JP2822194B2 - Method and apparatus for creating a two-dimensional projection diagram of a three-dimensional shape model using a computer - Google Patents

Description

The present invention relates to a method and an apparatus for creating a two-dimensional projection diagram of a three-dimensional model in a CAD apparatus or the like.

[Summary of the Invention]

The inner product of the vector in the projection direction and the normal vector set on the curved surface of the three-dimensional shape model is obtained, and a two-dimensional curve connecting the points at which the values are projected to a point where the value is substantially zero is generated. This is a graphic processing method that enables high-precision dimensional conversion by using a dimensional projection outline.

[Conventional technology]

CAD / CAM that uses a computer to design a shape model with a free-form surface using three-dimensional data, and generates an NC program (tool path data) from the shape model to automatically process products or dies with NC machine tools. The system has been put to practical use.

Generally, a milling machine (milling machine) is used as the NC machine tool. This type of machine tool is characterized in that, in principle, it can only cut transversely in a direction perpendicular to the tool axis and cannot cut in the tool axis direction, that is, cannot drill down.

Therefore, in order to run the NC program generated based on the designed shape model, it is necessary to preliminarily rough-cut the block material to be cut in the procedure shown in FIG. That is, since the final shape (target curved surface) such as the one-dot chain line C cannot be directly cut out from the block material A using the ball end mill, first, using the flat end mill, the maximum outline of the article projected on the XY plane is used. A columnar body B having S as a cross section is cut out. Next, using a ball end mill, the target curved surface C is cut by shaving upward from below the tool axis (Z axis). 0.5mm for cutting B and C
Roughing is performed once, leaving a sufficient finishing allowance, and then the tool diameter is reduced to finish finish the desired curved surface.

The maximum outline S of the article projected on the XY plane can be easily obtained from the data of the plan view when the plan view is drawn when designing a three-dimensional shape model with the CAD system. Based on this, tool path data for a flat end mill for cutting a columnar body can be generated.

However, when designing a three-dimensional model, a plan view may not be drawn, and even if there is a plan view, the block material may be inclined with respect to the tool axis (Z-axis) due to the uniqueness of the three-dimensional shape. . Therefore, it is necessary to calculate a two-dimensional outline when the three-dimensional model is projected from an arbitrary direction.

Conventionally, a method of creating a two-dimensional projection from an arbitrary direction has been used for a simple three-dimensional display graphic such as a wire frame model for a display.

[Problems to be solved by the invention]

In order to create a tool path for rough machining of the columnar body B as shown in FIG. 10 based on the two-dimensional projection on the display, it is necessary to consider a finishing allowance for a maximum outline of the two-dimensional projection on the display. This method is based on the procedure of creating an external polygonal (polygonal) figure and forming a tool path for cutting out a columnar body having the figure as a cross section. Since the projected figure displayed on the display only roughly represents the outline of the plane of the actual 3D model with low accuracy, the polygons for roughing should have enough room so as not to interfere with the final finished surface. It had to be set very loosely. Therefore, it is extremely difficult to perform high-precision external roughing with a uniform allowance of 0.5 mm. Based on experience and intuition, the time required to drive the finish allowance to 0.5 mm through several roughing processes Has been conventionally performed.

In view of this problem, the present invention provides a high-precision three-dimensional model capable of generating a two-dimensional figure (maximum outline) in an arbitrary projection direction from three-dimensional patch data of a three-dimensional model designed using a Bezier surface or the like. An object is to provide a two-dimensional conversion method. Therefore, according to the present invention, a highly accurate outline rough cutting tool path such as a finishing allowance of 0.5 mm can be directly generated from three-dimensional design data, no matter how complicated the three-dimensional model is.

[Means for solving the problem]

A method for creating a two-dimensional projection diagram of a three-dimensional shape model using a computer according to the present invention includes the steps of: accumulating surface element data representing a three-dimensional shape model in a computer storage unit; Calculating a large number of normal vectors on the curved surface so as to cover based on the surface element data; calculating an inner product value of a vector in the projection direction and each normal vector; Extracting a point sequence on a zero curved surface to obtain corresponding three-dimensional point sequence data; and calculating projection point data obtained by projecting the extracted point sequence on a projection surface based on the three-dimensional point sequence data. ,
A step of calculating a two-dimensional curve passing through the projection point on the projection plane based on the projection point data; and a step of displaying the two-dimensional curve.

