JP2003256012A - Tool path plane calculating method, tool path plane calculating program and recording medium recording tool path plane calculating program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To rapidly and accurately calculate a tool path plane by using a three- dimensional graphics display device. <P>SOLUTION: In a processing part, polyhedral model information of a workpiece and tool shape information are inputted (S300), and each shape element composing a sweep shape of a reverse tool with respect to each element of a polyhedral model is arranged (S305 and S306). The processing part stores an ID number, color information and geometric information with respect to each arranged shape element in a storing part (S307 and S308), and it determines subdivided point sequence data of a cross sectional line of an uppermost plane while shifting positions of arranged shape elements in x-axis and y-axis directions by predetermined distances by using a hidden- surface removal process of graphics hardware on the basis of the shape elements composing the sweep shape of the reverse tool (S310 and onward). The processing part detects a bending point of the cross sectional line on the basis of the pieces of determined adjacent point sequence data, and it inserts the bending point into the point sequence data of the cross sectional line. The processing part divides a space into accumulation of cubes, and it determines the uppermost plane of the sweep shape by a marching cube method. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a tool path calculation method, a computer-readable recording medium recording a tool path calculation program, and a tool path calculation device, and more particularly to a tool path attached to a numerically controlled machine tool. A computer-readable record of a tool path calculation method that records a tool path surface calculation program that generates a tool path surface (tool reference surface) that is expanded by the inverse shape of the tool when moving along a workpiece Regarding the medium.

[0002]

2. Description of the Related Art Molds used for manufacturing plastics and die-cast products are NC (N
It is manufactured by a cutting process. Since it is often carved deeply in mold processing,
It is common to use a machine tool with three-axis control that is excellent in rigidity. In NC cutting, the cutting tool repeatedly performs a huge number of minute linear movements to gradually remove unnecessary portions from the blank. Calculation of a complicated tool path requires several tens of minutes of processing time even if a high-speed computer is used, and thus there is a demand for speeding up the calculation. When calculating the tool path,
It is necessary to pay attention to a problem called a gouge in which a tool cuts into the inside of a mold.

FIG. 29 is an explanatory view showing an example of shaving in die machining, in which the radius of curvature of the die surface is smaller than the radius of a cutting tool (for example, a ball end mill). Shows an example. That is, the ball end mill that moves from the left to the right in the figure while maintaining contact with the product surface is in the part where the radius of curvature of the die surface is smaller than the tool radius (the gouging area shown by the diagonal lines in the figure). However, if the contact with the gouging region is missed, it will be cut into the inside of the mold product as it is.
Most commercially available tool path calculation programs spend most of their processing time to prevent gouge. The problem of gouge can be completely solved by generating a tool path surface (tool reference surface) in which the surface of the mold is inflated by the inverse shape of the cutting tool, and generating a path so that the tool always moves above the tool path surface.
The present invention relates to a computer program for calculating this tool path surface (tool reference surface) precisely and at high speed. Using this technique, it becomes possible to calculate a tool path for machining a complicated mold in a very short time.

[0004]

The tool path surface corresponds to the upper surface of the swept shape when the reverse shape of the tool is slid vertically and horizontally along the surface of the mold. In a strict modeling technique of a solid shape such as CSG or boundary representation method, a procedure for obtaining a swept shape becomes very complicated. Therefore, in the field of NC cutting, the reverse offset method, which approximately calculates the upper surface of the sweep shape, is often used. In this method, a coordinate system in which the z-axis is the rotation axis direction of the tool is considered, and a sufficiently fine orthogonal grid is prepared on the xy plane. Then, a straight line parallel to the z-axis is extended from each grid point, and the intersection with the uppermost surface of the sweep shape is calculated to obtain a dense point cloud covering the upper surface of the sweep shape. Finally, a polyhedron representing the tool path surface is generated by interpolating the gap between the point groups with a polygon. The inverse offset method is
Since the processing is simple, it is easy to program and the calculation is stable. Many tool path calculation methods using this technology have already been proposed, and practical systems have also been developed. The calculation method using the graphics hardware, which was invented by us, is particularly fast, and a plurality of vendors have begun commercialization of this technology (JP 2001-24).
2919 etc.).

In general, many dies have complicated indentations. The wall portion having such a shape can be beautifully finished by moving the cutting tool along a contour line path. In the inverse offset method, since the point cloud covering the tool path surface is calculated based on the grid on the xy plane, the point cloud is arranged at uniform intervals in the x-axis direction and the y-axis direction. Therefore, in a wall shape in which the tool path surface greatly changes in the z-axis direction, the distance between adjacent points increases, and when a polyhedron is generated from the point group, an unacceptably large error may occur in the calculation result. Further, since the shape changes in the x-axis direction and the y-axis direction of the vertical wall are recorded discretely at each lattice interval,
If the polyhedron is made by a simple method, an unnatural bending may occur on the tool path surface.

The former problem can be solved by changing the lattice spacing to a sufficiently small one. However, if the interval is set to 1 / n, the total number of lattices is increased n ² times, and this time, a load is added to the processing labor and the storage capacity. There is also a method of selectively refining only the grid of the portion where the change in the z-axis direction is drastic, but the existing method is by no means fast. Moreover, even if the lattice spacing is reduced, unnatural bending that occurs on the vertical wall cannot be eliminated. Therefore, conventionally, it has been difficult to use the reverse offset method for tool path generation for contour line machining. In view of the above points, the present invention has a shape of a product generated in order to prevent a cutting tool from being cut into a product when calculating a tool path for a three-axis numerical control (NC) machine tool. A high-precision tool path surface, which is a curved surface expanded by the inverse shape of the tool, is calculated with high speed and high accuracy by using the function of graphics hardware.

Further, the present invention divides a space into a collection of minute cubes, and calculates a polyhedron that accurately approximates the tool path surface based on the classification of the intersection of the edge of each cube and the tool path surface. An object is to provide a calculation method, a tool path calculation program, and a recording medium recording the program. Further, according to the present invention, the tool path plane is cut by a plane group perpendicular to the xy plane, which is equivalent to one obtained by raising an orthogonal lattice on the xy plane in the z-axis direction. An object of the present invention is to provide a tool path calculation method for efficiently calculating the intersection of tool path surfaces, a tool path calculation program, and a recording medium recording the program. The present invention provides a tool path calculation method, a tool path calculation program, and a recording medium in which the program is recorded, by using a function of graphics hardware to sample points on a contour line of a cross-sectional view at high speed and high density. With the goal. Further, the present invention uses a function of the graphics hardware to accurately calculate the tangential direction of the contour line at the sampled point, and based on the information, a tool path calculation method and a tool path calculation method for improving the accuracy of a sectional view. It is an object to provide a route calculation program and a recording medium recording the program.

[0008]

According to the solution of the present invention, when a tool attached to a numerically controlled machine tool is moved along a path to machine a workpiece, the tool is inflated by the inverse shape of the tool. A tool path surface calculation program for generating a path surface, wherein the processing unit inputs the polyhedral model information and the tool shape information of the object to be processed and stores it in the storage unit, and the processing unit is a polyhedral model. The step of arranging each shape element forming the swept shape of the reverse tool with respect to each element of, and the processing unit, for each arranged shape element, a unique ID number, unique color information, shape element The step of storing the geometric information of
A graphic that outputs coordinate data of a grid point group covering the uppermost surface of the swept shape and the normal or tangent data of the uppermost surface at the point, based on the input shape elements forming the swept shape of the reverse tool. By using the hidden surface removal processing of the hardware, the processing is repeated while shifting the position of the arranged shape element by a predetermined distance in the x-axis direction, and the cross-section line of the uppermost surface is x.
Obtaining the point sequence data including the coordinate data subdivided in the axial direction and the normal or tangent data, and the step of storing it in the storage unit, the processing unit, using the hidden surface removal process of the graphics hardware, The processing is repeated while shifting the position of the arranged shape element by a predetermined distance in the y-axis direction, and the point sequence data including the coordinate data obtained by subdividing the cross-section line of the uppermost surface in the y-axis direction and the normal line or tangent line data is obtained. The step of obtaining and storing it in the storage unit, the processing unit, based on the normal line or tangent data of the obtained adjacent point sequence data, detects the bending point of the cross-section line, the point sequence of the detected bending point The step of inserting the data into the point sequence data of the section line and storing it in the storage unit, the processing unit dividing the space into an accumulation of cubes according to the grid-like point group, and the processing unit storing it in the storage unit Dotted Day And a step of calculating an intersection of the cross-section line in the x-axis direction and the cross-section line in the y-axis direction of the uppermost surface of the swept shape of the reverse tool and each side of each of the divided cubes, and the processing unit calculates Based on the information of the intersected points, the step of arranging triangles inside the cube by the marching cube method by determining whether the vertex of each cube exists above or below the tool path surface, and the processing unit A method for calculating a tool path surface, including a step of outputting a triangle group arranged inside as an uppermost surface of a sweep shape to an output section or storing it in a storage section, a tool path surface calculation program for causing a computer to execute each of these steps. And a computer-readable recording medium in which a tool path surface calculation program is recorded is provided.

