JP2001242919A - Calculation method for cutter reference surface, computer readable storage medium to store program of cutter reference surface calculation and computer equipment for it - Google Patents

Abstract

PROBLEM TO BE SOLVED: To calculate a cutter reference surface fast by using a 3-D graphics display equipment. SOLUTION: A sweeping shape is formed while a reference point representing the center of a cutting tool is moving along the work surface after the shapes corresponding to vertex, side and polygon are assigned in accordance with the information about the polyhedron model and the cutting tool for the work objective (S100), based on this sweeping shape, the portions of the shape extruding into inside of each one of the adjacent shapes are eliminated, and the shapes after the elimination are transformed to the polyhedron (S103-S108). Based on this polyhedron, the polygon data is formed (S109) by selecting only the polygons with pre-designated norm directions, then, this polygon data is fed to the 3D graphics display equipment and, based on the depth value representing height of upper-most part of the sweeping shape calculated through processing by the hardware equipment (S110, S111), thus, the point group in the grid form covering the upper surface of the sweeping shape is calculated (S111). Based on this group of points the cutter reference surface is calculated by converting the selected adjacent points to the polygon (S113).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a tool reference plane calculation method, a computer-readable recording medium storing a tool reference plane calculation program, and a tool reference plane calculation apparatus, and more particularly, to a numerical control machine tool. A tool reference plane calculation method for generating a tool reference plane that is inflated by the inverse shape of a tool when processing a workpiece by moving the tool along a path, and a computer-readable recording medium storing a tool reference plane calculation program And a tool reference plane calculation device.

[0002]

2. Description of the Related Art Conventionally, many dies used for manufacturing die-cast products and sheet metal products of plastics and metals have complicated curved surface shapes. Many of such dies are numerically controlled (NC) using tools such as ball end mills, flat end mills, and round end mills.
It is manufactured by merical control). In die machining, a workpiece is often deeply engraved with a tool. Therefore, a three-axis control machine tool having excellent rigidity is generally used. In metal working using a three-axis control machine tool, a desired shape is input by inputting a movement path of a point representing a tool position (hereinafter, this point is referred to as a reference point) to a control device of the machine tool. It is known to cut.

FIG. 27 shows the types of end mills ((a) ball end mill, (b) flat end mill, (c) round end mill) used in die machining and the positions of their tool reference points (Cutter reference points). FIG. In die machining, a ball end mill with a hemispherical cutting edge is often used, but in rough machining where work efficiency is important, a flat end mill is used, and similarly, in machining of a smooth curved surface, a flat end mill is used. A round end mill having an annular cutting blade attached around the end mill may be used. In 3-axis NC machining, the movement path of a point representing these tool positions (hereinafter, this point is referred to as a tool reference point) is described in a program format called a G code.
The desired shape is cut out by inputting it to the control device of the machine tool. In ball end mills, it is common to use the center point of the cutting edge as a tool reference point. on the other hand,
In a flat end mill, a center point of a tool tip is used as a tool reference point, and in a round end mill, a point inside a center of the tool tip by a radius of an annular cutting edge is often used as a tool reference point.

[0004]

In processing a shape having many irregularities such as a mold, a tool repeatedly repeats an enormous number of minute linear movements, for example, to remove unnecessary portions little by little from the base material. To go. Since the calculation of such a complicated tool path requires a long processing time (for example, about several tens of minutes) even if a high-speed computer is used, it is desired to increase the processing speed.

[0005] In the case of machining a complicated shape such as a mold, a problem called a so-called gouge is apt to occur in a simple tool path calculation method in which a tool cuts into the inside of a mold product. . FIG. 28 is an explanatory diagram illustrating an example of shaving in die machining, and illustrates an example of shaving that occurs at a portion where the radius of curvature of the mold surface is smaller than the radius of a cutting tool (for example, a ball end mill). Is shown.
That is, the ball end mill that moves from left to right in the drawing while maintaining contact with the product surface is used in a portion where the radius of curvature of the mold surface is smaller than the tool radius (the gouging region indicated by hatching in the drawing). If the contact with the gouging area is missed, it is directly cut into the inside of the mold product. The automatic tool path generation program spends most of its calculation time in such a gouge prevention process.

In order to prevent this gouge, a shape called a tool reference surface, which is obtained by expanding the shape of a mold product by the inverse shape of a cutting tool, may be generated. This tool reference surface corresponds to the upper surface of the sweep shape when the reverse shape of the tool is slid vertically and horizontally along the surface of the mold product. Here, the calculation of the sweep shape is a classic problem in the field of solid modeling,
Several calculation methods have already been developed. For example, in a modeling technique that handles three-dimensional phase information such as a boundary representation method (B-reps), a procedure for obtaining a sweep shape and a tool reference plane becomes very complicated. Therefore, in the field of NC cutting, the “inverted offset method”, in which the upper surface of the sweep shape is approximately calculated as a dense point set, is often used.

In the inverse offset method, first, a coordinate system in which the rotation axis direction of the tool is the Z axis is considered, and a sufficiently fine orthogonal grid of about 1000 × 1000 is prepared on the XY plane. Then, by extending a straight line parallel to the Z axis from the center of each grid and calculating the intersection with the uppermost surface of the sweep shape,
Obtain a dense point cloud covering the top surface of the sweep shape. Finally, a polyhedron representing the tool reference plane is generated by interpolating the gap between the point groups with a polygon.

The inverse offset method is simple in processing, easy to program, and stable in calculation. However, since the intersection calculation is repeated for each of a huge number of grids, a large amount of calculation time is required, which is a practical obstacle. Choi et al. Have developed a technology that uses the geometrical features of tools to reduce computational effort by a fraction. However, it has been reported that even if such techniques are used, it takes several tens of minutes to calculate the tool reference plane, and there is a strong demand for further speeding up the processing.

In view of the above, it is an object of the present invention to use a three-dimensional graphics display device to calculate a tool reference plane at high speed. An object of the present invention is to instantly calculate a tool path generated based on a calculation result of a tool reference plane.

[0010]

Means for Solving the Problems The present inventors combine a discrete calculation technique of a tool reference plane by an inverse offset method and a processing technique using a three-dimensional graphics display device to obtain a tool reference. Stable and fast calculation of the surface was realized. This method can be applied to the calculation of the tool reference plane for machining using ball end mills, flat end mills, and round end mill tools, but the method must be extended so that it can be applied to tools with other shapes. Is easy. In the present invention, it is assumed that the shape of the mold to be processed is represented by a polyhedron. However, a shape with a hole in which a polygon is connected to only one of the left and right sides is also regarded as a polyhedron. An arbitrary curved surface shape can be approximated as such a polyhedron with desired accuracy.

Such a polyhedron technique is well studied in the field of computer graphics, and several high-speed algorithms are already known. The most time-consuming process in the inverse offset method is the process of calculating the intersection between the straight line extending from each grid and the uppermost surface of the sweep shape. This calculation can be performed at high speed by using the hidden surface elimination function that is provided as standard in the three-dimensional graphics display device. In order to utilize the functions of the hardware, it is necessary to appropriately approximate the spherical surface and the cylindrical surface constituting the sweep shape to a polyhedron. The time required for hidden surface removal is almost proportional to the total number of polygons of the polyhedral curved surface. Therefore, by removing portions that do not affect the calculation of the tool reference plane from the curved surface that constitutes the sweep shape, and selectively transforming only the remaining portion into a polyhedron, higher-speed processing is realized.

