JP2811430B2 - CAD system and data converter for Bezier curve in CAD system - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

TECHNICAL FIELD The present invention relates to CAD (Computer Aided Desi
gn) system and a data conversion device for Bezier curves in a CAD system.

[0002]

BACKGROUND ART Designers (or illustrators) and engineers sometimes collaborate when designing a new product. The designer creates an illustration of the new shape of the product, and based on this illustration, the engineer performs a detailed design (called a product design) from a technical point of view.

When a designer creates an illustration of a product, a CAD system (hereinafter referred to as a "simple CAD system") suitable for creating an illustration (an illustration program is incorporated) is used. In this simplified CAD system, illustrations of various products are created using graphic elements (sometimes called segments or parts) such as points, straight lines (line segments), free curves (cubic Bezier curves, etc.). Can be. In the simple CAD system, the data related to the illustrations created for the products is stored in EPSF (Encapsu
lated PostScript Format).

When an engineer designs a product,
A CAD system for design support is used. Design support C
Also in the AD system, it is possible to design various product shapes using graphic elements such as points, straight lines (line segments), and free curves (for example, quintic Bezier curves). In a CAD system for design support, data on a designed shape of a product is described in a format unique to the system.

Since data is described in different formats in the simple CAD system and the CAD system for design support, it is impossible to transmit a data file from one CAD system to the other CAD system. data·
Data exchange specifications are provided for format conversion. IGES (Initial
Graphics Exchange Specification). If data format conversion is performed according to this data exchange specification, data can be exchanged between different systems.

In a simple CAD system, a free curve is represented by a cubic Bezier curve. In a CAD system for design support, high accuracy is required.
Next) It is represented by a Bezier curve. Data representing a cubic Bezier curve cannot be converted to data representing a quintic Bezier curve according to the data conversion specifications. Therefore, the simple C
Illustration data for products including free curve data created by the AD system is directly used as CAD for design support.
It cannot be used in the system. Conventionally, the same shape as the product represented by the illustration created by the designer using the simple CAD system was created by the engineer from the beginning using a CAD system for design support that is different from the simple CAD system used by the designer. I had to fix it. That is, the illustration data created by the simple CAD system cannot be used in the CAD system for design support.

[0007]

DISCLOSURE OF THE INVENTION The present invention relates to a simple CAD system (first
This makes it possible to use the data relating to the illustration created by the CAD system (a CAD system) in a CAD system for design support (a second CAD system). In particular, in order to use the data of the simple CAD system in the CAD system for design support, it is necessary to convert the order of the data relating to the Bezier curve.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a Bezier curve data converter capable of converting an nth-order Bezier curve into a higher-order, lower-order, or the same mth-order Bezier curve in a CAD system. The invention also provides
A CAD system including such a data conversion device is provided. Here, n and m are integers of 3 or more.

A CAD system according to the present invention is a file of basic data required to display data representing an image on a bit map memory in order to display an image representing the product. And a CAD data base for storing a CAD data file containing control point data defining an n th order Bezier curve representing

According to the present invention, there is provided a data conversion apparatus for converting control point data defining an nth-order Bezier curve into control point data defining an mth-order Bezier curve, from a CAD data file stored in the CAD data base. Bezier curve extracting means for extracting data representing an nth-order Bezier curve,
a first parameter determining means for determining (m + 1) parameters that give (m + 1) points on the nth-order Bezier curve at equal intervals within a predetermined parameter range; Coordinate determination for determining coordinate data representing (m + 1) points on an nth-order Bezier curve using (m + 1) parameters determined by the parameter determination means and control point data defining an nth-order Bezier curve. A tangent vector determining means for determining two unit tangent vectors representing a gradient at each of a starting point and an ending point of the n-dimensional Bezier curve using control point data defining the n-dimensional Bezier curve; (M + 1) parameters giving (m + 1) points of the above, and coordinate data representing (m + 1) points on the n-th order Bezier curve, respectively. Based on the two unit tangent vectors at the start point and end point of the nth-order Bezier curve, the gradient at the start point and the end point of the nth-order Bezier curve is preserved, and the gradient is passed at or near a point on the nth-order Bezier curve. And a control point determining means for determining control point data defining an m-order Bezier curve.

[0011]

In one embodiment of the present invention, control point data defining a cubic Bezier curve is converted into control point data defining a quintic Bezier curve. That is, n = 3 and m = 5.