Further, in the present invention, in the hidden surface removal processing of the graphics hardware, the processing unit is configured such that a processing unit is configured to change a shape element forming a swept shape of a reverse tool to a downward portion of the shape element or the inside of another shape element. The step of removing the part not involved in the uppermost surface of the sweep shape such as the part included in the step, the processing section polyhedralizing the shape left unremoved, and the processing section. A step of reading a unique ID number, unique color information, and geometric information of the shape element from the storage unit for the shape element and passing the color information of the polygon forming each shape element to the graphics hardware; Is the depth representing the height of the top surface of the sweep shape at each point, using hidden surface removal processing by the depth buffer based on the color information received from the processing unit. Obtaining the value, the color information at each point,
Passing the obtained depth value and color information to the processing unit,
The processing unit, based on the coordinate data and the depth value of each point received from the graphic hardware, a step of generating point sequence data of the tool path surface indicating the uppermost surface of the sweep shape, and the processing unit, based on the color information. A step of obtaining the ID and geometric information of the shape element corresponding to each point on the uppermost surface by referring to the storage section and obtaining the normal direction at each point according to the coordinate data and geometric information of each point; May include a step of outputting coordinate data of a point group on the tool path surface and information on its normal or tangent.

Further, in the present invention, in the step of inserting the bending point into the point sequence data of the section line and storing it in the storage section, the processing section refers to the storage section and coordinates data representing the section line and The step of reading the normal or tangential data of the tool path surface at the point, and the processing unit, for two consecutive points on each cross section line, if the two tangent or normal directions differ by more than a predetermined value, Determining that the cross-section line has a bending point in between, the processing unit calculates a new bending point, and adds it to the point sequence data;
The processing unit may include updated point sequence data and a step of storing or outputting data indicating the length of the updated point sequence.

[0011]

BEST MODE FOR CARRYING OUT THE INVENTION 1. Related Art of the Present Invention In the present embodiment, a computer-readable recording medium and a tool reference surface calculation device (the inventor: Masatomo Inui) Japanese Patent Application No. 2000-056843 ”is used. Here, a technique related to the present invention will be described. 1-1. Tool Path Surface (Tool Reference Surface) FIG. 1 shows types of end mills used in die machining ((a) ball end mill, (b) flat end mill, (c) round end mill) and their tool path points (tool reference). Point) (Cutter reference
It is a figure which shows the position of (point). In mold processing,
A ball end mill with a hemispherical cutting edge is often used, but a flat end mill is used for rough machining where work efficiency is important, and an annular cutting edge around the flat end mill for gentle curved surface machining. Sometimes, a round end mill equipped with is attached. 3-axis N
In C cutting, a point representing the position of these end mills (hereinafter, this point is referred to as a tool path point (tool reference point) (Cut
A movement path of ter reference point) is given to the control device of the machine tool to cut out a desired shape. In the ball end mill, it is common to use the center point of the cutting edge as the tool path point (tool reference point). On the other hand, in the flat end mill, the center point of the tool tip is
Further, in the round end mill, a point inside the center of the tool tip by the radius of the circular cutting edge is often used as a tool path point (tool reference point).

FIG. 2 shows a tool path surface (a tool reference surface) (a) drawn by a reference point of a ball end mill that slides on a product surface, and a sweep shape (b) when a reference point having an inverse shape of the tool slides on the product surface. It is explanatory drawing which shows the geometrical relationship of. When the ball end mill slides vertically and horizontally on the surface of the mold product, the state of the surface drawn by the trajectory of the tool path point (tool reference point) of the ball end mill is shown by the thick line in FIG. This surface is the tool path surface (tool reference surface) (Cutter reference
surface). Tool path plane (tool reference plane)
Then, by moving the ball end mill so that its reference point always exists above this surface, it is possible to quickly calculate a tool path that does not cause cutting.

The tool path surface (tool reference surface) can be calculated by the following procedure. First, the ball end mill is rotated 180 degrees about the tool path point (tool reference point) to obtain an inverted shape. Then, as shown in FIG. 2B, the reference point is always the surface of the product (Designed surface).
ace), the sweep shape is generated by moving vertically and horizontally. At this time, the uppermost surface of the sweep shape corresponds to the tool path surface (tool reference surface). This calculation method can also be applied to cutting using a flat end mill or a round end mill. FIG. 3 is a geometrical diagram of a tool path surface (a tool reference surface) (a) drawn by a reference point of a flat end mill that slides on a product surface, and a sweep shape (b) when a reference point having an inverse shape of the tool slides on the product surface. It is an explanatory view showing a relationship. FIG. 3A shows a state of a surface drawn by a trajectory of a tool path point (a tool reference point) when a product surface is cut using a flat end mill. Further, FIG. 2B shows a swept shape state in which the reference point of the flat end mill slides vertically and horizontally on the surface of the product, considering the reverse shape of the flat end mill.

Similarly, FIG. 4 shows a tool path surface (a tool reference surface) drawn by reference points of a round end mill that slides on a product surface.
It is explanatory drawing which shows the geometrical relationship of (a) and the sweep shape (b) when the reference point of the reverse shape of a tool slides on a product surface. In any case, it can be seen that the tool path surface (tool reference surface) and the top surface of the sweep shape have the same shape. Therefore, in order to obtain the tool path surface (tool reference surface), it is only necessary to calculate the reverse sweep shape of the tool and select the uppermost surface. Next, FIG. 5 shows a state in which 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 (a), and the reverse shape of the ball end mill having the radius r is swept. It is explanatory drawing which shows the result (b) which calculated the shape and was made to slide the reverse shape of the flat end mill of radius R-r along the upper surface. The reverse shape of the round end mill with the radius R of the shaft part and the radius r of the annular cutting edge is the reverse shape of the flat end mill with radius R-r.
It can be regarded as a swept shape when it is slid along the surface of a ball end mill having a small radius r (see FIG. 5A). Therefore, the reverse swept shape of the round end mill (see FIG. 4 (b)) slides the reverse shape of the ball end mill of radius r along the mold surface to produce a swept shape,
Then, it can be calculated by sliding the reverse shape of the flat end mill having the radius R-r along the uppermost surface of the obtained shape (see FIG. 5B). The reverse shape of the round end mill is
Since the inverse shape of the ball end mill having the radius r can be regarded as the sweep shape when sliding along the inverse shape of the flat end mill having the radius R−r, the inverse sweep shape of the round end mill can be calculated by the reverse procedure. For this reason, the discussion will be limited to the embodiments for calculating the inverse swept shapes of the ball end mill and the flat end mill, but the present invention is not limited to this and can be appropriately applied.

1-2. Inverse offset method Sweep shape calculation is a classical problem in the field of solid modeling, and some calculation methods have already been developed. However, these conventional methods have problems in processing time and stability, and are generally difficult to apply to a solid body that moves on a surface having a complicated shape such as a mold. By combining the approximate calculation technology of the tool path surface (tool reference surface) by the inverse offset method and the processing technology using the 3D graphics hardware, we can make the tool path surface (tool reference surface) stable and stable. He invented a high-speed calculation algorithm and filed a patent for it. In the following discussion, it is assumed that the shape of the product to be processed is polyhedron. However,
Not only a normal closed polyhedron in which one polygon is connected to the left and right of each side, but an "open" shape in which a polygon is connected to only one of the left and right sides forgive. Arbitrary curved surface shapes can be approximately represented as such polyhedrons with desired accuracy. The technique of making a curved surface shape into a polyhedron is well studied in the field of computer graphics, and some high-speed algorithms are already known.

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 path surface (tool reference surface) is generated by the 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 its center always exists on the product surface. When the product is a polyhedron shape, the swept shape of the sphere is the sum of these shapes when the vertices, sides, and polygons of the polyhedron are replaced with spherical, cylindrical, and slab shapes by the following procedure. Figure 6
FIG. 3 is an explanatory diagram showing an example of a spherical surface (a), a cylindrical shape (b), and a thick plate shape (c) that form a sweep shape of a sphere. [Vertex] The vertex is replaced with a sphere centered at the vertex v and having a radius r (see FIG. 6A). [Side] The side is replaced by a cylinder having a radius r and having the side e as the central axis (see FIG. 2B). [Polygon] The polygon f is replaced with a thick plate having a thickness of 2r (see FIG. 7C).

On the other hand, in the case of cutting with a radius r flat end mill, the upper surface of the sweep shape corresponding to the tool path surface (tool reference surface) is the upper end of the reverse shape of the flat end mill.
It is generated by moving a disc-shaped cutting edge. When the product is a polyhedron, the sweep shape of the disc is the sides and polygons of the polyhedron.
When the slanted cylinder shape and the thick plate shape are replaced by the following procedure, the sum of these shapes is obtained. FIG. 7 is an explanatory view showing an example of a slanted cylinder shape (a) and a thick plate shape (b) which form a sweep shape of a disc. [Side] Replaced with a slanted cylindrical shape connecting two horizontal discs with a radius r, which are given to the vertices at both ends of the side e (Fig. 7).
(See (a)). [Polygon] A horizontal disk having a radius r is arranged at all vertices around the polygon f, the polygon is moved horizontally, and the polygon is positioned so as to contact the outer circumferences of all the disks. Two such positions are possible. Therefore, a slab shape corresponding to a region sandwiched by two polygons arranged at each place is generated, and the polygon f is replaced with this slab shape (see (b) of the same figure). When a complicated die shape is precisely made into a polyhedron, the number of polygons is often tens to hundreds of thousands. Since the number of sides and vertices is also proportional to the number of polygons, the calculation of the sweep shape by the above-mentioned method requires enormous number of spherical, cylindrical, and thick plate shape calculations, which is not practical. . The reverse offset method focuses on the fact that only the uppermost surface of the swept shape is finally required as the tool path surface (tool reference surface), and by performing the following procedure, the tool path surface (tool Realize efficient and stable calculation of reference plane).