[0012] Regarding the hardware implementation of geometric processing, the speed of CGS model drawing processing is increased (JPMenon, R.
J.Marisa and J.Zagajac: More Powerful Solid Modeli
ng through Ray Representations, IEEE Computer Grap
hics and Appl., 14, 3 (1994) 22.) Analysis of the approachable range of the probe of the three-dimensional measuring machine (SNSpitz, AJSpyridi
and AAGRequicha: Accessibility Analysis for Pla
nning of DimensionalInspection with Coordinate Mea
suring Machines, IEEE Trans. Robotics andAutomatio
n, 15, 4 (1999) 714.), calculation of discrete Voronoi diagrams (KEHoff III, T. Culver, J. Keyser, MCLin and DM
anocha: Fast Computation of Generalized Voronoi D
iagrams Using Graphics Hardware, Computer Graphic
s Proc., SIGGRAPH 99 (1999) 277.). In addition, the present inventors have already applied for a technique for speeding up the simulation of the cutting process using a technique substantially similar to the present invention (Japanese Patent Application No. 11-35296).
However, there is no known example other than the present invention in which the calculation of the tool reference plane, which plays an important role in generating the tool path, is accelerated by hardware.

According to a first aspect of the present invention, when a tool mounted on a numerically controlled machine tool is moved along a path to machine a workpiece, a tool reference surface inflated by an inverse shape of the tool is used. A computer-readable recording medium that records a tool reference plane calculation method and a tool reference plane calculation program to be generated, wherein the step includes inputting information on a polyhedral model and a tool shape of a workpiece and inputting the information by the inputting step. A first shape corresponding to the vertex portion, a second shape corresponding to the side portion, and a third shape corresponding to the polygonal portion, based on the information on the polyhedron model and the tool shape of the processing object, or By arranging the second shape and the third shape, a sweep shape is generated when the reference point representing the center of the tool moves along the surface of the workpiece. Removing, by the step and the shape generated by the generating step, a portion that enters the interior of each of the adjacent shapes; and a polyhedron for a partial shape of the shape obtained by the removing step. And generating polygon data by selecting only polygons whose normal direction is a predetermined direction based on the polyhedron obtained by the polyhedron conversion step, and generating the polygon data Providing the polygon data obtained by the step to the three-dimensional graphics display unit; and receiving a depth value representing the height of the uppermost surface of the sweep shape obtained by hardware processing by the three-dimensional graphics display unit. Obtaining a grid-like point cloud covering the upper surface of the sweep shape based on the depth value obtained in the receiving step. A tool reference plane calculation method and a tool reference plane comprising: a step; and a step of obtaining a tool reference plane by selecting adjacent points and replacing them with a polygon based on the point cloud obtained by the step of obtaining the point cloud. Provided is a computer-readable recording medium on which a calculation program is recorded.

According to a second solution of the present invention, when a tool attached to a numerically controlled machine tool is moved along a path to machine a workpiece, a tool reference surface inflated by an inverse shape of the tool is used. A tool reference plane calculation device for generating, comprising an input unit for inputting information on a polyhedron model and a tool shape of a workpiece, and a processing unit for calculating a tool reference plane, wherein the processing unit is configured by the input unit Based on the input information on the polyhedron model and the tool shape of the processing target, the first shape corresponding to the vertex portion, the second shape corresponding to the side portion, and the third shape corresponding to the polygonal portion, or Means for generating a sweep shape when the reference point representing the center of the tool moves along the surface of the workpiece by arranging the second shape and the third shape; and Generate Based on the shape, and means for removing the portion has entered the interior of the shape of each adjacent,
For the partial shape of the shape obtained by the removing means, based on the polyhedron obtained by the polyhedron and the polyhedron obtained by the polyhedron, by selecting only polygons having normal directions in a predetermined direction. Means for generating polygon data, means for providing polygon data obtained by the means for generating polygon data to a three-dimensional graphics display unit, and hardware processing by the three-dimensional graphics display unit. Means for receiving a depth value indicating the height of the uppermost surface of the sweep shape, means for obtaining a grid-like point group covering the upper surface of the sweep shape based on the depth value obtained by the receiving means, and obtaining the point group Means for obtaining a tool reference plane by selecting adjacent points based on a point group obtained by the means and replacing the selected points with polygons.

[0015]

BEST MODE FOR CARRYING OUT THE INVENTION Approximate Calculation Method of Upper Surface of Sweep Shape Using Inverse Offset Method FIG. 1 is an explanatory diagram showing a tool reference surface and a sweep shape by a ball end mill. FIG. 1A is a view showing a tool reference plane drawn by a reference point of a ball end mill that slides on a product surface, and FIG. 1B is a sweep when a reference point having an inverted shape of the tool slides on the product surface. It is the figure which showed the shape. As shown in FIG. 1 (a), when the ball end mill slides vertically and horizontally on the product surface while maintaining contact with the die product (without cutting into the inside), the surface on which the locus of the tool reference point of the ball end mill is drawn Is defined as a tool reference surface.
If this tool reference plane is obtained, the ball end mill is moved so that the reference point always exists above this plane, so that a tool path without cutting can be calculated at high speed. The tool reference plane can be calculated by the following procedure. First,
The reverse shape is obtained by rotating the ball end mill 180 degrees about the tool reference point. Next, this inverted shape is shown in FIG.
The reference point is always on the product surface (Designed
surface) and move it horizontally and vertically,
Generate the sweep shape. At this time, the uppermost surface of the sweep shape corresponds to the tool reference surface.

This calculation method can also be applied to cutting using a flat end mill or a round end mill. FIG.
FIG. 4 is an explanatory view showing a tool reference plane and a sweep shape by a flat end mill. FIG. 2A is a diagram showing a state of a surface drawn by a locus of a tool reference point when cutting a product surface using a flat end mill, and FIG. 2B is a diagram showing an inverted shape of the flat end mill. It is a figure showing the state of the sweeping shape when the reference point slides vertically and horizontally on the product surface.

FIG. 3 is an explanatory view (1) showing a tool reference surface and a sweep shape by a round end mill. FIG. 3 (a)
FIG. 3B is a diagram illustrating a tool reference surface drawn by a reference point of a round end mill that slides on a product surface, and FIG. 3B is a diagram illustrating a sweep shape when a reference point of an opposite shape of the tool slides on the product surface. It is. FIG. 4 is an explanatory diagram (2) illustrating a tool reference surface and a sweep shape by a round end mill. FIG. 4 (a)
FIG. 4B is a diagram showing a state where the reverse shape of the flat end mill having the radius (R−r) is slid along the surface of the reverse shape of the ball end mill having the radius (r), and FIG. FIG. 11B is a diagram showing a result of calculating a sweep shape of a reverse shape of the ball end mill of FIG. 7) and further sliding the flat shape of the flat end mill having a radius (Rr) along the upper surface thereof.
As shown in FIG. 4A, the reverse shape of the round end mill having the radius of the shaft portion (R) and the radius of the annular cutting edge (r) is the reverse shape of the flat end mill having the radius (R-r). It can be regarded as a sweep shape when slid along the surface of a ball end mill having a small radius (r). Therefore,
As shown in FIG. 4 (b), the reverse shape of the round end mill is obtained by sliding the reverse shape of the ball end mill having a radius (r) along the mold surface to generate a sweep shape, and then obtaining the sweep shape. It can be calculated by sliding the reverse shape of the flat end mill with the radius (Rr) along the upper surface of the bent shape. The reverse shape of the round end mill can be regarded as a sweep shape when the reverse shape of the ball end mill having the radius (r) is slid along the reverse shape of the flat end mill having the radius (R-r). However, it is possible to calculate the inverse sweep shape of the round end mill.