According to the present invention, conversion from low order to high order (n <
m), conversion from higher order to lower order (n> m) can also be performed. It is also possible to convert to the same order (n = m), which is particularly effective when eliminating degeneration of control points.

The CAD system and data converter according to the present invention are particularly useful in the following design systems.

This design system comprises a first CAD system and a second CAD system.

The first CAD system includes a first data file and first conversion means. The first data file is a collection of data representing an illustration of a product having a curve, and includes control point data defining an nth-order Bezier curve representing the curve. The first conversion means converts the first data file into a common data file having a data format common to a plurality of types of CAD systems.

The second CAD system has a second conversion means and a CAD database. The second conversion means converts the common data file transmitted from the first CAD system into a CAD data file having a data format unique to the second CAD system. The CAD data base stores a converted CAD data file including control point data defining an nth-order Bezier curve.

The CAD system according to the present invention corresponds to the second CAD system in the above-mentioned design system.

In the above example, the simple CAD system corresponds to the first CAD system, and the CAD system for design support corresponds to the second CAD system.

The data representing the illustration created in the simple CAD system is output after being converted into an IGES data file which is a common data file. In a CAD system for design support, an IGES data file is converted into a CAD data file by a CAD data conversion means and stored in a CAD data base. Since the free curve included in the IGES data file is represented by an nth-order (third-order) Bezier curve, the free curve included in the CAD data file stored in the CAD database is also nth-order (third-order). ) Represented by a Bezier curve.

According to the present invention, (m + 1) parameters that respectively provide (m + 1) points on the nth-order Bezier curve are determined at equal intervals within a range that a predetermined parameter can take. Using the (m + 1) parameters and the control point data that defines the nth-order Bezier curve, coordinate data representing (m + 1) points on the nth-order Bezier curve is determined. Two unit tangent vectors at the start point and the end point of the nth-order Bezier curve are determined using the control point data defining the nth-order Bezier curve. (M +
Based on 1) parameters, coordinate data representing (m + 1) points, and two unit tangent vectors, the gradients at the start point and end point of the nth-order Bezier curve are stored, and Pass through or near a point, m
Control point data that defines the next Bezier curve is determined.

That is, control point data defining an nth-order Bezier curve included in a CAD data file obtained by converting an IGES data file relating to an illustration of a product created in a simple CAD system is converted to a CAD system for design support. Is converted into control point data that defines the m-th order Bezier curve required in step (1). This converted C
A product shape can be created on a CAD system for design support based on an illustration (drawing) represented by an AD data file.

In this manner, the data representing the illustration created by the simple CAD system is transferred to the CAD for design support.
It can be used as CAD data in the system. In a CAD system for design support, an engineer can design a product using CAD data.

Therefore, the engineer does not need to recreate the same product shape as the product illustration created on the simple CAD system from the beginning on the CAD system for design support, thereby saving time and effort. Also, since the control point data of the m-th order Bezier curve preserves the gradient at the start point and end point of the n-th order Bezier curve, and is converted so that the m-th order Bezier curve passes through or near a point on the n-th order Bezier curve. The shape of the product is the same as or very similar to the illustration of the product created in the simple CAD system.

The CAD system according to the present invention includes display control means for displaying an image representing a product on a display device based on the CAD data thus obtained.

The display control means includes means for generating data for displaying a product based on CAD data including control point data defining the m-th order Bezier curve converted by the data conversion means, and converting the display data. There is provided a means for developing on a bit map memory. bit·
An image of the product reflected by the data developed on the map memory is displayed on the display device of the CAD system.

In some cases, the control points defining the nth-order Bezier curve are degenerated. Degeneration means that two control points overlap at the start point or end point of the Bezier curve. A tangent vector cannot be defined at the start point or the end point where the control points are degenerated.

According to the present invention, even when the control point is degenerate at the start point or the end point, the control point data defining the m-th order Bezier curve can be calculated.

In a preferred embodiment of the present invention,
When the control point is degenerate at the start point or end point of the nth-order Bezier curve, the unit tangent vector is determined by approximation.

In this way, even if the control point is degenerated at the start point or the end point, the unit tangent vector at the degenerated end point can be determined, so that the control point data defining the m-th order Bezier curve can be obtained. it can.

When the control points are degenerated at the start point or the end point of the n-th order Bezier curve, the control points defining the m-th order Bezier curve after the degree conversion may also be degenerated.