FIG. 8 shows a spherical surface, a cylindrical shape, and a thick plate shape forming a sweep shape of a sphere and a z-axis passing through the center of a lattice in order to obtain a tool path surface (tool reference surface) for ball end milling. It is a figure which shows a mode that the intersection of the straight line parallel to is investigated and the uppermost intersection is selected. Further, FIG. 9 shows a slanted cylinder shape and a thick plate shape forming a sweep shape of a disk in order to obtain a tool path surface (tool reference surface) for flat end milling,
Examine the intersection of straight lines passing through the center of the lattice and parallel to the z-axis,
It is a figure which shows a mode that the uppermost intersection is selected. First, an orthogonal coordinate system as a reference for processing is given so that its z axis coincides with the upward direction of the rotation axis of the end mill (see FIGS. 8 and 9). On the xy plane of the reference coordinate system, orthogonal grids that are parallel to the x axis and the y axis and are equally spaced are generated so as to cover the projection of the sweep shape to be calculated on the xy plane. In addition, in both the case of ball end mill processing and the case of flat end mill processing, the sweep shape projection figure corresponds to the product shape projection figure expanded by the radius of the end mill.
An orthogonal grid may be generated so as to cover this expanded figure. The smaller the grid interval w, the more accurate the calculation becomes possible, but the required memory capacity becomes enormous. When the tool path surface (tool reference surface) is calculated, the grid spacing is often adjusted so that the total number of grids is about 1,000 × 1,000.

Next, consider a straight line that passes through each grid point and is parallel to the z-axis, and examine the intersection of this straight line and all the shape elements that form the swept shape. For example, when calculating a tool path surface (tool reference surface) for ball end milling, a straight line passing through each grid point, a spherical surface at the apex, a cylindrical shape at the side, and a polygonal shape are arranged. Examine the intersection of the slab shapes that were made. Then, as shown in FIG. 8, the uppermost intersection, that is, the intersection having the largest z coordinate value is selected. Also in the case of calculating the tool path surface (tool reference surface) for flat end milling, as shown in FIG. 9, each straight line intersects the slanted cylinders arranged on the sides and the thick plate shapes arranged on the polygons. Examine
Select the top intersection. If these processes are repeated for all the grids, a dense point cloud arranged in a grid shape that covers the tool path surface (tool reference surface) can be obtained. Four adjacent points that correspond to the corners of each grid are selected, and two triangles having these points as vertices are defined. By repeating this process for all the squares, it is possible to obtain a group of triangles representing the tool path planes (tool reference planes) that are spread without gaps.

1-3. Utilization of three-dimensional graphics hardware In the inverse offset method, intersection points between a straight line passing through each grid point and parallel to the z-axis and a spherical surface or a cylindrical shape forming a swept shape are calculated. It has to be repeated for all combinations of grid and shape elements. The method we invented accelerates this process by utilizing the hidden surface removal function of the 3D graphics hardware. In 3D computer graphics, a depth buffer is used to create an image in which hidden surfaces that are hidden by other surfaces and invisible to the observer are erased. FIG. 10 shows the use of the depth buffer.
It is a figure which shows the example of generation of the image which erased the hidden surface of two cubes. This technique will be described by taking as an example the case where an image obtained by observing two cubes arranged as shown from the left side of the drawing is drawn on the screen by parallel projection. First, the coordinate system that serves as the reference for processing is placed at an arbitrary position on the screen so that its x-axis and y-axis are parallel to the grid of pixels that form the screen, and z
The direction of the axis is given so as to be opposite to the line of sight of the observer. It also consists of elements that correspond to each pixel on a one-to-one basis.
Prepare an array called a depth buffer and give sufficiently small numbers as initial values to all the elements. After the above preparations, polygons forming a cube are sequentially drawn on the screen by parallel projection. At that time, the z coordinate value of the point on the polygon projected onto each pixel of the screen is calculated and compared with the value of the corresponding depth buffer element (this is called the depth value). If the z coordinate value is greater than the depth value, the pixel is dyed with a polygonal color and the z coordinate value is recorded as the new depth value. When this process is repeated for all polygons, the z coordinate value of the point on the polygon closest to the viewpoint is stored in each element of the depth buffer. In addition, each pixel will be dyed with the color of that point,
As a result, the image with the hidden surface erased is drawn on the screen. In the example of this figure, the pixel marked with a circle is dyed with the color of the point p ₃ and the corresponding depth buffer element has the z of this point.
The coordinate value is stored as the depth value. When the line-of-sight direction of the observer is set to the downward direction of the rotation axis of the end mill, and the pixel group of the screen is associated with the orthogonal grid on the xy plane: -For all grid points, a straight line parallel to the z-axis passing therethrough , Calculating the intersection of the top surface of the sweep shape of a sphere or a disc (see FIGS. 8 and 9), and all shape elements (spherical, cylindrical,
Drawing an image in which a thick plate shape or the like is projected in parallel using a depth buffer (see FIG. 10) is a geometrically equivalent process. When all shape elements have been drawn, the z coordinate value of the uppermost intersection of the corresponding straight line and the swept shape is stored as the depth value in each element of the depth buffer, so the tool path plane (tool reference plane) ) Can be easily obtained. Many commercially available graphics boards have a function of directly executing the hidden surface removal processing of a polyhedron using a depth buffer by hardware.
Therefore, the tool path plane (tool reference plane) can be drawn by using the hardware function to draw an image of parallel projection of the obtained polygon group by appropriately approximating the spherical surface and cylindrical shape that make up the swept shape, etc. Can be calculated at high speed. It should be noted that the three-dimensional graphics display device is a semiconductor device that is expected to have a higher speed in the future, and therefore, by utilizing its function, the processing speed can be further increased in the future.

2. Tool path calculation The present invention mainly develops the above-mentioned technique, and eliminates the weakness of the inverse offset method, which is the weak point of the tool path surface. 2-1. Improvement of Accuracy of Inverse Offset Method FIG. 11 is an explanatory diagram showing a distribution of point groups obtained by the inverse offset method in a steep wall shape. FIG. 11 (a)
Shows a state as viewed from the direction A, and a large error occurs between the ideal tool path surface and the calculation result on the wall surface. FIG. 11B is a view as seen from the B direction, where x
Unnatural bends occur due to the inability to express a gentle change in direction. The inverse offset method divides the space by an elongated rectangular parallelepiped that stretches each square of the orthogonal grid in the z-axis direction, calculates the intersection of the vertical side and the uppermost surface of the swept shape of the inverse tool, and makes it a polyhedron. , Tool path surface (see FIG. 12A described later). This method cannot accurately represent the shape of the tool path surface, especially the shape corresponding to the "wall". FIG. 11 shows a state of intersections of a group of straight lines extending vertically from the lattice and the tool path surface in the vicinity of the wall shape. In the part where the tool path surface is horizontal and smooth (the upper and lower horizontal surfaces in the figure), the distance between the intersections is about the grid interval, so even if you interpolate between them with a polygon, it is sufficient for machining. Accuracy can be obtained. However, in a steep wall shape in which the tool path surface greatly changes in the z-axis direction, the distance between adjacent intersection points increases,
A large error may occur in the shape after interpolation (see FIG. 11A). Further, in this method, since the horizontal shape change is discretely recorded for each grid interval, a smooth shape change of the wall portion in the x-axis and y-axis directions cannot be expressed, and an unnatural bending occurs. In some cases (see FIG. 11B). For these reasons, it has been considered that the tool path surface calculated by the inverse offset method may be unsuitable for generating a tool path (for example, a contour line shape) for cutting a wall shape.

Therefore, in the present embodiment, the inverse offset method is extended so that the tool path surface is calculated by using not only the grid on the xy plane but also the grid on the yz plane or the grid on the zx plane. By solving these problems. xy
Similar to the lattice on the plane, an orthogonal lattice parallel to the y axis and the z axis and equidistantly on the yz plane, and an orthogonal lattice parallel to the z axis and the x axis on the zx plane are prepared. At this time, take care so that the three lattices have the same lattice spacing and that the lattice lines are not displaced. xy plane, yz plane,
Performing the inverse offset method using three grids on the zx plane divides the space into minute cubes corresponding to the product of three rectangular parallelepipeds based on the grids of each grid, and It is geometrically equivalent to expressing the tool path surface by calculating the intersection of the 12 sides and the uppermost surface of the sweep shape. FIG. 12 is a comparison diagram of the conventional reverse offset method (a) and the reverse offset method (b) of the present embodiment. Here, in addition to the conventional inverse offset method (a) based only on the grid on the xy plane and the grid on the xy plane, the yz plane and zx
We have shown the difference between the new inverse offset method (b) which also uses two gratings on a plane. In the new reverse offset method according to the present embodiment, unlike the conventional method, two adjacent points of the intersection point group forming the tool path surface always exist on the same cube, so the distance between them is Regardless of the shape of the path surface, the value is equal to or less than a constant value determined by the length of each side of the cube. In the present embodiment, the x-axis direction of the tool path surface and y
Since the shape change in the axial direction can be accurately recorded, the calculation can be performed with a much higher precision than the conventional method. If the intersection of each side of the minute cube that divides the space and the top surface of the sweep shape is obtained, a triangle group representing a part of the tool path surface is given inside the cube by an algorithm generally called the marching cube method. be able to. If this process is repeated for all cubes, the tool path surface can be approximately represented by a set of minute triangles. Assuming that each side of the cube and the top surface of the swept shape intersect at only one point,
Based on the information, it is determined whether the vertices at both ends of each side are above or below the tool path surface. So cubic 8
These vertices are classified into the vertices existing above the tool path surface and the vertices existing below.