That is, it can be seen that when the flat end mill and the round end mill are used for cutting, respectively, the tool reference surface and the upper surface of the sweep shape are the same. Therefore, in order to obtain the tool reference plane, it is only necessary to calculate the sweep shape of the inverse shape of the tool and perform the process of selecting the upper surface.

In the following discussion, it is assumed that the shape of the product to be processed is a polyhedron for the sake of explanation and in consideration of the processing speed. However, not only a normal closed polyhedron where one polygon is connected to each side of each side, the polygon is connected to only one of the left or right of the side,
An "open" shape can be tolerated. In general, an arbitrary curved surface shape can be approximately expressed as such a polyhedron with desired accuracy (see FIG. 16 described later and the description thereof).
Techniques for polyhedralizing curved shapes are well studied in the field of computer graphics, and some high-speed algorithms are already known. As described above, if the sweep shape of the inverse shape of the ball end mill and the flat end mill can be calculated as described above, the sweep shape of the inverse shape of the round end mill can be calculated by combining them. For this reason, a method of calculating the sweep shape of the inverse shape of the ball end mill and the flat end mill will be described below. By combining these, the sweep shape of the inverse shape of the round end mill can also be calculated.

FIG. 5 is an explanatory diagram of a sweep shape by a ball end mill. FIG. 5A is a diagram illustrating an example of a spherical surface constituting a swept shape of a sphere in a cutting process using a ball end mill, and FIG. 5B is a diagram illustrating an example of a cylindrical shape. FIG. 5C shows an example of a thick plate shape. In the case of cutting with a ball end mill having a radius (r), the upper surface of the sweep shape corresponding to the tool reference surface is generated by movement of a hemispherical cutting edge at the upper end of the inverted shape of the ball end mill. Therefore, instead of the inverse shape of the tool, consider the calculation of the sweep shape when a sphere having the same radius as the cutting edge is slid so that the center always exists on the product surface. When the product has a polyhedral shape, the sweep shape of the sphere is the sum of the vertices, sides, and polygons of the polyhedron when the vertices, sides, and polygons are replaced with spherical, cylindrical, and thick plate shapes in the following procedure. [Vertex] Replace with a spherical surface having a radius (r) centered on the vertex (v) (see FIG. 5A). [Side] ... radius (r) with the side (e) as the central axis
(See FIG. 5B). [Polygon] Replace with a thick plate having a thickness (2r) centered on the polygon (f) (see FIG. 5C).

FIG. 6 is an explanatory diagram of a sweep shape by a flat end mill. FIG. 6A is a diagram showing an example of an oblique cylindrical shape constituting a swept shape of a disk in cutting by a flat end mill, and FIG. 6B is an example of a thick plate shape. FIG. In the case of cutting with a radius (r) flat end mill, the upper surface of the sweep shape corresponding to the tool reference surface is generated by movement of a disk-shaped cutting edge at the upper end of the inverse shape of the flat end mill. When the product has a polyhedral shape, the sweep shape of the disk is the sum of the sides and polygons of the polyhedron when the oblique cylindrical shape and the thick plate shape are replaced by the following procedure, respectively. [Side] ... given to the vertices at both ends of the side (e),
Replace with an oblique cylindrical shape connecting two horizontal disks of radius (r) (see FIG. 6 (a)). [Polygon]: A horizontal disk with a radius (r) is arranged at all vertices around the polygon (f), and the polygon is moved horizontally so that it contacts the outer circumference of all disks. Position. There are two such positions. Therefore, a thick plate shape corresponding to a region sandwiched between two polygons arranged at each location is generated, and the polygon (f) is replaced with this thick plate shape (see FIG. 6B).

Therefore, when a complicated curved surface shape is made into a polyhedron, the number of polygons often becomes tens of thousands to hundreds of thousands. Since the number of sides and vertices is also proportional to the number of polygons, in the calculation of the sweep shape by the above-described method, a set operation of an enormous number of spherical, cylindrical, and thick plate shapes is repeated. In the present invention, the inverse offset method focuses on the fact that only the upper surface of the sweep shape is finally required as the tool reference surface, and performs the following procedure to efficiently and efficiently perform the tool reference surface. Achieve stable calculations.

FIG. 7 is an explanatory view for obtaining a tool reference surface for ball end milling. In FIG. 7, in order to obtain a tool reference plane for ball end milling, the intersection of a spherical surface, a cylindrical shape, a thick plate shape constituting a swept shape of a sphere and a straight line parallel to the Z axis passing through the center of the lattice is shown. Investigating and selecting the uppermost intersection is shown. Similarly, FIG. 8 is an explanatory diagram for obtaining a tool reference surface for flat end milling. In FIG. 8, in order to obtain a tool reference plane for flat end milling, the intersection of the oblique cylindrical shape or the thick plate shape forming the swept shape of the disk and the straight line parallel to the Z axis passing through the center of the lattice is shown. Investigating and selecting the uppermost intersection is shown.

First, as shown in FIGS. 7 and 8, an orthogonal coordinate system serving as a reference for processing is given such that its Z axis coincides with the upward direction of the rotation axis of the ball end mill and the flat end mill. Next, on the XY plane of the reference coordinate system, X
An orthogonal grid parallel to the axis and the Y axis and equally spaced is generated so as to cover the projection of the sweep shape to be calculated on the XY plane. In both ball end milling and flat end milling, the projected shape of the sweep shape is equivalent to the projected shape of the product shape expanded by the radius of the end mill.Therefore, an orthogonal grid is formed so as to cover the expanded shape. You just need to generate it. The smaller the grid interval (W), the more precise the calculation becomes possible. However, the number of grids increases in proportion to the square of (1 / W), and the required storage capacity becomes enormous. Therefore, this value is determined based on a balance between required processing accuracy and available storage capacity. When calculating the tool reference plane, as an example, the grid interval is 50 to 200 μm.
In many cases, adjustment is made so that the total number of lattices becomes 1000 × 1000 or less. However, the present invention is not limited to this, and an appropriate interval and total number can be used.