An apparatus for creating a two-dimensional projection diagram of a three-dimensional shape model using the computer of the present invention accumulates surface element data representing a three-dimensional shape model in its storage unit and performs the following calculations based on an accumulation program. A computer constituting the means, calculating means for calculating a large number of normal vectors on a curved surface set up so as to cover the surface of the three-dimensional shape model based on the surface element data, a vector in a projection direction and an individual method A calculating means for calculating an inner product value with a line vector, a calculating means for extracting a point sequence on a surface having an inner product value of substantially zero to obtain corresponding three-dimensional point sequence data, and a positive and negative inner product value Calculating means for interpolating between two adjacent points on the curved surface such that the inner product value becomes zero, adding the interpolated point data to the three-dimensional point sequence data, and projecting the extracted point sequence on a projection surface. The projection point data is calculated based on the three-dimensional point sequence data. And calculating calculating means, characterized by comprising a calculating means for calculating on the basis of the two-dimensional curve passing through the projected point on the projection plane to the projection point data, and display means for displaying the two-dimensional curve.

[Action]

If the projection direction is determined, the outermost contour line of the solid projected in that direction is generated with high accuracy using a two-dimensional curve. This two-dimensional curve is sufficiently accurate two-dimensional data obtained from three-dimensional solid data, and can be used for two-dimensional graphic processing. For example, rough machining tool path data for cutting a solid from a block material Can be used as the basic data for generating.

〔Example〕

FIG. 4 shows the overall configuration of the CAD / CAM system of the embodiment. In FIG. 4, a free-form surface generation unit 1 generates a shape data of a geometric model representing a three-dimensional free-form surface of an object based on an input operation of an operator in a portion corresponding to CAD, and accumulates the data in a file. The object is a machined article or a mold.

The created shape data is converted into machining data, that is, an NC program for determining a moving path of the cutting tool in the free-form surface cutting tool path generating unit 2. The machining data is dropped on a floppy disk and the NC milling machine 3 (NC
Automatic processing is performed by mounting a floppy disk on a milling machine or a machining center.

The free-form surface generating unit 1 and the free-form surface cutting tool path generating unit 2 are computers, and an input device 4 such as a keyboard or a digitizer for a user interface.
And a display device 5 such as a CRT.

The tool path generating unit 2 for free-form surface cutting shown in FIG. 4 includes a rough cutting process and a finish cutting process. The rough cutting process includes a rough machining process of cutting the columnar body B of FIG. B, a process of cutting the target curved surface C from which the finishing margin is left.

The principle of the method of the present invention is shown in the three-dimensional view of the main part in FIG. 1, and the processing procedure of the rough machining process included in the tool path generating unit 2 for free-form surface cutting is shown in FIGS.

First, as shown in FIG. 1, a projection direction vector J is input in step S1, and then, in step S2, a patch S of a curved surface is input.
Select (u, v). In this case, the projection direction is inclined with respect to the tool axis (Z axis).

In this example, the curved surface is designed as a Bezier curved surface which is an aggregate of quadrilateral surface elements (patches) as shown in FIG. Each patch is Is a bicubic parametric surface using parameters u, v (0 to 1) represented by the following equation, and 16 control point vectors P _ij
(I, j = 0 to 3).

In the next step S3, as shown in FIG.
Xn. n is a value specified arbitrarily and is set in consideration of accuracy. For example, in the case of 4, the parameters u and v are set to 0, 0.25, 0.5, 0.75 and 1, respectively, and S (u,
From the equation of v), the spatial coordinates (x,
y, z) are calculated. Next, in step S4, a normal vector N of the curved surface S (u, v) at the corner vertices of the triangle is determined. Next, in step S5, the inner product of the vector J in the projection direction and each normal vector N is determined, and in step S6, a point where the inner product value K is substantially zero is searched and extracted. In this case, a threshold at which the inner product value K can be regarded as zero is determined in consideration of the calculation error. The extracted point group is the outermost point of the solid viewed from the projection direction.