FIG. 13 is a view showing a crossing pattern which may occur between the minute cube and the uppermost surface of the swept shape of the inverted tool. There are 2 ⁸ = 256 possible classification patterns, but the pattern can be reduced to 20 shown in the figure in consideration of the symmetry. In the original paper of the marching cubes method, for example, patterns D and E are considered to be the same, so that there are 15 patterns, but in the present embodiment, these are treated as different patterns in consideration of the surface orientation. In this figure, the vertices located above the tool path plane are shown in white, and the vertices located below are shown in black. According to this pattern, the marching cubes method arranges a triangle representing a tool path surface inside a cube. If the side of the cube intersects the tool path surface a plurality of times, consider that there is no intersection when the number of times of intersection is an even number, and consider that it is "intersect at one point" when the number of times of intersection is an odd number. Processing can proceed without contradiction. In addition, in a study employing an expression partially similar to that of this embodiment, E proposed by Choi et al. Of KAIST in Korea.
There is a Z-map method. Their paper (Sculpture
d Surface Machining, Theo
ry and Applications, B.I. K.
Choi and R. B. Jerard, Kluwe
r Academic Press, 1998),
It has been proposed to calculate a cross-section line and use it for NC machining command generation as in the present embodiment, but a fast and highly accurate calculation method of the cross-section line has not been discussed. In addition, no method has been proposed for calculating a tool path surface with high accuracy by combining this technology with the marching cube method. On the other hand, in Japan, Fujio et al. Have proposed a method of expressing a product shape using the marching cubes method under the name of Boundary-Map expression, but their research does not consider the combination with the inverse offset method. (Boundary-
Development of CAD / CAM system based on Map data structure, Fujio, Yanagishita, Suzuki, Journal of Precision Engineering, Vol. 66,
No. 7, 2000).

2-2. Calculation of intersections based on cross-section lines With the above-mentioned technique, in order to precisely make the tool path surface polyhedral, twelve sides of a minute cube defined based on three orthogonal grids and the swept shape of the reverse tool It is necessary to calculate the intersection of the top surface of. As one of the methods, an algorithm is conceivable in which the intersection of the straight line including each side and the top surface is calculated, and the intersection of the side and the top surface is determined from the coordinates of the obtained points. Of the twelve sides, the four sides parallel to the z-axis have at most one intersection between the straight line parallel to the z-axis including each side and the uppermost surface, and the process of determining the coordinate values is the same as the conventional process. Since it is exactly the same as the inverse offset method, a high-speed calculation method using the hidden surface removal function of the graphics hardware can be used. However, in the case of eight sides parallel to the remaining x-axis and y-axis, the straight line parallel to the x-axis and y-axis including these and the uppermost surface of the sweep shape may intersect at a plurality of points. ,
The calculation method using the hidden surface removal function cannot be applied as it is. Therefore, in this embodiment, the uppermost surface of the sweep shape is cut by using a surface parallel to the yz plane or the zx plane, and then the cross-section line is used to determine the side parallel to the x-axis or the y-axis. A method of calculating the intersection point of the upper surface is used. That is, 12 cubic
Of the sides of the book, at the intersection of the four sides parallel to the y-axis and the uppermost surface, the uppermost surface can be cut using the plane parallel to the yz plane including these sides, and the section line can be obtained. , It can be easily calculated by checking the intersection of this and the side. This will be shown below with reference to the drawings.

FIG. 14 shows the construction based on the cross section line of the sweep shape.
In the figure which shows the example which calculated the intersection of each side of the tool path surface and the cube
is there. For example, two sides e parallel to the y-axis_ThreeAnd e₁₁And Mogami
The intersection of the faces is y containing the faces of the cube adjacent to these edges.
The top surface is cut using the plane parallel to the z-plane, and the section line
(Gray curve in the figure) and e_ThreeAnd e₁₁The positional relationship of
Can be calculated by_ThreeOnly intersect with
is doing). e_ThreeE ₁₁Since both are horizontal line segments,
It is easy to check the intersection of these and the section line and calculate the intersection.
It The remaining two sides e parallel to the y-axis₁And e₉And the intersection of the top
Also, use the plane including the faces adjacent to these to cut the top face.
If the surface line is calculated, it can be easily obtained from the result. same
Similarly, four sides e parallel to the x-axis₀, E_Two, E₈, E₁₀
And the top surface of the swept shape is also zx including these sides
Cut the top surface using a plane parallel to the plane, and then cut the section line
By checking the positional relationship between (black curve in the figure) and each side
Can be calculated. Parallel to the z-axis if the section line can be obtained
You can easily calculate the intersection of the four edges and the top surface.
All the information needed to apply the marching cubes method
Will be obtained.

2-3. Calculation of Section Line by Graphics Hardware Among the surfaces of the minute cube as described above, the section line when the uppermost surface of the sweep shape is cut by a surface parallel to the zx plane can be calculated by the following procedure. First, among the lattice lines on the xy plane, a straight line parallel to the x axis corresponding to the projection of the cut surface on the xy plane is selected, and sufficiently dense points are arranged on this straight line at equal intervals. Next, the intersection of the half line group extending parallel to the z axis from the arranged point and the uppermost surface of the swept shape of the reverse tool is calculated. When the obtained intersections are connected in order, it becomes the cross-section line of the uppermost surface by this cut surface. For the cross-section line by the plane parallel to the yz plane, select a grid line parallel to the y axis corresponding to the projection of that plane on the xy plane, and extend from the points densely arranged on the grid line parallel to the z axis. It can be calculated by calculating the intersection of the line group and the top surface and connecting them. Furthermore, in order to calculate a precise section line, x on the xy plane is calculated.
The distance between points arranged on a straight line parallel to the axis or the y-axis needs to be sufficiently small. In the present embodiment, the distance between the points arranged for calculating the cross-section line is 1 / m (for example, m is 8 to 10) of the distance between the original orthogonal lattices on the xy plane.
Set to about). If the section line refining technology described later is also used, the section line with sufficient accuracy can be obtained by calculating and plotting the intersection points of the half line parallel to the z axis and the uppermost surface at such intervals.

FIG. 15 is an explanatory diagram of the calculation of the cross section line using the hidden surface removal function. This figure shows a state in which a point group for calculating a cross-section line, which is arranged on a grid line parallel to the x-axis and the y-axis on the xy plane, is looked down. A calculation technique of the inverse offset method that was previously invented by the present invention using the hidden surface removal function (for example, Japanese Patent Application No. 2000-056843).
(See), the intersection point between the half line extending parallel to the z-axis from the point located on the grid (shown by a white circle in the figure) and the uppermost surface of the swept shape can be calculated at high speed. However, for other points (indicated by black squares in the figure), the corresponding intersection cannot be calculated directly by hardware. This point can be solved by displacing the positions of the graphic elements (spherical surface, cylindrical shape, thick plate shape, etc.) that form the sweep shape and then performing the reverse offset processing. Where [i,
j] For a point (indicated by a large black arrow in the figure) located at a position (dx, 0, 0) displaced from the lattice, z
Consider the case of calculating the intersection of the half line extending parallel to the axis and the top surface of the sweep shape. When all the graphic elements that make up the sweep shape are moved (-dx, 0, 0), this point moves just above the [i, j] lattice, so the intersection of the half line extending from this point and the top surface Can be calculated at high speed using the hidden surface removal function. Therefore, after the calculation, the obtained intersection is recorded as the one corresponding to the point before the movement. At the same time,
Intersections are also calculated for points indicated by other small gray arrows in the figure. Since the moving of the figure and the re-execution of the hidden surface removal are performed at high speed by the graphics hardware, the increase in the processing time accompanying them is negligible. By repeating the same process for the remaining points, the positions of the intersections to be plotted for all the cross section lines can be calculated at high speed.