In such a case, in the present invention, the control points that define the m-th order Bezier curve can be determined so that they do not degenerate.

In a further preferred embodiment of the present invention, the coordinate data representing (m + 1) points on the n-th order Bezier curve determined by the coordinate determining means is used.
A second method for determining (m + 1) parameters according to the length of the nth-order Bezier curve from the start point of the nth-order Bezier curve to each point
Is further provided. The control point determining means uses the parameters determined according to the length of the nth-order Bezier curve by the second parameter determining means instead of the parameters determined at equal intervals by the first parameter determining means. Then, the control point data is determined. This method of determining the control point data can be used even when the control points are not degenerated.

According to this embodiment, the coordinate data representing (m + 1) points on the n-th order Bezier curve is used to correspond to the length of the n-th order Bezier curve from the starting point of the n-th order Bezier curve to each point. (M + 1) parameters are determined. This n
(M + 1) parameters corresponding to the length of the next-order Bezier curve, coordinate data representing (m + 1) points on the nth-order Bezier curve, and two unit tangents at the start point and the end point of the nth-order Bezier curve Based on the vector, control point data that defines an m-order Bezier curve is determined.

Therefore, even when the control points are degenerate at the start point or end point of the n-th order Bezier curve, control point data that defines the m-th order Bezier curve where the control points do not degenerate can be obtained.

[0036]

【Example】

Table of contents 1 Outline 2 Bezier curve 3 Simple CAD system 3.1 Graphic element drawing 3.2 EPSF data file 3.3 IGES data file 4 CAD system for design support 4.1 CAD data file 4.2 Order conversion from cubic Bezier curve to quintic Bezier curve 4.2.1 Calculation of parameters 4.2.2 Calculation of points on cubic Bezier curve 4.2.3 Calculation of unit tangent vector at start point and end point 4.2.4 Calculation of control points of quintic Bezier curve 4.3 3 Degree conversion from cubic Bezier curve to quintic Bezier curve (when there is degeneration; Part 1) 4.3.1 Approximate calculation of unit tangent vector at start point and end point 4.4 Degree conversion from cubic Bezier curve to quintic Bezier curve (degeneration) 2) 4.4.1 Recalculation of parameters 4.5 Order conversion from nth-order Bezier curve to mth-order Bezier curve 5 Drawing of Bezier curve 5.1 Hardware structure 5.2 Processing for displaying Bezier curves

1 Outline FIG. 1 is a block diagram showing an outline of a software configuration of a simple CAD system and a CAD system for design support.

Simple CAD System 10 and Design Support C
Each of the AD systems 20 is realized by a programmed computer system. The simple CAD system 10 and the CAD system for design support 20 are connected by a communication cable or a network. Two CAD
When the system is not connected, a data file or the like is transmitted from the simple CAD system 10 to the design support 20 using a storage medium such as a floppy disk. The simple CAD system 10 and the CAD system 20 for design support can be realized by one computer system.

The simple CAD system 10 is a well-known system that allows a designer to draw a product illustration using a mouse or the like.

The simple CAD system 10 is provided with an EPSF (Encap
sulated PostScript Format) database 11 and I
A GES (Initial Graphics Exchange Specification) data conversion process 12 is provided.

The EPSF database 11 contains a simple CA
An EPSF data file relating to a product illustration created in the D system 10 is stored. The details of the EPSF data file will be described later, but the page description language
It is written in PostScript.

The IGES data conversion processing 12 converts an EPSF data file into an IGES data file (details will be described later), and is already known.

In the CAD system 20 for design support, an engineer creates data representing the shape of a product by using a mouse or the like.

The CAD system 20 for design support includes a CAD data conversion process 21, a CAD data base 22, and an order conversion process 23.

The CAD data conversion process 21 converts an IGES data file into a CAD data file (details will be described later), and is already known.

The CAD data base 22 includes a CAD data file representing the shape of a product designed in the CAD system 20 for design support, a CAD data file converted by the CAD data conversion processing 21, or a CAD data file described later. The CAD data file converted by the degree conversion processing 23 is stored.

The order conversion processing 23 is for converting control point data defining a cubic Bezier curve, which will be described later, into control point data defining a quintic Bezier curve.

