q2 is arranged, the depth buffer processing program 56 compares the d coordinate value of the distance shape model Q2 with the value held in the first distance value map 36a for each position on the map plane F. Is done. When the d coordinate value of the distance shape model Q2 is smaller, the value held in the first distance value map 36a is rewritten to the d coordinate value of the distance shape model Q2. As shown in FIG. 15, for example, at the point P1 (x _i , y _j , z ₀ ), the d coordinate value d1 of the distance shape model Q1 is smaller than the d coordinate value d2 of the distance shape model Q2. The 1-distance value map 36a holds the d-coordinate value of the distance shape model Q1. Note that a point R2 in the figure is a point on the distance shape model Q2 and is located in the positive d-axis direction of the point P1.
As shown in FIG. 15, on the distance shape model Q1, the d-coordinate value d1 of the point R1 having the same position in the xy direction as the point P1 is the minute point A1 from the position (x _i , y _j , z ₀ ) of the point P1. Is equal to the distance d1. On the distance shape model Q2, the d coordinate value d2 of the point R2 having the same position in the xy direction as the point P1 is the distance d2 from the position (x _i , y _j , z ₀ ) of the point P1 to the minute point A2. equal. That is, the distance d1 from the position (x _i , y _j , z ₀ ) of the point P1 to the minute point A1 by comparing the d coordinate values of the distance shape models Q1 and Q2 at the same position in the xy direction with the point P1. And the distance d2 to A2 can be compared.

When the distance value held in the first distance value map 36a is rewritten to the d coordinate value d2 of the distance shape model Q2, in the first approximate element map 38a, the identifier id described in the rewritten position. Is rewritten to the identifier id of the minute point A2. At the position where the distance value held in the first distance value map 36a has not been rewritten, the identifier id described in the first approximate element map 38a is held as it is.
As shown in FIG. 16, for example, at the point P1 (x _i , y _j , z ₀ ), the distance d1 to the minute point A1 is held in the first distance value map 36a. Holds the identifier id of the minute point A1. In the first approximate element map 38, the identifier id of the minute point A1 is described for the position in the range N1 (shaded portion in the figure) of the map plane F, and for the position in the range N2 of the map plane F. The identifier id of the minute point A2 is described.

The processes in steps S10 and S12 are performed on all the small element groups constituting the mathematical model B. As a result, in the first distance value map 36a, the d coordinate of the distance shape model Q located at the lowermost position in the d-axis direction among all the arranged distance shape models Q for each position on the map plane F. The value is retained. Thereby, in the first distance value map 36a, for each position on the map plane F, a distance value d from the position to the closest minute element is described. That is, the shortest distance value from the position to the mathematical model B is described for each position on the map plane F in the first distance value map 36a.
In addition, in the first minute element map 38a, for each position on the map plane F, the identifier id of the minute element located closest to the position is held.
When the above process is performed for all the minute elements, the answer is yes in step S14, and the process proceeds to step S16.

  Note that the processes in steps SS10 and S12 are substantially the same as the hidden surface removal process of the three-dimensional graphics display technique. In the three-dimensional graphics display technology, hidden surface removal processing is used when drawing a solid. In this hidden surface erasing process, an array called a depth buffer is prepared, which is composed of elements that correspond one-to-one with the pixels constituting the screen. A value can be described in each element of the depth buffer. For example, a sufficiently large value is given as an initial value. After preparing such a depth buffer, polygon faces constituting a solid are drawn in order. At this time, the depth distance (so-called depth value) from the screen is calculated for the position on the polygonal surface drawn at each pixel of the screen, and compared with the value of each element of the depth buffer. If the calculated depth value is smaller than the value of the depth buffer element, the calculated depth value is held in the depth buffer element, and the color of the polygonal plane is displayed at the corresponding pixel. On the other hand, if the calculated depth value is larger than the value of the depth buffer element, the value of the depth buffer element is held as it is, and the color of the polygonal surface is not displayed for the pixel. When the above processing is performed on all the polygonal surfaces constituting the solid, an image when the solid is viewed from the screen direction is displayed on the screen. Comparing the hidden surface removal process of the three-dimensional graphics display technique and the process of step S12 of this embodiment, the depth buffer and the distance value map 36 correspond, and the image displayed on the screen and the approximate element map 38 correspond. Yes.