2-4. Improving the accuracy of cross-section lines This section describes a technique for further improving the accuracy of cross-section lines calculated by the method described in the previous section. FIG.
[Fig. 6] is an explanatory diagram for deriving a bending point based on a tangent line passing through two adjacent points on a section line. In the following, consider the case where the correct cross-section line has a bend as shown in this figure. When plotting the points on the cross section line, if you use a point different from the point where bending is occurring, between the cross section line obtained by connecting them and the correct cross section line,
There will be an error. If the tangent direction of the section line at the plotted point can be obtained, this point can be solved by calculating the bending point based on the information, adding the point, and re-plotting the section line. When the tangential directions of two adjacent plot points on the cross-section line differ greatly by a certain threshold value, it is considered that a bend occurs somewhere between the two points. In that case, the tangent line passing through each plot point is calculated, and the crossing line is corrected by considering the intersections as correct bending points. By setting the distance between adjacent plot points to be sufficiently small, the bending point corrected in this way can be made very close to the accurate bending point. If the tangential direction at the plotted point on the cross-section line is the normal direction of the uppermost surface of the sweep shape at this point, this normal direction and the normal direction of the cut surface (in the case of a cut surface parallel to the yz plane, x-axis direction, xz
It can be easily calculated as the outer product of the cutting plane parallel to the plane (y-axis direction). Next, a method for calculating the normal direction of the uppermost surface at the plotted points by using the function of the graphics hardware will be described. In the reverse offset method using the hidden surface removal function, for example, in the case of ball end milling, the spherical and cylindrical shapes that make up the swept shape of a sphere, and the shape of a thick plate are approximated to a polyhedron, and the tool path is drawn by drawing those images. Get a face. Therefore, a unique ID number is given to each of the spherical surface, the cylindrical shape, and the thick plate shape, and each piece of geometric information (for example, in the case of a spherical surface, the center coordinates and radius) is recorded in advance using that unique ID number. Next, a unique color is assigned to each assigned ID. Three
In three-dimensional computer graphics, for example, two colors
Since it is expressed by 4 to 32 bits, it is possible to allocate more than 1 million ways. At the time of the reverse offset processing, the spherical surface, the cylindrical shape, and the thick plate shape that form the sweep shape are colored and drawn using the colors corresponding to the respective IDs. When the image in which the hidden surfaces of these figures are erased is drawn, each pixel on the screen is dyed with a color representing an ID of a sphere or a cylinder that forms the top surface of the sweep shape, and a slab shape. . Therefore, in order to plot the points on the cross-section line, when the depth value corresponding to each pixel is acquired, its color is also checked and the corresponding spherical, cylindrical, or plank-shaped ID is acquired. The recorded geometric information is searched from this ID, and the normal direction of the plotted point is calculated. Note that the tangential direction may be calculated instead of the normal direction.

3. Hardware Configuration FIG. 17 is a hardware configuration diagram according to the present embodiment. This hardware includes a processing unit (CPU) 1 which is a central processing unit, an input unit 2 for inputting data, a storage unit 3 for storing the input data, an output unit 4, and a three-dimensional graphics display unit. 5 and. Also, CPU
1, the input unit 2, the storage unit 3, the output unit 4, and the three-dimensional graphics display unit (graphics hardware) 5 are connected by an appropriate connecting means such as a star or a bus. Three
The three-dimensional graphics display unit 5 includes a depth buffer,
This is a hardware device that generates the above-described hidden surface removal image by using this depth buffer. The three-dimensional graphics display unit 5 can perform depth buffer processing at high speed by hardware processing. Further, 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. Output part 4
Is a device for displaying the hidden surface elimination image generated in the three-dimensional graphics display unit 5 and drawn in the frame buffer on the display or for outputting to another device. It should be noted that the output unit 4 can also be configured to be directly connected to the bus.

4. The flow chart attached to the flow of the processing algorithm summarizes the highly accurate tool path surface calculation procedure that we invented. This flowchart shows two subroutines (Subroutine A
And B) and the main routine are described separately. In the following flowchart, the data in the normal direction is used, but the data in the tangential direction may be used instead. 4-1. Subroutine A FIG. 18 shows a flowchart of the subroutine A. This subroutine calculates the shape element group (spherical shape, cylindrical shape, thick plate shape in the case of ball end milling, slanted cylinder shape and thick plate shape in the case of flat end milling) that constitutes the swept shape of the reverse tool. When input, using the hidden surface removal function of the graphics hardware (3D graphics display unit) 5, the coordinate values of the point group covering the uppermost surface of the sweep shape in a grid pattern and the modulus of the uppermost surface at those points. Output the line direction. The basic part of the processing of this subroutine uses the technology that has already been filed, and Japanese Patent Application No. 2000-
The contents described in 56843 can be incorporated herein by reference.

The processing of each step will be described below with reference to the drawings. Step S100: The processing unit 1 inputs the shape element group forming the sweep shape of the reverse tool. The processing unit 1 can read this information from the storage unit 3. In addition, these pieces of information may be input from the input unit 2, another recording medium, an external device, or the like as necessary. Step S101: The processing unit 1 removes in advance, from the input shape element, a portion that is obviously not related to the uppermost surface of the sweep shape. Specifically, for example, the downward portion of the shape element or the portion included in another shape element is detected and removed. Step S102: The processing unit 1 polyhedralizes the shape that remains without being removed. Step S103: The processing unit 1 previously sets the shape element to I
D number is assigned and corresponds to the processing of the graphics hardware (3D graphics display unit) 5.
A unique color is assigned to each ID. The geometric information of each shape element is stored in the database using the ID as a key. With this assigned color,
Color the polygons that make up each (polyhedral) shape element. The colored polygon data is passed to the graphics hardware 5. Step S104: graphics hardware 5
Prepares a depth buffer composed of elements corresponding to the orthogonal lattice on the xy plane in a one-to-one correspondence. An image obtained by observing the colored polygon group from the positive direction of the z-axis is drawn on the screen by parallel projection. The hidden surface removal function of the graphics hardware 5 automatically updates the contents of the depth buffer. Step S105: Graphics hardware 5
When the drawing of all polygons is completed, each depth value of the depth buffer represents the z coordinate value of the uppermost intersection of the sweep shape and a straight line parallel to the z axis passing through the corresponding grid. The color of each pixel represents the ID of the shape element corresponding to these points. All the obtained depth values and pixel color data are passed to the software processing on the processing unit 1 side. Step S106: The processing unit 1 receives the position information (coordinate data) and the depth value of the orthogonal grid from the graphics hardware 5, and covers the uppermost surface of the sweep shape based on the position information (coordinate data) and the depth value. Generate a dense point cloud. Step S107: The processing unit 1 determines the ID of the shape element corresponding to each point covering the uppermost surface from the color data, and obtains the geometric information of the shape element from the database using the ID as the search key. The normalized normal direction at each point is determined from the coordinate values of the point and the obtained geometric information. Step S108: The processing unit 1 outputs the coordinate values of the point cloud covering the uppermost surface of the sweep shape in a grid pattern and its normal direction.

4-2. Subroutine B FIG. 19 shows a flowchart of the subroutine B. This sub-routine consists of m * n point sequence data representing cross-section lines (polygonal lines) for n rows on the top surface of the reverse tool sweep shape, and the (normalized) normal direction of the top surface at each point. When the data of (1) is input, a bending point on the cross section line is detected, and the point is inserted into the point sequence data of the cross section line and output. Here, the maximum number of bending points is k.
It is supposed to be an individual. As a method for inserting the newly detected bending point, a more efficient technique may be considered, but here, description is given with priority on the ease of understanding. The processing of each step will be described below with reference to the drawings. Step S200: The processing unit 1 sets the point sequence data sec [n] [m * n + k] [3] representing the cross section line and nrml representing the normalized normal direction of the surface at each point.
Input [n] [m * n + k] [3]. Alternatively, the processing unit 1 reads these data from the storage unit 3. In this example, n lines of cross-section lines are recorded, and the data of each line consists of m * n points. However, in the following processing, maximum k
Since there is a possibility that a new number of points will be inserted, an extra storage area is reserved in the storage unit 3 by that amount. The storage area in the normal direction is defined similarly. Step S201: The processing unit 1 sets the local variable i to 0.
Initialize to. The following processing is repeated for the cross-section line in each column while increasing i until i changes from 0 to n-1. Step S202: The processing unit 1 sets the local variable j to 0.
Initialize to. The following process is repeated for two consecutive points on each polygonal line while increasing j until j becomes 0 to final-2. final is initially set to m * n. Step S203: The processing unit 1 coordinates coordinate sec [i].
From [j] and the normal direction nrml [i] [j], s
Get the tangent tan0 at ec [i] [j]. The processing unit 1 similarly uses sec [i] [j + 1] and nrm.
From l [i] [j + 1] to sec [i] [j + 1]
Obtain the tangent tan1 at. Step S204: The processing unit 1 makes two tangent lines tan0.
If the directions of tan1 and tan1 are significantly different, two points se
Between c [i] [j] and sec [i] [j + 1],
Consider that the cross-section line has a bend. The processing unit 1 stores the point sequence data after sec [i] [j + 1] again in sec [i] [j + 2] in order to obtain the storage location of the new bending point in the storage unit 3. Similarly, the processing unit 1 sets the normal line data after nrml [i] [j + 1] to nrml [i] [j + 2] of the storage unit 3.
Store it again. Step S205: The processing unit 1 makes the tangent lines tan0 and ta.
A new bending point is calculated as the intersection of n1 and stored in sec [i] [j + 1]. Step S206: Since the point sequence data has increased by one, the processing unit 1 increases j and final accordingly. Step S207: The processing unit 1 outputs the updated point sequence data sec and final indicating the length of the updated point sequence.