The data bases 11 and 22 are realized by a memory device. The memory device includes a semiconductor memory, a magnetic disk, an optical disk, and the like, and may be an internal memory of a computer system or an external memory. The various processes 12, 21, and 23 mean a series of systematic operations or functions performed by a computer system in accordance with a program in order to achieve each purpose. Therefore, various processes are realized by combining a computer system and a program for causing a computer to execute the processes.

Simple CAD System 10 and Design Support C
On the AD system 20, a product illustration and shape are created by combining a plurality of graphic elements such as points, straight lines, free curves, and free-form surfaces. Generally, a free curve is represented by a Bezier curve, a rational B-spline curve, or the like. In the simple CAD system 10, the free curve is represented by a cubic Bezier curve, and the CAD for design support is used.
In the system 20, the free curve is represented by a cubic Bezier curve.

Simple CAD System 10 and Design Support C
In the AD system 20, the graphic elements are mathematically described in order to perform objective description of the graphic elements, processing and analysis of the graphic elements, and the like. The graphic elements are described in a data file for each system in a format that allows easy processing and the like in the system. Simple CAD system
In 10, the data file is described in EPSF, and in the CAD system 20 for design support, it is described in a format unique to the system.

As described above, since each CAD system has a data file of a different format,
Cannot transfer data files between systems. A data exchange specification for data format conversion is provided.
There is GES.

The simple CAD system 10 includes an IGES data conversion processing 12 for converting an EPSF data file and an IGES data file between each other.
Data files can be input and output.

The CAD system 20 for design support is a CAD data conversion process 21 for mutually converting a CAD data file unique to the system and an IGES data file.
IGES data file can be input and output.

In order to design the product shape on the design support CAD system 20 using the data representing the product illustration created by the designer in the simple CAD system 10 as basic data, Good.

An EPSF data file relating to a product illustration created in the simple CAD system 10 is
The EPSF data file is read from the PSF data base 11 and the EPSE data file is
Convert to S data file. This IGES data
Files are converted from simple CAD system 10 to CAD for design support
It is provided to the system 20 via data transfer or a recording medium.

In the CAD system 20 for design support,
The given IGES data file is converted into a CAD data file by a CAD data conversion process 21, and the CAD data file is stored in a CAD database 22.

As described above, in the simple CAD system 10, the free curve is represented by a cubic Bezier curve, and in the CAD system 20 for design support, the free curve is represented by a quintic Bezier curve. A cubic Bezier curve is extracted from the CAD data file converted from the IGES data file, and the control point data relating to the cubic Bezier curve is converted into control point data relating to the quintic Bezier curve by the degree conversion processing 23.

The engineer designs a product on the CAD system 20 for design support based on the shape represented by the CAD data file containing the control point data on the converted quintic Bezier curve.

This eliminates the need for the engineer to create data representing the same shape as the illustration of the product created by the designer from the beginning, and makes it possible to design using the illustration data of the product created by the designer. it can.

2 Bezier Curve Simple CAD System 10 and CAD System for Design Support
A Bezier curve used to represent a free curve in 20 will be described.

Generally, an n-th order Bezier curve P (t) is represented by the following vector equation. Where P (t) = (x
(T), y (t), z (t)).

[0062]

(Equation 1)

(Equation 2)

In equation (1), Q _i is a control point that defines an nth-order Bezier curve. The control point Q _i is expressed as Q _i = (Q _{i, x} , Q _{i, y} , Q _{i, z} ) using XYZ three-dimensional orthogonal coordinates. The control points are Q ₀ , Q ₁ ,
There are (n + 1) Q ₂ ,..., Q _n . t is a parameter that gives a point on the nth-order Bezier curve.

In equation (2), B _{i, n} (t) is
It is an in basis function (Bernstein Basis Function).

The cubic Bezier curve P (t) is expressed by the following equation by setting n = 3 in equation (1).

[0066]

(Equation 3)

The cubic Bezier curve has four control points Q ₀ ,
It is defined by Q ₁ , Q ₂ and Q ₃ .

In equation (2), n = 3 and
Substituting into (3) and rearranging, the cubic Bezier curve P (t) is expressed by the following equation.

P (t) = (− t ³ + 3t ² −3t + 1) Q ₀ +3 (t ³ −2t ² + t) Q ₁ +3 (−t ³ + t ² ) Q ₂ + t ³ Q ₃ (4)

By rearranging equation (4) for t, t ² and t ³ , the equation representing the cubic Bezier curve P (t) is as follows.