In the next step S16, it is determined whether or not the z coordinate of the map plane F is an initial value. If the z coordinate of the map plane F is an initial value, the process proceeds to step S18, and if not, the process proceeds to step S32. Here, according to the flow of this description, the process proceeds to step S18 to continue the description.
In step S18, the z coordinate value of the map plane F is changed by a predetermined width Δz (z _{k + 1} = z _k + Δz), and the map plane F moves by a predetermined amount Δz in the z-axis direction. Here, the z coordinate value is changed from z ₀ to z ₁ = z ₀ + Δz. Then, the process returns to step S8.
When returning to step S8, the processing of steps S8 to S14 is performed again, and a second distance value map 36b and a second minute element map 38b are newly created. Through the above processing, the two distance value maps 36 of the first and second distance value maps 36a and 36b and the two minute element maps 38 of the first and second minute element maps 38a and 38b are created. Stored in the storage unit 30. Since the z coordinate of the map plane has been moved from the initial value in the previous step S18, the result in step S16 is no and the process proceeds to step S32.

In steps S <b> 32 to S <b> 42, the processing unit 70 creates the offset surface model description data 40 using the offset surface element selection program 58 and the offset point determination program 60. The offset surface model description data 40 is data describing an offset surface model obtained by performing offset processing for a predetermined distance with respect to the machining surface D described by the curved surface model description data 32. The offset surface model description data 40 can be used as, for example, tool path information taught to a 5-axis controlled NC machine tool.
In step S32, the offset surface element selection program 58 arranges the first distance value map 36a and the second distance value map 36b in the xyz space. As shown in FIG. 17, when the first and second distance value maps 36a and 36b are arranged in the xyz space, the positions where the distance values are described in the first and second distance value maps 36a and 36b are used as vertices. A rectangular parallelepiped space group can be partitioned. For example, the rectangular parallelepiped space G can be defined by eight points P1 to P8. A z coordinate value _{z 0} of the first distance value map 36a, cuboid since z-coordinate value of the second distance value map 36b is _{z 1,} z coordinate values in the xyz space between _{z 0} of _{z 1} Space G group is divided. In addition, the rectangular parallelepiped here is intended to be a hexahedron in which three sides extending from one vertex are orthogonal to each other, and includes a cube (a hexahedron in which all faces are equal squares).

At step S34, offset surface element selection program 58, z coordinate values from rectangular space G group was divided into xyz space between z ₀ of z _1, selects one of a rectangular parallelepiped space G. Here, for example, it is assumed that a rectangular parallelepiped space G partitioned by eight points P1 to P8 is selected.
In step S36, as shown in FIG. 18, with respect to the rectangular parallelepiped space G selected in step S34, the distance value described in each vertex position is extracted from the first and second distance value maps 36a and 36b, and each extracted The distance value is compared with the offset distance. The description d (P1) in FIG. 18 indicates the distance value described for the position P1. The offset distance can be the radius r of the cutting edge surface 100 of the tool 100, for example. The offset distance r can be appropriately set by a user or the like.
If the distance value described for each vertex position in the cuboid space G is larger than the offset distance r, it can be determined that the vertex position is located outside the offset plane M with respect to the mathematical model B. Conversely, if the distance value is smaller than the offset distance r, it can be determined that the vertex position is located inside the offset plane M with respect to the mathematical model B. In FIG. 18, only the distance value of the position of the point P5 is smaller than the offset distance r, and the distance values of the positions of the other points P1, P2, P3, P4, P6, P7, and P8 are larger than the offset distance r. Illustrated. That is, at each vertex position of the rectangular parallelepiped space G, only the position of the point P5 is located inside the offset surface M (inner point), and the other vertex positions are located outside the offset surface M (outer point). ) Can be determined.

  The offset plane is located between the position determined to be inside the offset plane with respect to the mathematical model and the position determined to be outside the offset plane with respect to the mathematical model. Further, since the rectangular parallelepiped space G is sufficiently small, it can be determined that there is no offset plane between two positions determined to be both inside or outside. Therefore, for example, in the case shown in FIG. 18, an offset surface upper point m51 can be assumed on a line segment g51 connecting the point P5 determined as the inner point and the point P1 determined as the outer point. Further, an offset surface upper point m56 can be assumed on a line segment g56 connecting the point P5 determined as the inner point and the point P6 determined as the outer point. Also, an offset surface upper point m57 can be assumed on a line segment g57 connecting the point P5 determined as the inner point and the point P7 determined as the outer point. From the assumed offset plane upper points m51, m56, and m57, the element model Me that becomes a part of the offset plane model can be arranged in the rectangular parallelepiped space G.