4-3. Main Routine FIGS. 20 and 21 show flowcharts (1) and (2) of the main routine. The processing of each step will be described below with reference to the drawings. Step S300: The processing unit 1 reads the data stored in the storage unit 3 according to an instruction from the input unit 2 to obtain information on the polyhedron model of the object to be machined, information on the tool shape (tool type and cutting edge type). Shape, etc.) and the number n of divisions of the orthogonal lattice prepared for the inverse offset method. Further, the processing unit 1 inputs or reads the number m of subdivision of the grid to obtain the section lines and the upper limit k of the number of points to be inserted to refine each section line. When calculating the cross-section line, the processing unit 1 plots the points on the cross-section line with a division m times finer than the division of the grid in order to improve the accuracy when calculating the cross-section line, as in the following steps. Further, the processing unit 1 detects the bending of a maximum of k cross-section lines and inserts a new point therein in order to refine each cross-section line as in the following steps. Step S301: The processing unit 1 prepares a coordinate system in which the axial direction of the tool is the z axis, and generates an n × n size orthogonal grid on the xy plane so as to cover the projected figure of the model after the reverse offset. To do. Step S302: The processing unit 1 generates an orthogonal grid on the yz plane or the zx plane, which is consistent with the size d or the position of the grid mass on the xy plane and covers the projected figure of the polyhedral model after the reverse offset. Steps S303 and S304: The processing unit 1 includes the storage unit 3
In order to record the coordinates of the point sequence on the cross section line in the x-axis direction and the y-axis direction respectively,
Secure. Further, the processing unit 1 secures the areas xnrml and ynrml in the storage unit 3 in order to record the normal direction of the sweep shape of the reverse tool at each point. As aforementioned,
The section line is recorded for n columns, and the data of each column is composed of m * n points. Since there is a possibility that a maximum of k points will be newly inserted in the refinement process of the cross-section line, an extra storage area for that is reserved in the storage unit 3. Steps S305 and S306: The processing unit 1 defines each of the vertices of the polyhedral model in order to define the swept shape of the inverse tool.
Place shape elements on sides and polygons. Specifically, for example, if the tool shape is a ball end mill,
Spherical, cylindrical, and slab shapes are arranged on each of the sides and polygons, while in the case of a flat end mill, inclined cylinders and slab shapes are arranged on the sides and polygons. Steps S307 and S308: The processing unit 1 gives a unique ID number to each of the arranged shape elements (each element such as a sphere, a cylinder, and a slab). Next, the ID is used as an index to record geometric information of the shape element (spherical surface, cylindrical shape, slab shape, oblique cylinder shape, slab shape, etc.) in the database. Further, a color corresponding to each ID is assigned to each ID. Step S309: The processing unit 1 initializes the counter ii to 0, increments the counter ii one by one, and repeatedly executes the processes of steps S310 to S313 until the counter ii becomes equal to m. By this iterative process, the cross-section line group for n columns in the x-axis direction is obtained. Steps S310, S311, S312, S31
3: The processing unit 1 determines the position of the placed shape element.
After shifting by [(-d / m) * ii, 0, 0],
Invokes subroutine A. Then, the lattice-shaped point cloud covering the uppermost surface of the sweep shape is [(-d / m) * ii, 0,
Since it is obtained at a position shifted by 0], the processing unit 1 shifts these coordinates by [(d / m) * ii, 0, 0] and corrects them to correct positions. Then, the grid [i, j]
The coordinate of the point corresponding to is xsec [j] in the storage unit 3.
The process of storing in [m * i + ii] is repeated for all points. Since the sub-routine A also returns the normal direction of the uppermost surface in the obtained point group, the processing unit 1 determines the normal direction corresponding to the grid [i, j] as well as the coordinate values.
The process of storing in xnrml [j] [m * i + ii] of the storage unit 3 is repeated for all normal directions. Step S314: The processing unit 1 initializes the counter ii to 0, increments the counter ii one by one, and repeatedly executes the processing of steps S315 to S318 until it becomes equal to m. By this iterative process, a section line group for n columns in the y-axis direction is obtained this time. Steps S315, S316, S317, S318:
The processing unit 1 has a substantial content of processing in step S310.
~ Same as S313, but this time, the figure is shifted along the y-axis, and then the subroutine A is started. The processing unit 1 sets the grid-shaped point cloud covering the uppermost surface of the sweep shape obtained by the subroutine A and the normal direction, and the coordinates of the points corresponding to the [i, j] grid are ysec [i ] [M * j + ii]
And the normal direction at that point is yn in the storage unit 3.
The processing is repeated so that it is stored in rml [i] [m * j + ii]. Steps S319 and S320: The processing unit 1 activates the subroutine B to refine the cross section lines xsec and ysec. That is, the processing unit 1 detects a bending point and stores it in the storage unit 3 so as to insert the point into the point sequence data. Step S321: The processing unit 1 divides the space into a collection of minute cubes based on the three lattices on the xy plane, the yz plane, and the zx plane. Step S322: The processing unit 1 stores the cross section line xsec in the x-axis direction of the uppermost surface of the sweep shape stored in the storage unit 3, and y.
The intersection of the top surface and the 12 sides of each cube is calculated based on the axial section line ysec. Step S323: The processing unit 1 arranges minute triangles inside the cube by the marching cube method based on the information of the intersections. Step S324: The processing unit 1 outputs the group of triangles arranged inside the entire cube to the output unit 4 as the uppermost surface (tool path surface) of the sweep shape. The processing unit 1 also stores this data in the storage unit 3. The processing unit 1 may appropriately store the initial data, the intermediate data or the final data obtained by the processing in the storage unit 3, read out from the storage unit 3, and output to the output unit 4. The processing unit 1 may further include a step of obtaining a tool path based on the obtained tool path surface. Further, the processing unit 1 may further include a step of displaying the tool path surface and / or the tool path.

5. Example and Evaluation In order to verify the effectiveness of the present embodiment, a program for calculating a highly accurate tool path surface was created using the hidden surface removal function of graphics hardware, and a calculation experiment was performed. For calculation, the total number of grids is 1,000 x 1,0
An orthogonal grid adjusted to be 00 was used. The computer used is Pentium IV (trademark) (1.7GH)
z) is a CPU with a main memory of 2 GB. This computer has a GeForce
Dedicated hardware for 3D graphics display called 3 Ti500 is provided. When a polygonal shape to be drawn is described in a program according to the specifications of a library called OpenGL, the compiler automatically generates a machine language code for executing hidden surface removal using a depth buffer by hardware. FIG. 22 shows 30,
It is a figure which shows an example of the polyhedron which consists of 528 polygons. FIG. 23 shows a result of calculating the tool path surface by using the conventional reverse offset method for cutting the polyhedron of 30,528 polygons shown in FIG. 17 using a ball end mill with a radius of 1 mm. Show. FIG. 24 is a diagram showing an example of an image obtained by partially enlarging the processing result of the normal reverse offset method. This figure is an enlarged display of the vertical wall portion of FIG. It can be seen that the “bend” perpendicular to the wall has occurred, and the accuracy of the tool path surface is insufficient. Figure 25
FIG. 7 is a diagram showing an example of an image obtained by partially enlarging the processing result of the highly accurate reverse offset method according to the present embodiment. This figure shows the result of calculating the tool path surface for the same cutting tool using the highly accurate reverse offset method proposed this time.
Unlike the result by the conventional method, the bend disappears from the part of the vertical wall. Further, in this figure, fine irregularities which cannot be observed because they are buried in the error appear, and thus it is understood that a tool path surface with much higher accuracy is obtained. FIG. 26 is a diagram showing an example of a contour-shaped tool path calculated using the tool path surface obtained by the highly accurate reverse offset method. FIG. 27 is a diagram showing an example of a result of a cutting machining simulation using a contour-shaped tool path calculated based on a highly accurate tool path surface. From the image of such a machining simulation, it can be seen that an appropriate tool path that does not cause cutting is generated. FIG. 28: is a figure which shows an example of the result which calculated the tool path | route using the tool path surface obtained by the conventional reverse offset method, and performed the cutting simulation. From the comparison of the two simulation results, the tool path based on the new inverse offset method according to the present embodiment is
You can see that the vertical wall of the product can be finished much more beautifully. As described above, the experimental program for calculating the tool path for cutting the wall surface of the die into the contour lines by using the highly accurate tool path surface obtained by the present embodiment was developed. The contour-shaped tool path can be calculated by repeatedly performing a process of cutting the tool path surface along a plane parallel to the xy plane to obtain a section line while changing the height of the cut surface. The calculation of each cross-section line is divided into a process of obtaining an intersecting line of a minute triangle covering a tool path surface and a cutting plane, and a process of connecting the obtained minute intersecting lines into one curve. In the new inverse offset method that we invented, the group of triangles forming the tool path surface is defined inside a minute cube parallel to the x, y, and z axes that divide the space. By using this cube information, the calculation of the cross section line can be speeded up for the following reasons.・ From the height of the cut surface, it is possible to narrow down the cubes that intersect this surface in advance. Only the triangles contained inside the narrowed cube can intersect the cutting plane. When a triangle inside a cube intersects a cut surface, the cube containing the intersection line that can be connected to the obtained intersection line can be narrowed down by using the adjacency relation between the cubes. In the present invention, the tool is not limited to a ball end mill, a flat end mill and a round end mill, and a proper tool such as a cutting tool or a die-casting tool can be used, and the sweep shape is not limited to a spherical surface and a cylindrical shape. Depending on the tip shape of the tool, it can be used in an appropriate shape such as an elliptical surface, a polygonal surface, or an uneven surface.
Further, the present invention is not limited to the mold, and the present invention can be applied to various works made of various materials such as plastic and metal. In the above description, the necessary or all depth data and the necessary or all polygon data are mainly input or output to the processing unit and the three-dimensional graphics display unit, etc. Not limited to this, a part of each data may be exchanged. Furthermore, although a polyhedron and a triangle have been described as examples of the approximation of the surface, the present invention is not limited to this, and an appropriate polygon can be used. The tool path calculation method or tool path calculation device / system of the present invention,
A tool path calculation program for causing a computer to execute each of the procedures, a computer-readable recording medium recording the tool path calculation program, a program product that includes the tool path calculation program and can be loaded into an internal memory of a computer, and the program It can be provided by a computer such as a server.