For each grid, consider a straight line passing through the center and parallel to the Z axis, and examine the intersection of this straight line and all the shape elements constituting the sweep shape. For example, when calculating the tool reference plane for ball end milling, as shown in FIG. 7, a straight line passing through the center of each lattice, a spherical surface arranged at the vertex, a cylindrical shape arranged at the side, Examine the intersection of the slabs arranged in a square. Then, the uppermost intersection, that is, the intersection having the largest Z coordinate value is selected. On the other hand, when calculating the tool reference plane for flat end milling,
As shown in FIG. 8, the intersection of each straight line with the oblique cylindrical shape arranged on the side and the thick plate shape arranged on the polygon is examined, and the uppermost intersection is selected. When these processes are repeated for all grids, a dense point cloud covering the tool reference plane can be obtained. Since these point groups are arranged in a lattice, a polyhedron representing a tool reference plane can be calculated by appropriately selecting adjacent points and replacing them with polygons.

2. Use of Three-Dimensional Graphics Display Device In the inverse offset method, a straight line parallel to the Z-axis passing through the center of each grid and a shape element (a spherical surface arranged at a vertex, a It is necessary to repeat the calculation of the intersection of the placed cylinders and the like for all combinations of grids and shape elements. Therefore, a simple implementation method requires a great deal of processing time, and is not practical. In the present invention, this processing is speeded up by utilizing the hidden surface erasing function of the three-dimensional graphics display device.

FIG. 9 is an explanatory diagram of a hidden surface erased image of two cubes by using a depth buffer. In three-dimensional computer graphics, in order to generate an image in which “hidden surfaces” hidden by other surfaces and invisible to an observer are generated,
Use a depth buffer. This technique will be described by taking, as an example, a case where an image obtained by observing two cubes 201 and 202 arranged as shown in the drawing from the left side of the drawing is drawn on a screen by parallel projection.

Here, when the cubes 201 and 202 have a positional relationship as shown in the figure, a visible image from the observer's viewpoint 203 is considered. The frame buffer 204 is a secondary plane that projects the visible image at that time. Cube 201
And 202 are observed in the frame buffer 204 by parallel projection. As shown, points P ₃ and P ₂ on the surface of the cube 201 and points P ₁ and P ₀ on the surface of the cube 202 are represented by the same pixel 205 on the frame buffer 204. It should be noted that the X axis, Y axis, and Z axis in the figure each represent coordinates serving as a reference for processing. In three-dimensional computer graphics, a data structure called a depth buffer (or Z-buffer) is used to generate an image in which a hidden surface hidden by another surface among three-dimensional surfaces and invisible to an observer is eliminated. Is used. By using this depth buffer, the viewpoint 203
And closest point P ₃ is selected in the frame buffer 204, color pattern pattern information such as that corresponding to the point P ₃ is given to the pixels 205. For example, if the corresponding information is a color, the frame buffer 204 is dyed in the corresponding color.

Next, a description will be given of a specific processing technique for drawing an image in which the hidden surfaces of the two cubes 201 and 202 have been erased into the frame buffer 204 by parallel projection. In the following description, as an example, a case where a color corresponding to each surface is given to each pixel will be described. As shown in the drawing, a coordinate system serving as a reference for processing is determined at an arbitrary position on the frame buffer 204, and the direction of the Z axis is determined so as to be opposite to the direction of the viewpoint 203 of the observer. Also, frame buffer 2
Prepare an array called a depth buffer consisting of elements corresponding to each pixel of 04 in a one-to-one correspondence. Here, a sufficiently small numerical value is given to each element as an initial value, and each polygon forming the cube is , Are sequentially drawn on the frame buffer 204 by parallel projection. At this time, a Z-axis coordinate value of a point on a polygon (a square) projected to each pixel is calculated and compared with a value of a depth buffer element corresponding to the pixel (this is called a depth value). When the Z-axis coordinate value is larger than the depth value, the pixel is dyed with the color of a point on the surface, and the Z-axis coordinate value is recorded as a new depth value. This series of processing is called depth buffer processing. When such processing is repeated for all surfaces, the image from which the hidden surface has been erased is consequently stored in the frame buffer 204.
Will be drawn.

If the downward direction of the rotation axis of the ball end mill is defined as the direction of the line of sight of the observer, and the pixels on the screen are associated with the orthogonal grids on the XY plane, the following is obtained: "All grids shown in FIGS. Calculate the intersection of the straight line parallel to the Z axis passing through the center and the uppermost surface of the sweep shape of a sphere or a disk ”, and“ All the shape elements (spherical surfaces) constituting the sweep shape shown in FIG. , Using a depth buffer to draw an image obtained by projecting a parallel projection of a cylindrical shape, a thick plate shape, and the like) using a depth buffer. When all the shape elements have been drawn, the Z coordinate value of the uppermost intersection of the corresponding straight line and the sweep shape is stored as a depth value in each element of the depth buffer, and thus represents the tool reference plane. Point clouds can be easily obtained.

Many three-dimensional graphics displays are:
It has the function of directly executing the hidden surface elimination processing of a polyhedron using a depth buffer by hardware. Therefore, an image obtained by appropriately approximating a spherical surface or a cylindrical shape constituting a sweeping shape to a polyhedron, and parallel-projecting the obtained polygon group into 3 is obtained.
By drawing using a three-dimensional graphics display device,
Tool reference plane can be calculated at high speed. Since the three-dimensional graphics display device is a semiconductor device that is expected to have a higher speed in the future, a higher speed can be expected in the hidden surface erasing process of the polyhedron using the depth buffer.

3. Removal of Unnecessary Parts Many parts of the mold have a smooth curved surface.
When such a shape is made into a polyhedron, most polygons covering its surface are connected to other adjacent polygons in a very gentle manner. Therefore, in order to calculate the tool reference plane for ball end milling, if a spherical surface, a cylindrical shape, and a thick plate shape are arranged at each of the vertices, sides, and polygons of the polyhedron, most parts of each cylindrical shape are Since it enters the inside of the thick plate shape arranged on the left and right, it cannot be the upper surface of the sweep shape of the sphere. Similarly, the sphere located at the apex of the polyhedron is irrelevant to the top surface of the sweep shape, since most of the sphere enters the interior of the cylinder located at the side connected to the apex.

Therefore, before the spherical or cylindrical shape is converted into a polyhedron, a portion which has entered the adjacent cylindrical shape or thick plate shape and cannot be the upper surface of the sweep shape is removed. Since the number of polygons of the approximate spherical surface and the approximate cylindrical surface is almost proportional to the surface area, the number of polygons for performing hidden surface elimination processing can be significantly reduced by removing unnecessary curved surface parts and converting them to polyhedrons. As a result, the calculation of the tool reference plane can be further speeded up.

FIG. 10 is a diagram showing a combination of a cylindrical shape and a thick plate shape. 10, as an example, shown a cylindrical C _i arranged on a side with a polyhedron, the state of the thick plate-shaped P _j and P _k which are arranged in two polygons to be connected to the left and right of the side FIG. As shown, the most part of the cylindrical C _i intrudes into the interior of the plank-shaped P _j and P _k. Therefore, the number of polygons is reduced by removing these portions from the cylindrical shape and making only the remaining elongated wedge shape (white portion in the figure) polyhedral.

FIG. 11 is a diagram showing a combination of a spherical surface and a cylindrical shape. FIG. 11A is a diagram showing a state of a spherical surface S _i arranged at a certain vertex and cylindrical shapes C _j , C _k , and C ₁ arranged on three sides connected to this vertex. As in the case of cylindrical, most part of the sphere S _i is because it enters the interior of the cylindrical _{C j, C k, C l} , is independent of the upper surface of the sweep shape. Therefore, only the remaining shape obtained by removing these portions from the spherical surface (the triangular portion surrounded by a thick line in the center of the figure) needs to be polyhedralized.