  When the rectangular parallelepiped space G is divided into the xyz space and it is determined whether the eight vertex positions are located inside or outside the offset plane M, the rectangular parallelepiped space G is determined based on the combination of the inside / outside determination. The offset surface element model Me that becomes a part of the offset surface M can be arranged inside the. FIG. 19 shows the relationship between the combination of the inside / outside determination of each vertex position in the rectangular parallelepiped space G and the arrangement pattern of the offset surface element model Me. As shown in FIG. 19, there are 15 arrangement patterns of the offset surface element model Me. In the rectangular parallelepiped space G group shown in FIG. 19, one of the vertex positions with (black circles) and the vertex positions without (black dots) means an interior point for each rectangular parallelepiped space G. Means outside point. For example, in the cubic lattice G of FIG. 19A, all the vertex positions are located inside the offset plane M with respect to the mathematical model B, and all the vertex positions are offset plane M with respect to the mathematical model B. It also means the case where it is located outside. The offset plane element selection program 58 selects the rectangular parallelepiped space G, performs the above-described inside / outside determination for each vertex position, and arranges the offset plane element model Me corresponding thereto.

In the next step S38, processing by the offset point determination program 60 is performed. The offset point determination program 60 determines the position of the point on the offset plane (for example, m51, m56, m57) based on the offset plane element model Me selected by the offset plane element selection program 58.
Processing performed by the offset point determination program 60 will be described with reference to FIG. Here, it is assumed that the offset surface element model Me is selected in the previous step S36 as shown in FIG. As shown in FIG. 20, the offset surface element model Me is a triangular plane model having apexes on the surface point m51, the surface point m56, and the surface point m57. The on-plane point m51 is located on a line segment g51 connecting the points P5 and P1. The on-surface point m56 is located on a line segment g56 connecting the points P5 and P6. The on-plane point m57 is located on a line segment g57 connecting the points P5 and P7. The point P1 is located at the coordinates (x _i , y _j , z ₀ ), and the point P5 is located at the coordinates (x _i , y _j , z ₁ ). Let the coordinates of the point M51 be (xm, ym, zm).

FIG. 20 shows how the offset point determination program 60 determines the position of the surface point m51 of the offset element surface Me. The offset point determination program 60 determines the position of the surface point m51 on the line segment g51. Since the line segment g51 is parallel to the z-axis, only the z-coordinate value of the on-plane point m51 is corrected. The x coordinate value and the y coordinate value are not changed. The offset point determination program 60 extracts from the first and second distance value maps 36a and 36b distance values d of both end points P1 and P5 of the line segment g51 where the position of the surface point m51 is assumed. Here, it is assumed that the distance value of the point P1 is d1, and the distance value of the point P5 is d5. The offset point determination program 60 determines the position of the on-surface point m51 based on the ratio between the difference between the distance value d1 of the point P1 and the offset distance r and the difference between the distance value d2 of the point P2 and the difference of the offset distance r. Specifically, the division ratio at which the on-plane point m51 divides the line segment g51 is a ratio of the difference between the distance value d1 of the point P1 and the offset distance r and the difference between the distance value d2 of the point P2 and the difference of the offset distance r. Next, the position of the surface point m51 is determined. That is,
_{(Zm-z 0) :( z} 1 -zm) = (d1-r) :( r-d5)
The z-coordinate value of the surface point m51 is corrected so as to satisfy the relationship. Therefore,
_{zm = {(d5-r)} z 0 + (r-d1) z 1} / (d5-d1)
It becomes.
Similarly, the position of the surface point m56 is determined on the line segment g56. The position of the surface point m57 is determined on the line segment g57. By determining the on-surface points m51, m56, and m57, the position of the offset surface element model Me is determined.
In step S40, the determined offset surface element model Me is stored in the data storage unit 30 as a part of the three-dimensional model of the offset surface, and a part of the offset surface description data 40 is created.