In order to perform the process of step S6 with higher accuracy, K =
The interpolation processing shown in FIG. 3 is preferably performed in combination with the search for the zero point. That is, in step S6a, a triangle having both positive and negative inner product values as vertices is extracted. Such a triangle has two positive inner product values and one negative inner product value at the vertex, or 2
This corresponds to one of the cases having two negative inner product values and one positive inner product value at the vertex. Triangles consisting solely of other positive or negative inner product values are excluded without being selected.

Next, in step S6b, as shown in FIG. 7, a perpendicular line having the height of the inner product value K is made perpendicular to the plane _formed by the vertices Q _ij1 , Q _ij2 and Q _{ij3 of the triangle} from each vertex, and the positive and negative inner product values Is linearly interpolated. In the example of FIG. 7, Q _ij1 and Q _ij2 (inner product + k ₁ , −k ₂ )
Points and between Q _IJ3 and Q _ij2 (inner product + k _3, -k ₂₎ Since there is a point where the inner product is zero during, between points _{Q ij1, Q ij2, Q ij3} k 1: k 2 And points Ma and Mb proportionally divided by k ₃ : k ₂ are obtained. These points are the outermost points of the solid as viewed from the projection direction.

By repeating the processing of the above steps S2 to S6 (S6a, S6b) for patches of all curved surfaces, a row of the outermost points M of the solid is obtained as shown in FIG.

In the next step S7, as shown in FIG. 8, the intersection G of the extension line of the projection direction vector J passing through each outermost point M (x, y, z) and the projection plane R orthogonal to the vector J
(X, y, z) is determined. Projection plane R passes through the origin of the X-Y-Z coordinate axes, a virtual plane inclined at a predetermined angle theta _x, by theta _y correspond to the direction of the vector J with respect to the X-axis and Y-axis. Next, at step S8, a point G '(x, y) on the XY plane corresponding to the intersection G when rotated by-[theta] _x ,-[theta] _y so that the projection plane R coincides with the XY plane. ) Is determined by coordinate rotation calculation. This point G 'is the outermost point of the solid when the J direction is reviewed as the tool axis (Z axis).
This row of the outermost points G 'is displayed on the display 5 in the next step S9. The line connecting the point sequence G 'is the outermost contour line S to be cut.

Next, in step S10 in FIG. 2, a display point sequence G 'is selected. That is, an appropriate point G 'is set such that the point sequence G' is distributed substantially uniformly along the outermost contour line of the solid viewed from the projection direction.
Select and thin others. Next, a spline curve S passing through the point sequence is generated in step S11, and is displayed on the display 5 in step S12. If there is a discontinuous point corresponding to the solid edge in the point sequence G ', separate spline curves are generated on both sides of the discontinuous point.

As a result, the outermost line S shown in FIG. 9 is obtained.
Next, in step S11, the tool path T offset by the sum t + r of the finishing allowance t (for example, 0.5 mm) and the tool radius r of the flat end mill 8 is defined as a normal vector having a length of t + r set at a point on the line S. Generated by a spline curve connecting the vertices. At this time, if there is a tool interference portion where the spline curve of the tool path T is generated by crossing, this is checked in step S14, and a continuous tool path that protrudes at the intersection is formed.

Based on the tool path T generated as described above, the columnar body B is cut out of the block material A by a flat end mill as shown in FIG. At this time, if necessary, the tool axis (Z
The block material A is directed in the direction of the projection direction vector J with respect to (axis). Next, the target curved surface C in FIG. 10 is cut using a ball end mill in accordance with the rough cutting tool path calculated from the data of the designed three-dimensional model. As a result, it is possible to obtain an intermediate processed product having a rough processing curved surface C with a finishing allowance of 0.5 mm, and a final three-dimensional object can be cut out by performing the finishing processing while changing the tool diameter.