When a number of sides are connected to a vertex, the calculation of the remaining shape becomes considerably troublesome.
Therefore, in the present invention, as shown in FIG. 11 (b), the two sides that are most smoothly connected to the vertices are selected, and only the part that enters the inside of the cylinder corresponding to these two sides is removed from the spherical surface. This saves time and effort in calculations. In other words, for example, only the portion that enters into the cylindrical shapes C _j and C _k is removed from the spherical surface S _i . The end faces of the cylinders C _j and C _k are
Since passing through the center of the spherical surface S _i, when the removal of these portions, so that the shaped like a "watermelon" remains.
When calculating the tool reference plane, the “watermelon” shape may be rendered as a polyhedron.

On the other hand, when calculating the tool reference plane for flat end milling, the number of polygons can be reduced by a substantially similar method. If a slanted cylinder and a thick plate are placed on each of the sides and polygons of the polyhedron, most of the slanted cylinder will enter the inside of the thick plate placed on the left and right sides of the polygon. It cannot be the top. FIG.
FIG. 4 is a diagram showing a combination of an oblique cylindrical shape and a thick plate shape. FIG. 12 shows an oblique cylinder C arranged on one side of a polyhedron.
and _i, is a diagram showing a state of two plank shape arranged in a polygon P _j and P _k which connects the left and right of the side. Most parts of the oblique cylinder C _i consist of the adjacent plank shapes P _j and P
_k . Therefore, these parts are removed, and only the remaining “oblique wedge shape” (white part in the figure) is made into a polyhedron, thereby reducing the number of polygons to be drawn.

4. FIG. 13 is an explanatory diagram of a technique for polyhedralizing the shape after removing unnecessary portions. FIG. 13A shows a wedge-shaped polyhedralization method, FIG. 13B shows a watermelon-shaped polyhedralization method, and FIG.
FIG. 3 (c) shows a polyhedron forming method of oblique wedge shape. As shown, obtained by removing unnecessary parts,
The wedge shape, the watermelon shape, and the oblique wedge shape are polyhedralized by the following procedure. (1) The remaining wedge shape obtained by removing unnecessary portions from the cylindrical shape is approximated by a polyhedron as a shape in which rectangles having the same width are connected in an armor shape (see FIG. 13A). (2) The remaining watermelon shape from which unnecessary parts have been removed from the spherical surface is
By dividing the spherical portion into several equal-width strips and further dividing them at equal intervals, a polyhedron approximation is made as a set of small quadrilaterals (triangles only at both ends of the strip) (FIG. 13).
(B)). (3) The remaining oblique wedge shape obtained by removing unnecessary portions from the oblique cylindrical shape is approximated to a polyhedron by connecting elongated rectangles, as in the case of making the wedge shape polyhedral (FIG. 13).
(C)).

Of the polygons thus obtained, for example, a polygon whose normal direction is downward cannot be the upper surface of the sweep shape. Therefore, the processing time can be further reduced by excluding these downward polygons from the target of the hidden surface erasing processing. In the polyhedral method described above, the approximation accuracy of the curved surface is determined by the width of the rectangular piece forming the wedge shape and the maximum size (length d in FIG. 13) of the quadrilateral forming the watermelon shape. When the length d is increased, the number of polygons of the approximated curved surface is reduced, but the shape error is increased, and the accuracy of the obtained tool reference surface is reduced. Here, assuming that the allowable amount of error due to the polyhedralization is ε, for example, the length d needs to satisfy the following inequality (where r represents the radius of a spherical surface or a cylindrical shape). d ² <8rε

In the calculation of the tool reference plane, it is sufficient if the allowable amount ε of the approximation error is suppressed to about 0.001 mm. Therefore, when the radius r of the spherical or cylindrical shape is 1.0 mm, the length d is 0.1 mm or less. What is necessary is just to make a polyhedron so that it may become.

5. Hardware Configuration FIG. 14 is a configuration diagram of hardware according to the present invention. The hardware includes a processing unit (CPU) 1 as a central processing unit, an input unit 2 for inputting data, a storage unit 3 for storing input data, an output unit 4, and a three-dimensional graphics display unit. And 5. In addition, CPU1,
The input unit 2, the storage unit 3, the output unit 4, and the three-dimensional graphics display unit 5 are connected by appropriate connection means such as a star or a bus.

The three-dimensional graphics display unit 5 is a hardware device that generates the above-described hidden surface erasure image by using a depth buffer. The three-dimensional graphics display unit 5 can perform high-speed depth buffer processing by hardware processing. In addition, the three-dimensional graphics display unit 5 is configured as, for example, a board, a card, or another device, and may be configured integrally with the CPU 1 or the like, or may be configured separately. The output unit 4 is a device that displays an image of hidden surface removal generated on the three-dimensional graphics display unit 5 and drawn on the frame buffer on a display or outputs the image to another device. The output unit 4
Can also be configured to be directly connected to the bus.

6. Processing Algorithm Flow FIG. 15 is a flowchart (1) of a procedure for calculating a tool reference plane according to the present invention. First, a polyhedral model of a workpiece (die product) and shape data of a cutting tool (for example, a ball end mill or a flat end mill) required for calculating a tool reference plane are input (S).
100). Next, an orthogonal coordinate system serving as a reference for processing is given so that the Z axis thereof coincides with the upward direction of the rotation axis of the ball end mill, and the X coordinate is set on the XY plane of the reference coordinate system.
An orthogonal lattice parallel to the Y axis and the Y axis is
A projection graphic on the Y plane is generated so as to cover the shape expanded by the tool radius (S101). If it is desired to calculate only the tool reference plane relating to a part of the product shape with particularly high accuracy, an orthogonal grid is generated so as to cover only the projected figure on the XY plane of the portion desired to be calculated with high accuracy (S102). )
(See below).

When a ball end mill is used as a cutting tool, first, a sphere having the same radius as the cutting edge is placed at the center (ie, at the center).
Consider the calculation of the sweep shape when the tool is moved vertically and horizontally while keeping the tool reference point always on the product surface. This shape is a set sum of shapes obtained by replacing the vertices, sides, and polygons of the object model with spherical, cylindrical, and thick plate shapes, respectively (S103). Almost all of the spherical shape and the cylindrical shape constituting the sweep shape enter the inside of the adjacent cylindrical shape or thick plate shape, and cannot be the upper surface of the sweep shape. Therefore, from each spherical surface or cylindrical shape, a portion that enters the inside of the adjacent cylindrical shape or thick plate shape is removed, and a watermelon shape and a wedge shape are generated (S104). In addition, watermelon shape,
The wedge shape and the thick plate shape are made polyhedral (S105).