In the next step S42, it is determined whether or not the processes in the above steps S34 to S40 have been performed for all the partitioned rectangular spaces G, and the processes in S34 to S40 are repeated for all the rectangular spaces G. It is.
FIG. 21 schematically shows a state after the offset plane element model Me is arranged and the positions thereof are determined for all of the partitioned rectangular parallelepiped spaces G. For example, the arrangement pattern of the offset surface element model Me shown in FIG. 19A is applied to the rectangular parallelepiped spaces G1 and G4 in FIG. In addition, the arrangement pattern of the offset surface element model Me shown in FIG. 19C is applied to the rectangular parallelepiped spaces G2 and G3 in FIG. As shown in FIG. 21, steps S34~S40 are by carried out for all the rectangular space G which is partitioned, a three-dimensional offset plane M z coordinate value in the xyz space between _{z 0} of _{z 1} A model is created.

In the next step S44, it is determined whether or not the set z coordinate value of the map plane is the final value. If yes in step S44, the flow ends. If no in step S44, the process moves to step S18.
In step S18, the z coordinate value of the map plane F is changed by a predetermined width, and the map plane F moves by a predetermined amount in the z coordinate direction. Here, the z coordinate value is changed from z1 to z2. Next, the process returns to step S8.
Returning to step S8, the distance value held in the first and second distance value maps 36a and 36b stored in the data storage unit 30 is sufficiently large only in the map created earlier. It is rewritten to the initial value. Similarly, in the first and second minute element maps 38a and 38b stored in the storage unit 30, only in the map created earlier, the identifier of the retained minute element becomes a dummy identifier. It can be rewritten as In the flow of this description, the first distance value map 36a and the first minute element map 38a are rewritten. On the other hand, the second distance value map 36b and the second minute element map 38b are held in the data storage unit 30 as they are.
A new first distance value map 36 a and a first minute element map 38 a are created and stored in the storage unit 30 by the processes of steps S <b> 10 to S <b> 14.
When the new first distance value map 36a and the first minute element map 38a are created, the process moves to step S32 through step S16, and the first and second distance value maps are again obtained by the processing from step S32 to step 42. A part of the three-dimensional model of the offset plane M is created using 36a and 36b. Here, z coordinate values of the first distance value map 36a is the _{z 2,} since the z-coordinate value of the second distance value map 36b is at _{z 1,} z coordinate values offset the xyz space between the z1 z2 A three-dimensional model of the surface M is created.

  Thereafter, as described above, the distance value map 36 and the minute element map 38 are created by changing the z coordinate value, and a part of the model of the offset plane M is obtained using the first and second distance value maps 36a and 38a. Repeat the process to create. Thereby, as shown in FIG. 22, a three-dimensional model of the offset surface M with respect to the processing surface D is sequentially created along the z-axis direction. When the z coordinate value reaches the final value (Yes in step S42), the flow ends, and the creation of the three-dimensional model of the offset surface M with respect to the processing surface D is completed.

As mentioned above, although embodiment of this invention was described in detail, these are only illustrations and do not limit a claim. The technology described in the claims includes various modifications and changes of the specific examples illustrated above.
In addition, the technical elements described in the present specification or the drawings exhibit technical usefulness alone or in various combinations, and are not limited to the combinations described in the claims at the time of filing. The technology illustrated in this specification or the drawings achieves a plurality of objects at the same time, and achieving one of the objects itself has technical utility.

The figure which shows the offset surface described by several z coordinate value with respect to the position of xy direction The figure which shows the structure of the preparation apparatus of the three-dimensional model of an Example. The flowchart which shows the flow of a process of the preparation apparatus of the three-dimensional model of an Example. Diagram showing the machining surface described by the curved surface model description data Diagram showing a mathematical model in which the machined surface is discretely approximated by a set of microelements The figure which shows the distance d from the position on a map plane to a microelement The figure which shows the distance shape model for the minute point located on the map plane The figure which shows the distance shape model for the minute point located above the map plane The figure which shows the distance shape model for the minute point located under the map plane The figure which shows the distance shape model for the minute line segment where both ends are located on the map plane The figure which shows the distance shape model for the minute line segment where only one end is located on the map plane The figure which shows the distance shape model for the minute line segment where both ends are located above the map plane The figure which shows the distance shape model for the minute line segment where both ends are located across the map plane The figure which shows the distance shape model for a small triangular plane Diagram explaining distance value map Diagram explaining approximate element map The figure which shows the rectangular parallelepiped space divided into xyz space Diagram explaining how to place an offset surface element model Diagram showing the layout pattern of the offset surface element model The figure explaining how to determine the position of the offset point The figure which shows a mode that the three-dimensional model of the offset surface was created in a part of xyz space. The figure which shows a mode that the three-dimensional model of an offset surface is created in xyz space. The figure which shows the offset surface described by one z coordinate value with respect to the position of xy direction The figure which shows a mode that the z coordinate value of an offset surface is determined