As a special case, when the projection direction is coincident with the tool axis (Z axis), the processing in steps S7 and S8 in FIG. 2 is unnecessary, and the projection outline on the XY plane is directly You can ask.

The above is an example in which the present invention is applied to the roughing process. However, the present invention can also be applied to general dimension conversion processing for creating a two-dimensional projection from a three-dimensional solid model.
Such a dimension conversion is used when evaluating the cross-sectional outline of a design solid or transferring data from a three-dimensional CAD system to a two-dimensional CAD system.

Opening (pocket) inside the solid like a donut shape
Exists, the innermost line of the opening can be obtained as the outermost line. Therefore, a three-dimensional rough machining two-dimensional projection having a pocket can be created in a similar procedure.

〔The invention's effect〕

According to the present invention, a two-dimensional projection diagram (outermost line) can be calculated and obtained from a three-dimensional three-dimensional shape model, and highly accurate dimensional conversion can be performed. Since the converted data is obtained with sufficient accuracy that can be used as design data, three-dimensional two-dimensional processing can be performed in a short time based on the converted data.

For example, finding the two-dimensional outermost line of the solid in the tool axis direction,
By generating a tool path (NC program) along the outermost contour line, rough machining of a solid with a finishing margin of about 0.5 mm can be performed with high accuracy in a short time. Conventionally, in order to generate this kind of tool path for rough machining, a tool path is generated by an external polygon (polygonal line) on a display, so that only extremely rough external machining can be performed. A significant improvement over time is obtained.

[Brief description of the drawings]

FIG. 1 is a view of a main part of a three-dimensional solid model showing the principle of the present invention, FIG. 2 is a flowchart showing a roughing process when cutting a solid from a block material, and FIG. FIG. 4 is an overall block diagram of a CAD / CAM system, FIG. 5 is a three-dimensional diagram showing patches of a Bezier surface, FIG. 6 is a three-dimensional diagram showing division of patches, FIG. Is a diagram showing an interpolation method, and FIG.
FIG. 9 is a diagram showing a procedure for obtaining the outermost point on a plane, FIG. 9 is a diagram showing a rough machining path, and FIG. 10 is a three-dimensional diagram showing a rough machining process. In addition, in the reference numerals used in the drawings, 1 ... free-form surface generation processing unit 2 ... free-form surface cutting tool path generation unit 3 ... NC milling machine 4 ... input device 5 ... display 8 ... flat end mill J ... Projection direction vector M: outermost point S: outermost line

Claims (2)

(57) [Claims] 1. A step of accumulating surface element data representing a three-dimensional shape model in a computer storage unit, and converting a plurality of normal vectors on a curved surface set up to cover the surface of the three-dimensional shape model into the surface element data. And calculating the inner product value of the vector in the projection direction and each normal vector. Extracting a point sequence on a surface having an inner product value of approximately zero and corresponding three-dimensional point sequence data And calculating the projected point data obtained by projecting the extracted point sequence on the projection plane based on the three-dimensional point sequence data; and calculating the two-dimensional curve passing through the projection point on the projection plane with the projection point data A method for creating a two-dimensional projection diagram of a three-dimensional shape model using a computer, comprising the steps of: 2. A computer which stores surface element data representing a three-dimensional shape model in a storage unit thereof and constitutes each of the following calculation means based on a storage program, and a stand which covers a surface of the three-dimensional shape model. Calculating means for calculating a large number of normal vectors on the curved surface based on the surface element data; calculating means for calculating an inner product value between the vector in the projection direction and each normal vector; Calculating means for extracting a sequence of points on the surface to obtain corresponding three-dimensional point sequence data; and calculating the inner product value between two adjacent points on the surface having positive and negative inner product values so that the inner product value becomes zero. Interpolation and interpolation point data
Calculating means for adding the extracted point sequence to the projection surface based on the three-dimensional point sequence data; calculating means for adding the extracted point sequence to the projection plane based on the three-dimensional point sequence data; An apparatus for creating a two-dimensional projection diagram of a three-dimensional shape model using a computer, comprising: calculation means for calculating a curve based on the projection point data; and display means for displaying the two-dimensional curve. .