P (t) = (− Q ₀ +3 Q ₁ −3 Q ₂ + Q ₃ ) t ³ +3 (Q ₀ −2 Q ₁ + Q ₂ ) t ² +3 (−Q ₀ + Q ₁ ) t + Q ₀ (5)

The starting point of the cubic Bezier curve is given by the following equation by setting t = 0 in equation (5).

P (0) = Q ₀ (6)

The end point of the cubic Bezier curve is given by the following equation by setting t = 1 in equation (5).

P (1) = Q ₃ (7)

As can be seen from equations (6) and (7), 3
Origin P of the next Bezier curve (0) coincides with the control point Q _0, the end point P (1) corresponds to the control point Q _3. This property generally holds for an nth-order Bezier curve.

The tangent vector at the point P (t) on the cubic Bezier curve is obtained by differentiating the cubic Bezier function P (t) of the equation (5) with the parameter t, which is expressed by the following equation. .

[0078]

(Equation 4)

The tangent vector at the starting point P (0) of the cubic Bezier curve can be obtained by setting t = 0 in equation (8).
It is given by:

[0080]

(Equation 5)

The tangent vector at the end point P (1) of the cubic Bezier curve is obtained by rearranging the equation (8) with t = 1, and is given by the following equation.

[0082]

(Equation 6)

As can be seen from equations (9) and (10), 3
Tangent vector at the starting point P (0) of the next Bezier curve is represented using control points Q ₀ and Q _1, the tangent vector at the end point P (1) is expressed using the control point Q ₂ and Q _3. This property generally holds for an nth-order Bezier curve.

3 Simple CAD System 3.1 Drawing of Graphic Elements The creation of an illustration in the simple CAD system 10 will be briefly described. The illustration is drawn by combining a plurality of straight lines and cubic Bezier curves as described above.

FIGS. 2A to 2D and FIGS. 3A to 3D show how a designer draws a cubic Bezier curve on the simple CAD system 10.
This is shown in FIG. 3c. In these figures, arrows indicate the positions of cursors on the display screen of the simple CAD system 10.

Referring to FIGS. 2A to 2D, the designer first operates the mouse to move the cursor to a desired position (point A), and presses the mouse button to specify the starting point A (FIG. 2A). . Next, the mouse is dragged from the start point A to move the cursor to a desired position (point B), the tangent direction (tangent vector) at the start point is determined, and the mouse button is released (FIG. 2B). A straight line connecting the point B with the position of the point object and the point B with the point A as a center is displayed so that the tangent direction at the start point A can be easily understood. Then, the user operates the mouse to move the cursor to a desired position (point C), and presses the mouse button to specify the end point C (FIG. 2).
c). Finally, the mouse is dragged from the end point C to move the cursor to a desired position (point D) to determine the tangent direction at the end point, and release the mouse button. Then, the point E is designated at a position symmetrical to the point D with respect to the point C (FIG. 2D). The curve from point A to point C is 3
This is a next Bezier curve, and four points A, B, E and C become control points Q ₀ , Q ₁ , Q ₂ and Q ₃ , respectively.

The EPSF data for the cubic Bezier curve thus drawn is as follows.

Q _{0, x} Q _{0, ym} Q _{1, x} Q _{1, y} Q _{2, x} Q _{2, y} Q _{3, x} Q _{3, y} c

“M (moveto)” is a graphics command indicating that the point described before this command “m” is the starting point, and “c (curveto)” is the command “C (curveto)”. Is a graphics command indicating that a cubic Bezier curve should be drawn using the point described before "" as a control point. Since the simple CAD system 10 draws a two-dimensional illustration, the coordinate data of the control point is only the x coordinate and the y coordinate. A cubic Bezier curve is defined by two graphics commands and four sets of control point data.

When another cubic Bezier curve or straight line is drawn successively to the cubic Bezier curve represented by the above EPSF data, the EPSF data representing the other cubic Bezier curve or straight line is represented by Q _3, It is described following the data of the EPSF with _x , Q3 _{, and y} as starting points.

After specifying the point C by pressing the mouse button (FIG. 2c), even if the mouse button is released without specifying the tangential direction (point D) at the end point C, the point A
A cubic Bezier curve from to is drawn. In this case, since the point E is not defined, so that the control point Q ₂ is not defined.

The data related to the cubic Bezier curve drawn as described above is described as follows.