Explanation of symbols

10.3D model creation device 30.Data storage unit 32.Surface model description data 34.Mathematical model description data 36.Distance value map 38.Approximation element map 50.Program storage unit 52. Mathematical model creation program 54 .. Distance shape model arrangement program 56. Depth buffer processing program 58.. Offset surface element selection program 60.. Offset point determination program 70. ..Point C constituting the curved surface model..Line segment S constituting the curved surface model..Surface A constituting the curved surface model..Small point H constituting the mathematical model..Micro line segment U constituting the mathematical model.・ Small triangular planes constituting the mathematical model

Claims (5)

A three-dimensional model creation device that creates an offset surface model that is offset from a surface model by an offset distance,
Model storage means for storing the surface model as a set of minute elements arranged in the xyz space;
plane setting means for setting a plane parallel to the xy plane in the xyz space;
Means for disposing a distance shape model located in the z-axis direction from the set plane position by a distance from the set plane position to the microelement in the xyz space;
Among the arranged distance shape models, the distance in the z-axis direction from the position on the set plane to the distance shape model closest to the z-axis direction is set to the position on the set plane. Distance value storage means for storing in association with each other;
Means for comparing the distance value stored in the distance value storage means with the offset distance value;
Offset surface position determining means for determining the position of the offset surface based on the comparison result of the distance value comparing means;
A three-dimensional model creation device. The distance value comparison means determines whether the position where the distance value storage means stores the distance value is outside or inside the offset surface;
2. The tertiary according to claim 1, wherein the offset surface position determining unit determines a position of the offset surface on a line segment that connects the position determined by the distance value comparing unit to the outside and the position determined to be the inside. Original model creation device. A method of creating a three-dimensional model that creates an offset surface model offset by an offset distance from a surface model,
A model storing step of storing the surface model as a set of minute elements arranged in the xyz space;
setting a plane parallel to the xy plane in the xyz space;
Disposing a distance shape model located in the z-axis direction from the set plane position by a distance from the set plane position to the microelement in the xyz space; and
Among the arranged distance shape models, the distance in the z-axis direction from the position on the set plane to the distance shape model closest to the z-axis direction is set to the position on the set plane. A distance value storing step for storing in association with each other;
A distance value comparison step of comparing the distance value stored in the distance value storage step with the offset distance value;
A step of determining the position of the offset surface based on the comparison result of the distance value comparison step;
A method for creating a three-dimensional model comprising: This is a 3D model creation program that creates an offset surface model that is offset from the surface model by an offset distance.
A process of storing the surface model as a set of minute elements arranged in the xyz space;
a process of setting a plane parallel to the xy plane in the xyz space;
A process of arranging a distance shape model located in the z-axis direction from the set position by a distance from the set position on the plane to the minute element in the xyz space;
Among the arranged distance shape models, the distance in the z-axis direction from the position on the set plane to the distance shape model closest to the z-axis direction is set to the position on the set plane. A distance value storing process for storing in association with each other;
A distance value comparison process for comparing the distance value stored in the distance value storage process with the offset distance value;
A process for determining the position of the offset surface based on the comparison result of the distance value comparison process;
A program that executes A method of creating an offset surface model offset by an offset distance from a surface model,
Storing data describing the surface model as a set of microelements arranged in xyz space in an electronic computer in a readable manner;
A grid point is set in a plane parallel to the xy plane, and a distance shape model located in the z-axis direction away from the grid point by a distance equal to the distance from the grid point to the micro element is set for each micro element for each grid point. The computer calculates the distance in which the distance in the z-axis direction from the lattice point is the shortest in the distance shape model group calculated for the microelement group, and compares the calculated distance with the offset distance. Storing in a readable manner;
A step of arranging an offset surface between lattice points having different comparison results by an electronic computer;
A method of creating a three-dimensional model that executes at least.

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