On the other hand, when a flat end mill is used as a cutting tool, a horizontal disk having the same radius as the cutting edge is moved vertically and horizontally while maintaining the center (ie, the tool reference point) always on the product surface. Consider the calculation of the sweep shape when This shape is a set sum of shapes obtained by replacing the sides and polygons of the object model with oblique cylinders and thick plates, respectively (S106). Most of the oblique cylindrical shape is
It penetrates the inside of the adjacent plank shape and cannot be the upper surface of the sweep shape. Therefore, from each of the oblique cylindrical shapes, a portion entering the inside of the adjacent thick plate shape is removed, and an oblique wedge shape is generated (S107). Further, the oblique wedge shape and the thick plate shape are made polyhedral (S108). In addition, in the case where only one of the ball end mill and the flat end mill is used, the determination after step S102 is made in step S102.
Processing of 103 to S105 or steps S106 to S108
May be included.

Next, among the polygons that cover the obtained polyhedron group, only those whose normal direction is upward can be the upper surface of the sweep shape. Then, such an upward polygon is selected, and the necessary or all polygon data is sent to the three-dimensional graphics display device (S10).
9). From here, hardware processing by the three-dimensional graphic display device is started. That is, a depth buffer including elements corresponding to the orthogonal lattice on the XY plane on a one-to-one basis is prepared. An image obtained by observing the selected polygon group from the positive direction of the Z axis is drawn on the screen by parallel projection.
The three-dimensional graphics display device updates the contents of the depth buffer according to the hidden surface erasing procedure (S11).
0). Next, when all the polygons have been drawn, each depth value of the depth buffer is set to Z passing through the corresponding grid center.
It represents the Z coordinate value of the uppermost intersection of the sweep shape of a straight line parallel to the axis and a sphere or a horizontal disk. The necessary or all of the obtained depth values are passed to the processing on the software side (S111). Note that a display unit provided in the three-dimensional graphics display device can display an image such as a color, a pattern, or a pattern indicating the state of hardware processing.

Thus, the processing by the software is started again. Based on the position information of the orthogonal grid and the depth value, a dense point group covering the tool reference plane is generated (S11).
2). Since the point groups are arranged in a lattice, a polyhedron representing a tool reference plane is generated by appropriately selecting adjacent points and replacing them with polygons (S113). The obtained tool reference plane is sent to CAM software for generating a tool path (S114). The CAM software executes appropriate processing such as graphic display or the like, desired machining simulation, actual machining, etc., based on the obtained tool reference surface.

Here, step S102 will be described. The number of orthogonal lattices on the XY plane used in the inverse offset method is about 1000 × 1000. When such a grid is applied to the entire workpiece to calculate the tool reference plane, if a part of the workpiece has a rapidly changing shape, a sufficiently accurate tool reference plane is obtained for that part. May not be possible. Therefore, when high-precision calculation is required, an orthogonal grid is generated so as to cover only a projected figure of a partial shape in which such a shape change is remarkable, and a tool reference plane is calculated. 1000x1000 for very few shapes
Therefore, a more accurate tool reference plane can be obtained for this portion.

FIG. 16A shows a state in which a grid is applied to the entire workpiece and the tool reference plane is calculated by the inverse offset method. In this case, even if there is a portion where the shape changes rapidly, only a small number of grids can be applied to this portion, so that the accuracy of the obtained tool reference surface becomes insufficient. FIG. 16B shows a state in which an orthogonal grid is generated so as to cover only the projected figure of the portion where the shape change is drastic, and the tool reference plane is calculated. It can be seen that a more accurate tool reference plane can be obtained for this part.

Here, a case where a round end mill is used as a cutting tool will be described. FIG. 17 is a flowchart (2) of a procedure for calculating a tool reference plane according to the present invention. Here, for convenience of explanation, as shown in FIG. 4, the radius of the shaft of the round end mill was R, and the radius of the annular cutting edge was r. First, a ball end mill having an annular cutting edge radius r of a round end mill is input as information relating to a tool shape (S201), and a tool reference plane calculation method is executed according to steps S102 to S113 in the above-described flowchart (S203). ). Further, the polyhedron model of the tool reference plane obtained in step S113 is input as information on the polyhedron model of the object to be machined in step S100 (S205), and an annular cut is obtained from the radius R of the shaft of the round end mill. A flat end mill having a radius Rr obtained by subtracting the radius r of the blade is input as information on the tool shape (S20).
7) Again, step S102 in the above-described flowchart
According to steps S114 to S114, a tool reference plane calculation method is executed (S209). Thereby, a tool reference plane when a round end mill is used as a cutting tool can be obtained.

The tool reference plane calculation method of the present invention can be provided by a computer-readable recording medium storing a tool reference plane calculation program or a tool reference plane calculation program product.

7. Experiment and Comparison Here, in order to verify the effectiveness of the method invented, a program for calculating a tool reference plane using the depth buffer processing function of the three-dimensional graphics display device was created, and a calculation experiment was performed. In the experiment, the number of grids was 1000 × 1
An orthogonal lattice adjusted to 000 was used. The computer used was a workstation with a main memory of 486 MB using Pentium III (450 MHZ) as a CPU. This workstation has a 3 called Cobalt
Dedicated hardware for dimensional graphics display is provided. The shape of the polygon to be drawn is OpenGL
When a program is described in accordance with the specifications of a library called (Open Graphics Library), a compiler automatically generates machine language code for executing the depth buffer processing by hardware.

FIG. 18 shows a polyhedron composed of 30,528 polygons. FIG. 19 shows the number of polygons 30,528.
The result of calculating the tool reference plane for cutting a polyhedron using a ball end mill with a radius of 5 mm is shown.
The time required for this calculation was 1.84 seconds. FIG. 20 shows a state in which a tool path having a total length of about 40,000 mm that reciprocates so that the cutting edge slides on the surface of the polyhedron based on the calculation result of the tool reference plane, and FIG. 21 shows the path. The result of performing the simulation of the cutting process based on this is shown. Since the calculation of the tool reference plane has been completed, the calculation of the tool path ends instantaneously. From the results of the machining simulation, it can be seen that an appropriate tool path without cutting is generated.

FIG. 22 shows the result of calculating a tool reference plane for cutting a polyhedron having 30,528 polygons using a flat end mill having a radius of 5 mm. The time required for this calculation was 1.30 seconds. FIG. 23 shows a state where a tool path is generated based on the calculation result of the tool reference plane, and FIG. 24 shows a result obtained by performing a cutting simulation based on the path. From the simulation results, it can be seen that an appropriate route is also generated in this example.

Next, a program in which the calculation of the tool reference plane by the reverse offset method is entirely performed by software,
A program was prepared using the depth buffer processing function of the three-dimensional graphics display device, and the time required for processing under the same conditions was compared. In addition, the program which processes everything by software is also devised so as not to uselessly calculate by making full use of methods such as box check. The specifications of the computer used in the experiment are the same as those described above.

FIG. 24 is a diagram showing the result of comparing the time required to calculate the tool reference plane for ball end milling. FIG. 24A shows the result of a calculation experiment performed using a simple polyhedron having 1,908 polygons. The first column shows the radius of the ball end mill used. The second column shows the processing time when all necessary calculations are performed by software, and the third column shows the processing time when the same calculations are performed using the function of the three-dimensional graphics display device. . The numerical values in the fourth column represent the ratio of these processing times.