Q _{0, x} Q _{0, y} m Q _{1, x} Q _{1, y} Q _{3, x} Q _{3, y} y

"Y" is also a graphics command indicating that a cubic Bezier curve should be drawn. Since the graphics command is not the coordinate data control points Q ₂ is at "y", the control point Q ₂ is made to have the same coordinate data and forcibly control point Q _3. That is, the control point Q ₂ and Q ₃ are identical. Such a coincidence of two control points is referred to as degeneracy, and a coincidence between the end point (control point Q ₃ ) and the control point Q ₂ is referred to as degeneracy of the end point.

A cubic Bezier curve can be drawn as follows.

A description will be given with reference to FIGS. 3A to 3C. The designer operates the mouse to move the cursor to the desired position (point A).
And click the mouse to specify the starting point A (FIG. 3a). Next, operate the mouse to the desired position (point B)
And press the mouse button to specify the end point B (FIG. 3b). Finally, drag the mouse from the end point B to move the cursor to a desired position (point C), determine the tangential direction, and release the mouse button to specify the point C (FIG. 3c). At this time, the point D is designated at a position symmetrical with the point C with respect to the point B. The curve from point A to point B is a cubic Bezier curve. The three points A, D and B become control points Q ₀ , Q ₂ and Q _{3 respectively} , and the control point Q ₁ is not defined.

The data relating to the cubic Bezier curve thus drawn is described as follows.

Q _{0, x} Q _{0, y} m Q _{2, x} Q _{2, y} Q _{3, x} Q _{3, y} v

"V" is a graphics command indicating that a cubic Bezier curve should be drawn. Since the graphics command is not the coordinate data is the control point Q ₁ at the time of the "v", the control point Q ₁ will have the same coordinate data and forcibly control point Q _0. That is, the control points Q ₀ and Q ₁ match. Thus, the fact that the start point (control point Q ₀ ) and the control point Q ₁ coincide with each other is called that the start point is degenerated.

A straight line is drawn as follows.

Referring to FIGS. 3A and 3B, the designer operates the mouse to move the cursor to a desired position (point A) and clicks the mouse to specify the starting point A (FIG. 3).
a), an end point B is designated by clicking the mouse at another desired position (point B) (FIG. 3B). A straight line is drawn between the start point A and the end point B.

The EPSF data for a straight line is represented as follows.

[0103] _{x 0 y 0 m x 1 y} 1 l

X ₀ and y ₀ represent the coordinates of the start point A, and x ₁ and y ₁ represent the coordinates of the end point B, respectively. “L (lineto)” is a graphics command indicating that a straight line should be drawn.

As described above, graphic elements are drawn in the simple CAD system.

3.2 EPSF Data File FIG. 4 shows an example of a product illustration drawn in the simple CAD system. The illustration of this product shows a bottle, a top view and a front view of the bottle. The area indicated by hatching is actually colored.

FIGS. 5, 6 and 7 show an example of the EPSF data file, which contains EPSF data representing a part of the bottle illustration shown in FIG. This EPSF data
The file is the EPSF data of the simple CAD system 10
Stored in the base 11.

In this EPSF data file,
The first "%! PS- * d * b * -3.0 ... %% Endsetup"
In the portion from the line to the sixth line in FIG. 6, a creation system (software) name, a creator name, a file name, a comment such as a creation date and time, and a setting parameter such as a color are described. Last"%%
The end of the setting parameter is described in the portion of “PageTrailer.
Data relating to the graphic element is described between them.

For example, in this EPSF data file, data relating to the first graphic element (third-order Bezier curve (no reduction)) (lines 15 to 16 in FIG. 6) relates to element C1 shown in FIG. . The first and second rows in FIG. 7 are data on a straight line representing the element L21, and the third row in FIG. 7 is data on a graphic element (cubic Bezier curve (the starting point is degenerated)) representing the element C22. It is.

3.3 IGES Data File As described above, the EPSF data file stored in the EPSF data base 11 is subjected to the IGES data conversion processing.
It is converted to an IGES data file by 12.

FIGS. 9, 10 and 11 show an example of an IGES data file. This IGES data file was obtained by converting the EPSF data file shown in FIGS.

The IGES data file includes a start part (S), a global part (G), a directory part (D), a parameter part (P), and a termination part (T).

At the start, a comment or the like is described. The beginning is indicated by an S in the 73rd digit.

In the global part, precision, units, and the like are described. The global part is represented by a G in the 73rd digit.