[0035]

As described above, according to the present invention, when a tool path for a three-axis numerical control (NC) machine tool is calculated, it is generated to prevent a cutting tool from being cut into a product. Further, a highly accurate tool path surface, which is a curved surface obtained by expanding the shape of the product by the inverse shape of the tool, can be calculated at high speed and with high accuracy by using the function of the graphics hardware. Further, according to the present invention, it is possible to divide a space into a collection of minute cubes and calculate a polyhedron that precisely approximates the tool path surface based on the classification of the intersection of the edge of each cube and the tool path surface. Further, according to the present invention, the tool path plane is cut by a plane group perpendicular to the xy plane, which corresponds to one obtained by raising an orthogonal lattice on the xy plane in the z-axis direction, and the side of the cube is cut based on the cross-sectional view. It is possible to efficiently calculate the intersection of the tool path surface and the tool path surface. According to the present invention, it is possible to sample points on the contour line of a sectional view at high speed and with high density by using the function of graphics hardware. Furthermore, according to the present invention, the tangential direction of the contour line at the sampled point can be accurately calculated using the function of the graphics hardware, and the sectional view can be made highly accurate based on the information.

[Brief description of drawings]

FIG. 1 (a) shows the positions of a ball end mill and its tool reference points used in die machining, and FIG. 1 (b) shows the positions of a flat end mill and its tool reference points,
(C) is an explanatory view showing the positions of the round end mill and its tool reference point.

FIG. 2 (a) shows a tool reference surface drawn by reference points of a ball end mill that slides on a product surface, and FIG. 2 (b) shows a swept shape when an inverted reference point of a tool slides on a product surface. Fig.

FIG. 3 (a) shows a tool reference surface drawn by reference points of a flat end mill that slides on a product surface, and FIG. 3 (b) shows a swept shape when a reference point having an inverted shape of the tool slides on the product surface. Fig.

FIG. 4 (a) shows a tool reference surface drawn by a reference point of a round end mill that slides on a product surface, and FIG. 4 (b) shows a swept shape when a reference point having an inverse shape of the tool slides on the product surface. Fig.

FIG. 5 (a) shows a state in which an inverted shape of a flat end mill having a radius (R−r) is slid along a surface of an inverted shape of a ball end mill having a radius (r), and (b) shows Explanatory drawing which shows the result of having calculated the reverse sweep shape of the ball end mill of radius (r), and also sliding the reverse shape of the flat end mill of radius (R-r) along the upper surface.

FIG. 6 (a) shows a spherical surface forming a swept shape of a sphere in a cutting process by a ball end mill, FIG. 6 (b) shows a cylindrical shape, and FIG. 6 (c) shows a thick plate shape. The figure which shows an example.

FIG. 7A is a diagram showing an oblique cylinder shape which constitutes a sweep shape of a disk in a cutting process by a flat end mill, and FIG. 7B is a view showing an example of a thick plate shape.

[FIG. 8] In order to obtain a tool reference surface for ball end milling, the intersection of a spherical surface, a cylindrical shape, and a slab shape forming a sweep shape of a sphere and a straight line parallel to the Z axis passing through the center of the lattice is examined. , Showing the selection of the uppermost intersection.

[Fig. 9] In order to obtain a tool reference surface for flat end milling, the intersection of a slanted cylinder shape and a thick plate shape forming a sweep shape of a disk and a straight line parallel to the Z axis passing through the center of the lattice is examined. , Showing the selection of the uppermost intersection.

FIG. 10 is an explanatory diagram of hidden surface erased images of two cubes by using a depth buffer.

FIG. 11 is an explanatory diagram showing a distribution of point groups obtained by the inverse offset method in a steep wall shape.

FIG. 12 is a comparison diagram of the conventional reverse offset method (a) and the reverse offset method (b) of the present embodiment.

FIG. 13 is a diagram showing a crossing pattern that can occur between a minute cube and a top surface of a swept shape of an inverted tool.

FIG. 14 is a diagram showing an example in which the intersection of each side of the tool path surface and the cube is calculated based on the cross section line of the sweep shape.

FIG. 15 is an explanatory diagram of calculation of a cross section line using a hidden surface removal function.

FIG. 16 is an explanatory diagram for deriving a bending point based on a tangent line passing through two adjacent points on a section line.

FIG. 17 is a block diagram of hardware according to the present invention.

FIG. 18 is a flowchart for subroutine A.

FIG. 19 is a flowchart for subroutine B.

FIG. 20 is a flowchart (1) of a main routine.

FIG. 21 is a flowchart (2) of the main routine.

FIG. 22 is a diagram showing an example of a polyhedron composed of 30,528 polygons.

FIG. 23 is a view showing an example of a tool path surface when the polyhedron shown in the previous figure is cut by a ball end mill having a radius of 1 mm.

FIG. 24 is a diagram showing an example of an image obtained by partially enlarging the processing result of a normal reverse offset method.

FIG. 25 is a diagram showing an example of an image obtained by partially enlarging the processing result of the highly accurate reverse offset method according to the present embodiment.

FIG. 26 is a diagram showing an example of a contour-shaped tool path calculated using a tool path surface obtained by a highly accurate reverse offset method.

FIG. 27 is calculated based on a highly accurate tool path surface,
The figure which shows an example of the result of the cutting processing simulation using a contour-shaped tool path.

FIG. 28 is a diagram showing an example of a result of performing a cutting simulation by calculating a tool path using a tool path surface obtained by the conventional reverse offset method.

FIG. 29 is a view showing an example of shaving in die processing.

[Explanation of symbols]

1 processing unit 2 input unit 3 storage unit 4 output unit 5 three-dimensional graphics display unit (graphics hardware)

Claims (12)