FIGS. 24 (b) and 24 (c) show the same experiment with 23,184 polygons and 30,52 polygons, respectively.
Figure 8 shows the results of applying to eight relatively complex polyhedra. The case of cutting a polyhedron having 30,528 polygons with a tool having a radius of 5 mm corresponds to FIGS.
As a result, it is understood that the speed can be increased up to about 40 times at the maximum, and the degree of the speed increase becomes more remarkable when a tool having a larger radius is applied to a complicated polyhedron.

FIG. 25 is a view showing the result of the same comparative experiment performed on the calculation of the tool reference plane for flat end milling. The case of cutting a polyhedron having 30,528 polygons with a tool having a radius of 5 mm corresponds to FIGS. 18 and 22. As a result, in the case of flat end milling, as in the case of ball end milling,
It can be seen that the higher the speed of the tool, the greater the speed of the tool applied to a complex polyhedron.

In the present invention, the tool is not limited to a ball end mill, a flat end mill and a round end mill, but may be any other appropriate tool such as a cutting tool, a molding tool, and the like. Not limited to this, it is also possible to use a tool having an appropriate shape such as an elliptical surface, a polygonal surface, or an uneven surface depending on the tip shape of the tool. In addition, the present invention is not limited to molds, and the present invention can be applied to various workpieces made of various materials such as plastic and metal. In the above description, the necessary or all depth data, the necessary or all polygon data are mainly input or output to the processing unit and the three-dimensional graphics display unit. The invention is not limited to this, and some data may be exchanged. Furthermore, although a polygon has been described as an example of a polyhedron and a polygon as an approximation of the surface, the present invention is not limited to this, and an appropriate polygon can be used.

[0060]

According to the present invention, a tool reference plane can be calculated at high speed by using a three-dimensional graphics display device. Further, according to the present invention, the tool path generated based on the calculation result of the tool reference plane can be calculated instantaneously.

[Brief description of the drawings]

FIG. 1 (a) shows a tool reference surface drawn by a reference point of a ball end mill sliding on a product surface, and FIG. 1 (b) shows a sweep shape when a reference point of an opposite shape of the tool slides on the product surface. FIG.

FIG. 2 (a) shows a tool reference surface drawn by a reference point of a flat end mill sliding on a product surface, and FIG. 2 (b) shows a sweep shape when a reference point of an opposite shape of the tool slides on the product surface. FIG.

FIG. 3 (a) shows a tool reference plane drawn by a reference point of a round end mill sliding on a product surface, and FIG. 3 (b) shows a sweep shape when a reference point of an inverted shape of the tool slides on the product surface. FIG.

FIG. 4 (a) shows a state where a reverse shape of a flat end mill having a radius (Rr) is slid along a surface of a reverse shape of a ball end mill having a radius (r), and FIG. FIG. 9 is an explanatory diagram showing a result of calculating a sweep shape of a reverse shape of a ball end mill having a radius (r) and sliding the reverse shape of a flat end mill having a radius (Rr) along an upper surface thereof;

5 (a) shows a spherical surface constituting a swept shape of a sphere in cutting by a ball end mill, FIG. 5 (b) shows a cylindrical shape, and FIG. 5 (c) also shows a thick plate shape. The figure which shows an example.

FIG. 6A is a diagram illustrating an oblique cylindrical shape constituting a swept shape of a disk in a cutting process using a flat end mill, and FIG. 6B is a diagram illustrating an example of a thick plate shape.

FIG. 7 In order to obtain a tool reference surface for ball end milling, the intersection of a spherical surface, a cylindrical shape, and a thick plate shape constituting a swept shape of a sphere and a straight line parallel to the Z-axis passing through the center of the lattice is examined. The figure which shows a mode that the uppermost intersection is selected.

FIG. 8 In order to obtain a tool reference plane for flat end milling, the intersection of a slanted cylinder or a thick plate forming a swept disk shape and a straight line parallel to the Z-axis passing through the center of the grid is examined. The figure which shows a mode that the uppermost intersection is selected.

FIG. 9 is an explanatory diagram of a hidden surface erased image of two cubes using a depth buffer.

FIG. 10 shows a cylindrical C _i arranged on one side of the polyhedron,
The figure which shows the mode of the thick plate shape _Pj and _Pk arrange | positioned at two polygons connected to the right and left of the edge.

FIG. 11A shows a spherical surface S arranged at a certain vertex.
_i and the states of the cylindrical shapes C _j , C _k , and C ₁ arranged on three sides connected to the apex, and (b) shows the smoothest connection to the apex of (a). The figure which shows a mode that a side is selected and only the part which has entered into the inside of the cylindrical shape corresponding to these two sides from a spherical surface is removed.

FIG. 12 shows an oblique cylinder C arranged on one side of a polyhedron
_The figure which shows the aspect of _i and thick board shape _Pj and _Pk arrange | positioned at two polygons connected to the right and left of the edge.

13A shows a wedge-shaped polyhedron technique after removing unnecessary portions, FIG. 13B shows a watermelon-shaped polyhedron technique, and FIG. 13C shows an oblique wedge-shaped polyhedron. FIG.

FIG. 14 is a configuration diagram of hardware according to the present invention.

FIG. 15 is a flowchart (1) showing a procedure for calculating a tool reference plane according to the present invention.

FIG. 16 (a) shows a state in which a tool reference plane is calculated by applying a grid to the entire object to be processed, and FIG.
The figure which shows a mode that a grid is applied only to the part in which a shape changes rapidly among workpieces, and a highly accurate tool reference plane is calculated.

FIG. 17 is a flowchart (2) showing a procedure for calculating a tool reference plane according to the present invention.

FIG. 18 is a diagram showing a polyhedron composed of 30,528 polygons.

FIG. 19 shows a polyhedron having 30,528 polygons having a radius of 5
The figure which shows the result of having calculated the tool reference surface in order to cut using a ball end mill of mm.

20 is based on the calculation result of the tool reference plane in FIG. 19;
A total length of about 40, which reciprocates as the cutting blade slides on the surface of the polyhedron
The figure which shows a mode that the tool path | route of 000mm was produced | generated.

FIG. 21 is a diagram showing a result obtained by performing a simulation of cutting based on the path in FIG. 20;

FIG. 22 shows a polyhedron having 30,528 polygons having a radius of 5
mm using a flat end mill,
The figure which shows the result of having calculated the tool reference plane.

FIG. 23 is a diagram illustrating a state in which a tool path is generated based on the calculation result of the tool reference plane in FIG. 22;

FIG. 24 is a diagram showing a result obtained by performing a simulation of cutting based on the route in FIG. 23;

FIG. 25 (a) shows the results of a calculation experiment on a polyhedron having 1,908 polygons by ball end milling, and FIG. 25 (b) shows the results of a calculation experiment on a polyhedron having 23,184 polygons. (C) is a diagram showing the result of a calculation experiment on a polyhedron having 30,528 polygons.

26A shows the results of a calculation experiment on a polyhedron having 1,908 polygons by flat end milling, and FIG. 26B shows the results of a calculation experiment on a polyhedron having 23,184 polygons. (C) is a diagram showing the result of a calculation experiment on a polyhedron having 30,528 polygons.

FIG. 27 (a) shows the position of a ball end mill used in die machining and its tool reference point, FIG. 27 (b) shows the same of the flat end mill and its tool reference point,
(C) is an explanatory view similarly showing the position of the round end mill and its tool reference point.