In the directory portion, for each graphic element (straight line or rational B-spline function), a number indicating the type of graphic element (straight line: TYPE 110, rational B-spline function: TYPE 1)
26), level, line width, etc. are described. The 73rd digit of the directory part is represented by D.

In the parameter part, graphic elements are described in different formats. In the parameter part, the 73rd digit is P, and the numerical value before it indicates the line number in the directory part.

Parameters relating to the straight line include the coordinates of the start point and the coordinates of the end point of the straight line.

Parameters relating to the rational B-spline function include a knot vector, a weight vector, a control point, and the like. By properly selecting the knot vector and the weight vector, the cubic Bezier curve of the EPSF data file can be accurately represented by the rational B-spline curve. The order of the rational B-spline function and the Bezier curve are the same, and the control point of the rational B-spline function and the control point of the cubic Bezier curve are equivalent.

The start point and end point of the straight line and the control points of the rational B-spline function are represented by x coordinates, y coordinates, and z coordinates. In the EPSF data file, the coordinate data is x
Since only the coordinates and the y coordinates were used, the z coordinates are all "0.0" in the IGES data file. EPS
Since different unit systems are used in the F data file and the IGES data file, the numerical values of the x coordinate and the y coordinate are different.

In the end part (T), the number of records (the number of lines) of the start part, the directory part and the parameter part is described. In the IGES data file shown in FIGS.
The number of records S in the start part is “1”, the number of records G in the global part is “3”, the number of records D in the directory part is “78”, and the number of records P in the parameter part is P
Is "103".

The IGES data file converted by the IGES data conversion processing 12 is supplied from the simple CAD system 10 to the CAD system 20 for design support.

4. CAD System for Design Support A processing procedure relating to data conversion in the CAD system for design support 20 will be described below. Fig. 12 CAD for design support
2 shows an overall processing procedure in the system 20.

IG output from simple CAD system 10
The ES data file is fetched (step 101), and this IGES data file is converted to the CAD data conversion processing 21
Is converted to a CAD data file (step
102). By this transformation, the rational B-spline function becomes 3
It is converted to the next Bezier curve. Converted CAD data
The file is stored in the CAD database 22 (step 103).

The CA stored in the CAD database 22
The control point data defining the cubic Bezier curve is extracted from the D data file for each element (step 104), and the control point data defining the cubic Bezier curve is converted into control point data defining the quintic Bezier curve. The conversion is performed by the processing 23 (step 105). In the CAD data file,
The four control point data defining the extracted cubic Bezier curve are updated to the six control point data defining the converted quintic Bezier curve (step 106). Steps 104 to 106 are performed for all the cubic Bezier curves included in the CAD data file (step 107).
).

4.1 CAD Data File FIG. 13 shows an example of a CAD data file. This is a CA obtained by converting the IGES data file shown in FIGS.
D data file.

The CAD data file contains an element number,
Contains element type and coordinate data.

An element number is a number for identifying an element.

The element type indicates whether the element is a straight line (LINE) or a free curve (CRVE). The free curve is a fifth-order Bezier curve as described above. The types of the elements are not limited to two, namely, a straight line and a free curve. In addition, a circle, a circular arc, or the like may be used. In such a case, a symbol representing those types is used.

If the type is LINE, the coordinate data is the coordinate data of the start and end points of the straight line, and the type is CRVE.
In the case of (1), it is coordinate data of the control point.

In the CAD data conversion, the IGES data
In the file, the coordinate data of the start and end points of the parameter part for the graphic element of TYPE 110 (straight line)
NE), and the coordinate data of the control point of the parameter part regarding the graphic element of the rational B-spline function of TYPE 126 becomes the coordinate data of the free curve (CRVE) (the control point of the cubic Bezier curve) as it is.

FIG. 14 is a drawing of a product represented by the CAD data file shown in FIG. This figure is
(Each color information is lost when the EPSF data file is converted to the IGES data file.)

FIG. 15 is a diagram showing control points (represented by “x”) for elements C1 and C22, which are cubic Bezier curves. Since the element C1 is not degenerated, there are four control points. However, since the start point of the element C22 is degenerated, there are apparently only three control points.

4.2 Degree conversion from cubic Bezier curve to quintic Bezier curve (when there is no degeneration) Conversion processing of cubic Bezier curve to quintic Bezier curve performed in order conversion processing 23 (FIG. 12, step 105) Will be described in detail below. Part or all of the processing in the degree conversion processing 23 can be realized by a dedicated arithmetic circuit (hardware).