[Claims] 1. A tool path surface calculation method for generating a tool path surface expanded by an inverse shape of a tool when a tool attached to a numerically controlled machine tool is moved along the path to machine a workpiece. The processing unit inputs the polyhedron model information of the workpiece and the tool shape information and stores the information in the storage unit, and the processing unit sets the sweep shape of the inverse tool for each element of the polyhedron model. Arranging each shape element that makes up the shape element, and the processing unit storing a unique ID number, unique color information, and geometric information of the shape element in the storage unit for each arranged shape element, The processing unit, based on the shape elements that form the input swept shape of the reverse tool, the coordinate data of the grid-like point group covering the uppermost surface of the swept shape and the normal line or tangent line data of the uppermost surface at that point. Output graphics This process is repeated while shifting the position of the placed shape element by a predetermined distance in the x-axis direction by using the hidden surface removal process of the computer hardware, and coordinate data obtained by subdividing the cross-sectional line of the uppermost surface in the x-axis direction. A step of obtaining point sequence data including normal line or tangent line data and storing it in a storage section, and the processing section uses the hidden surface removal processing of the graphics hardware to determine the position of the arranged shape element by y. The process is repeated while shifting a predetermined distance in the axial direction to obtain point sequence data including coordinate data obtained by subdividing the cross-section line of the uppermost surface in the y-axis direction and normal or tangent data, and storing it in the storage unit. The step and the processing unit detect the bending point of the section line based on the normal or tangent data of the obtained adjacent point sequence data, and convert the point sequence data of the detected bending point into the point sequence data of the section line. Insert A step of storing in the storage part, a step of dividing the space into an accumulation of cubes according to a lattice-shaped point group, and a step of the processing part referring to the point sequence data stored in the storage part, A step of calculating an intersection of the cross-section line in the x-axis direction and the cross-section line in the y-axis direction on the uppermost surface of the sweep shape and each side of each of the divided cubes; and the processing unit based on the information of the calculated intersection point. Then, by deciding whether the vertex of each cube is above or below the tool path surface, the step of arranging triangles inside the cube by the marching cubes method, and the processing unit is the group of triangles arranged inside each cube. Is output to the output unit as the uppermost surface of the sweep shape or is stored in the storage unit. 2. The step of arranging each shape element, the processing unit, when the tool shape information is a ball end mill, corresponding to each of the vertices, sides, and polygons as the elements of the polygonal model. The tool path surface calculation method according to claim 1, wherein a spherical surface, a cylindrical shape, or a thick plate shape is arranged as the shape element. 3. The step of arranging each shape element, the processing unit, when the tool shape information is a flat end mill, the shape corresponding to each of the sides and polygons as elements of the polygon model. The tool path surface calculation method according to claim 1, wherein an oblique cylinder shape and a thick plate shape are arranged as elements. 4. The hidden surface removal processing of the graphics hardware, wherein the processing unit, from the shape elements forming the sweep shape of the reverse tool,
The step of preliminarily removing the part not related to the uppermost surface of the swept shape, such as the downward part of the shape element or the part included in other shape elements, and the processing part The processing unit reads the unique ID number, the unique color information, and the geometric information of the shape element for each arranged shape element from the storage unit, and obtains the color information for the polygons forming each shape element. Based on the color information received from the processing unit, the graphics hardware uses the hidden surface removal processing by the depth buffer to determine the depth of the top surface of the sweep shape at each point. Obtaining a value and color information at each point, and passing the obtained depth value and color information to the processing unit, the processing unit receives each value received from the graphic hardware. The step of generating point sequence data of the tool path surface indicating the uppermost surface of the sweep shape based on the coordinate data of the points and the depth value, and the processing unit refers to the storage unit based on the color information and refers to the uppermost surface. Obtain the ID and geometric information of the shape element corresponding to each point,
The method includes the step of obtaining a normal direction at each point according to the coordinate data and geometric information of each point, and the processing section outputting the coordinate data of the point group on the tool path surface and the normal or tangent information thereof. The tool path surface calculation method described in 1. 5. The step of inserting the bending point into point sequence data of a section line and storing it in a storage section, the processing section refers to the storage section, coordinate data representing the section line, and a tool path at each point. The step of reading the normal or tangent data of the surface, and the processing unit, for two consecutive points on each section line, if the two tangent or normal directions differ by more than a predetermined value, the section line between the two points. Has a bending point, the processing unit calculates a new bending point and adds it to the point sequence data, and the processing unit updates the point sequence data and the length of the updated point sequence. 5. The tool path surface calculation method according to claim 1, further comprising the step of storing or outputting data indicating the height. 6. The step of adding to the point sequence data, the processing section stores the point sequence data after the corresponding point sequence data in order to obtain a place to store the obtained point sequence data indicating a new bending point. 6. The method according to claim 5, further comprising a step of shifting and storing the normal line or tangent line data again, and a step of storing the point sequence data indicating the obtained new bending point in a shifted and vacant area. The tool path surface calculation method described. 7. The processing unit, based on the obtained tool path surface,
5. The method according to claim 1, further comprising the step of obtaining a tool path.
The tool path surface calculation method according to any one of 5 above. 8. The tool path surface calculation method according to claim 1, further comprising a step of displaying the tool path surface and / or the tool path in the processing unit. 9. A tool path surface calculation program for generating a tool path surface expanded by an inverse shape of the tool when a tool attached to a numerically controlled machine tool is moved along the path to machine a workpiece. The processing unit inputs the polyhedron model information of the workpiece and the tool shape information and stores the information in the storage unit, and the processing unit sets the sweep shape of the inverse tool for each element of the polyhedron model. Arranging each shape element that makes up the shape element, the processing unit stores a unique ID number, unique color information, and geometric information of the shape element in the storage unit for each arranged shape element, The processing unit, based on the shape elements that form the input swept shape of the reverse tool, the coordinate data of the grid-like point group covering the uppermost surface of the swept shape and the normal line or tangent line data of the uppermost surface at that point. Output graph By using the hidden surface removal processing of the fixed hardware, the processing is repeated while shifting the position of the arranged shape element by a predetermined distance in the x-axis direction, and coordinate data obtained by subdividing the cross-section line of the uppermost surface in the x-axis direction. A step of obtaining point sequence data including normal line or tangent line data and storing it in a storage section, and the processing section uses the hidden surface removal processing of the graphics hardware to determine the position of the arranged shape element by y. The process is repeated while shifting a predetermined distance in the axial direction to obtain point sequence data including coordinate data obtained by subdividing the cross-section line of the uppermost surface in the y-axis direction and normal or tangent data, and storing it in the storage unit. The step and the processing unit detect the bending point of the section line based on the normal or tangent data of the obtained adjacent point sequence data, and convert the point sequence data of the detected bending point into the point sequence data of the section line. Inputting and storing in the storage unit, the processing unit dividing the space into an accumulation of cubes according to the lattice-shaped point group, and the processing unit referring to the point sequence data stored in the storage unit, The step of calculating the intersection of the cross-section line in the x-axis direction and the cross-section line in the y-axis direction of the uppermost surface of the swept shape of the reverse tool and each side of each divided cube, and the processing unit, The step of arranging the triangle inside the cube by the marching cube method by determining whether the vertex of each cube exists above or below the tool path plane based on the information, and the processing unit is arranged inside each cube. A tool path surface calculation program for causing a computer to execute the step of outputting the group of triangles as an uppermost surface of the sweep shape to the output unit or storing the same in the storage unit. 10. The hidden surface erasing process of the graphics hardware, wherein the processing unit comprises a shape element forming a sweep shape of the reverse tool,
The step of preliminarily removing the part not related to the uppermost surface of the swept shape, such as the downward part of the shape element or the part included in other shape elements, and the processing part The processing unit reads the unique ID number, the unique color information, and the geometric information of the shape element for each arranged shape element from the storage unit, and obtains the color information for the polygons forming each shape element. Based on the color information received from the processing unit, the graphics hardware uses the hidden surface removal processing by the depth buffer to determine the depth of the top surface of the sweep shape at each point. Obtaining a value and color information at each point, and passing the obtained depth value and color information to the processing unit, the processing unit receives each value received from the graphic hardware. The step of generating point sequence data of the tool path surface indicating the uppermost surface of the sweep shape based on the coordinate data of the points and the depth value, and the processing unit refers to the storage unit based on the color information and refers to the uppermost surface. Obtain the ID and geometric information of the shape element corresponding to each point,
The processing unit causes the computer to execute the step of obtaining the normal direction at each point according to the coordinate data and geometric information of each point, and the step of outputting the coordinate data of the point group on the tool path surface and its normal or tangent information. The tool path surface calculation program according to claim 9 for. 11. A step of inserting the bending point into point sequence data of a section line and storing the point sequence data in a storage section, the processing section refers to the storage section, coordinate data representing the section line, and a tool path at each point. The step of reading the normal or tangent data of the surface, and the processing unit, for two consecutive points on each section line, if the two tangent or normal directions differ by more than a predetermined value, the section line between the two points. Has a bending point, the processing unit calculates a new bending point and adds it to the point sequence data, and the processing unit updates the point sequence data and the length of the updated point sequence. The tool path surface calculation program according to claim 9 or 10, for causing a computer to execute a step of storing or outputting data indicating the height. 12. A tool path surface calculation program for generating a tool path surface expanded by an inverse shape of the tool when a tool attached to a numerically controlled machine tool is moved along the path to machine a workpiece. Is a computer-readable recording medium in which the processing unit inputs the polyhedral model information and the tool shape information of the object to be processed, and stores the information in the storage unit; and the processing unit includes each element of the polyhedral model. The step of arranging each shape element forming the swept shape of the reverse tool, the processing unit, for each arranged shape element, a unique ID number, unique color information, and geometric information of the shape element. The step of storing in the storage unit, the processing unit, based on the input shape elements forming the sweep shape of the reverse tool, the coordinate data of the grid point group covering the uppermost surface of the sweep shape, and the point Using the hidden surface erasing process of the graphics hardware that outputs the normal or tangent data of the uppermost surface, the processing is repeated while shifting the position of the arranged shape element by a predetermined distance in the x-axis direction. A step of obtaining point sequence data including coordinate data obtained by subdividing the cross-section line in the x-axis direction and normal or tangent line data, and storing the data in a storage unit; and the processing unit performing hidden surface removal processing of graphics hardware. Using the above, the process is repeated while shifting the position of the arranged shape element in the y-axis direction by a predetermined distance, and includes the coordinate data and the normal line or tangent line data obtained by subdividing the cross-section line of the uppermost surface in the y-axis direction. The step of obtaining the point sequence data and storing it in the storage unit, the processing unit detects the bending point of the cross section line based on the obtained normal line or tangent line data of the adjacent point sequence data, and detects it. The step of inserting the point sequence data of the bending point into the point sequence data of the section line and storing it in the storage unit, the processing unit dividing the space into an accumulation of cubes according to the grid-like point group, and the processing unit Refers to the point sequence data stored in the storage unit, and intersects the cross-section line in the x-axis direction and the cross-section line in the y-axis direction of the uppermost surface of the swept shape of the reverse tool with each side of each divided cube. Based on the information of the calculated intersections, the processing unit determines whether the apex of each cube is above or below the tool path plane, and the triangle is formed inside the cube by the marching cube method. The arranging step, the processing section outputs the triangle group arranged inside each cube to the output section as the uppermost surface of the sweep shape, or stores it in the storage section, and a computer readable recording tool path surface calculation program. Do recording medium.