FIG. 28 is a diagram showing an example of shaving in mold processing.

[Explanation of symbols]

 1 processing unit 2 input unit 3 storage unit 4 output unit 5 3D graphics display unit

Claims (11)

[Claims] 1. A tool reference plane calculation method for generating a tool reference plane inflated by an inverse shape of a tool when processing a workpiece by moving a tool attached to a numerically controlled machine tool along a path. Inputting information on the polyhedron model and the tool shape of the object to be processed; and, based on the information on the polyhedron model and the tool shape of the object to be processed inputted by the inputting step, a first vertex corresponding to the vertex portion. By arranging the second shape corresponding to the shape and the side portion and the third shape corresponding to the polygonal portion, or by arranging the second shape and the third shape, the reference point representing the center of the tool is processed. Generating a sweep shape when moving along the surface of the target object, based on the shape generated by the generating step,
A step of removing a portion that enters the interior of each of the adjacent shapes; a step of polyhedralizing a partial shape of the shape obtained by the step of removing; and a polyhedron obtained by the step of polyhedralization Generating polygon data by selecting only polygons whose normal direction is a predetermined direction based on the above, and converting the polygon data obtained by the polygon data generating step into a three-dimensional graphics display unit. And receiving a depth value representing the height of the uppermost surface of the sweep shape obtained by hardware processing by the three-dimensional graphics display unit. Based on the depth value obtained by the receiving step,
A step of obtaining a grid-like point group covering the upper surface of the sweep shape; and, based on the point group obtained by the step of obtaining the point group,
Obtaining a tool reference plane by selecting adjacent points and replacing them with a polygon. 2. The method according to claim 1, wherein at least a part of the shape of the product to be processed is
2. The tool reference plane calculation method according to claim 1, further comprising the step of generating an orthogonal grid so as to cover only a part of the projected figure in order to perform calculation with high accuracy. 3. The tool reference plane calculation method according to claim 1, further comprising a step of obtaining a tool path based on the obtained tool reference plane. 4. The tool reference plane calculation method according to claim 1, further comprising a step of displaying a tool reference plane and / or a tool path. 5. The input step includes inputting information about a ball end mill as information relating to a tool shape. The step of generating a sweep shape includes forming a sweep shape of a sphere at vertices, sides, and polygons of a polyhedral model. By arranging spherical, cylindrical and thick plate shapes, a sweep shape is generated by a sphere having the same radius as the cutting edge of the ball end mill.The shape after being removed in the removing step is a watermelon shape and a wedge. The tool reference plane calculation method according to any one of claims 1 to 4, wherein the tool reference plane calculation method is a shape. 6. The inputting step includes inputting information about a flat end mill as information relating to a tool shape, and the step of generating a sweeping shape comprises forming a sweeping shape of a disk into sides and polygons of a polyhedral model. By arranging the oblique cylindrical shape and the thick plate shape, a sweep shape is generated by a disk having the same radius as the cutting edge of the flat end mill, and the shape after being removed in the removing step is an oblique wedge shape. The tool reference plane calculation method according to claim 1, wherein: 7. The method for calculating a tool reference plane according to claim 1, wherein in the inputting step, information on a tool shape of a ball end mill having an annular end radius of the round end mill is input. To obtain a tool reference plane, and further, in the inputting step, input the obtained tool reference plane as information regarding a polyhedron model,
5. The flat end mill having a radius obtained by subtracting the end radius from the radius of the shaft of the round end mill is input as information relating to the tool shape, and again, the information is input.
The tool reference plane calculation method according to any one of claims 1 to 6, wherein a tool reference plane of the round end mill is obtained by executing the tool reference plane calculation method according to any one of (1) to (6). 8. A tool reference plane calculation program for generating a tool reference plane inflated by an inverse shape of a tool when processing a workpiece by moving a tool attached to a numerically controlled machine tool along a path. Inputting information on a polyhedron model and a tool shape of the object to be processed, based on the information on the polyhedron model and the tool shape of the object input by the inputting step. By arranging the first shape corresponding to the vertex portion and the second shape corresponding to the side portion and the third shape corresponding to the polygonal portion, or by arranging the second shape and the third shape, Generating a sweep shape when the reference point representing the center of the tool moves along the surface of the workpiece; and a shape generated by the generating step. On the basis,
Removing a portion that has entered the inside of each adjacent shape; polyhedralizing a partial shape of the shape obtained by the removing step; and polyhedron obtained by the polyhedralizing step Generating polygon data by selecting only polygons whose normal direction is a predetermined direction based on the above, and displaying the polygon data obtained by the step of generating the polygon data on a three-dimensional graphics display unit. And receiving a depth value representing the height of the uppermost surface of the sweep shape obtained by hardware processing by the three-dimensional graphics display unit. Based on the depth value obtained by the receiving step,
Obtaining a grid-like point group covering the upper surface of the sweep shape; and
Obtaining a tool reference plane by selecting adjacent points and replacing the selected points with polygons. A computer-readable recording medium recording a tool reference plane calculation program. 9. A tool reference plane calculation device for generating a tool reference plane inflated by an inverse shape of a tool when processing a workpiece by moving a tool attached to a numerically controlled machine tool along a path. An input unit for inputting information on the polyhedron model of the workpiece and the tool shape; and a processing unit for calculating a tool reference plane, wherein the processing unit comprises: a polyhedron model of the workpiece input by the input unit. And a third shape corresponding to a polygonal portion and a first shape corresponding to a vertex portion and a third shape corresponding to a polygonal portion, or the second shape and third By arranging the shape, a means for generating a sweep shape when the reference point representing the center of the tool moves along the surface of the object to be processed, based on the shape generated by the generating means, Means for removing a portion that has entered the interior of each shape, a means for polyhedralizing a partial shape of the shape obtained by the means for removing, and a polyhedron obtained by the means for polyhedralization. ,
Means for generating polygon data by selecting only polygons whose normal direction is a predetermined direction, and means for providing the polygon data obtained by the means for generating polygon data to a three-dimensional graphics display unit And 3
Means for receiving a depth value representing the height of the uppermost surface of the sweep shape obtained by hardware processing by the three-dimensional graphics display unit; and a lattice shape covering the upper surface of the sweep shape based on the depth value obtained by the receiving means. Tool reference plane calculation comprising: a means for obtaining a point group; and a means for obtaining a tool reference plane by selecting adjacent points and replacing them with a polygon based on the point group obtained by the means for obtaining the point group. apparatus. 10. A hidden surface elimination process is performed based on the polygon data obtained by the providing unit of the processing unit, and a depth value of each element of a depth buffer is updated or stored.
Means for executing a depth buffering process; means for obtaining a depth value representing the height of the uppermost surface of the sweep shape stored in each element based on the depth buffer stored by the means for executing the depth buffering process; The tool reference plane calculation device according to claim 9, further comprising: a three-dimensional graphic display unit having means for outputting a depth value obtained by means for obtaining a depth value to the processing unit. 11. The tool reference plane calculation device according to claim 9, further comprising means for displaying or outputting a tool reference plane, a tool machining state, or a tool machining simulation state.