As described above, the free curve is a cubic Bezier curve in the simple CAD system 10 and a quintic Bezier curve in the CAD system 20 for design support.

The illustration of the product created in the simple CAD system 10 and the shape of the product represented by the data obtained by the degree conversion processing 23 in the CAD system 20 for design support must have the same shape.

In order to satisfy this requirement, the degree conversion from the cubic Bezier curve to the quintic Bezier curve is performed by storing the tangent vectors at the start point and end point of the cubic Bezier curve in the quintic Bezier curve, respectively. This is performed so that the curve has substantially the same shape as the cubic Bezier curve. That is, four control points Q _i (i
= 0 to 3), the tangent vectors at the start point and the end point of the cubic Bezier curve are stored in the quintic Bezier curve, respectively, and the tangential Bezier curve is set to have substantially the same shape as the cubic Bezier curve. Define the next Bezier curve 6
Find control points.

The six control points defining the fifth-order Bezier curve are designated as K ₀ , K ₁ , K ₂ , K ₃ , K ₄ and K ₅ .
Hereinafter, the control points of the quintic Bezier curve are defined as K _i (i = 0, 1,
..., 5). Where K _i = (a _i , b _i , c _i )
It is. The start and end points of the quintic Bezier curve are
It matches the start and end points of the cubic Bezier curve.

FIG. 16 shows a procedure for converting a cubic Bezier curve into a quintic Bezier curve. FIGS. 17A to 17C are diagrams illustrating the degree conversion from a cubic Bezier curve to a quintic Bezier curve.

4.2.1 Calculation of Parameters (FIG. 16; Step
121) Four control points Q _i (i = 0 to 0) defining a cubic Bezier curve
Based on 3), the tangent vectors at the start point and the end point of the cubic Bezier curve are stored in the quintic Bezier curve, respectively, and the quintic Bezier curve is made to have substantially the same shape as the cubic Bezier curve. In order to calculate the six control points K _i (i = 0 to 5) defining the following, it is necessary to specify six points on the cubic Bezier curve. In order to calculate six points on a cubic Bezier curve, six parameters that provide those points are required.

From t = 0 (the starting point of the cubic Bezier curve) to t =
Six parameters t ₀ , t ₁ , t ₂ , t ₃ , t _4, and t ₅ are calculated by dividing the interval between 1 (the end point of the cubic Bezier curve) into five equal parts. Hereinafter, six parameters that give points on the cubic Bezier curve are represented by the following equations.

T _j = j / 5 (j = 0, 1,..., 5) (11)

The calculated six parameters t _j = (j =
0-5) are temporarily stored in a memory associated with the degree conversion process 23.

4.2.2 Calculation of Points on Cubic Bezier Curve (FIG. 1)
6; Step 122) Next, the calculated six parameters t _j (j = 0 to 5)
Is used to calculate six points on the cubic Bezier curve (FIG. 17).
a).

The point on the cubic Bezier curve at t = t _j is set as P _j (= (x _j , y _j , z _j )). The point P _j is given by the equation
From (3), it is expressed by the following equation.

[0145]

(Equation 7)

When the point P _j (j = 0 to 5) is calculated using the equation (12), the amount of calculation becomes enormous and the calculation time becomes longer.
The point P _j (j = 0 to 5) is calculated by the forward difference method. Since B _{i, 3} (t _j ) (i = 0 to 3, j = 0 to 5) are constants, these are calculated in advance and P
_j (j = 0 to 5) may be calculated according to equation (12). The backward difference method may be used instead of the forward difference method,
Other methods may be used.

In the forward difference method, the initial value (t = t ₀ =
The 0-order difference P ₀ at 0), the first-order difference [Delta] P _0, the second
A floor difference Δ ² P ₀ and a third floor difference Δ ³ P ₀ are calculated. Each of these is expressed by the following equation using four control points Q _i (i = 0 to 3) defining a cubic Bezier curve.
Here, δ is the forward difference.

Δ = 1/5 (13) P ₀ = P (0) = Q ₀ (14) ΔP ₀ = ΔP (0) = P (δ) −P (0) = (− Q ₀ + 3Q ₁ −3Q ₂ + Q ₃ ) δ ³ +3 (Q ₀ −2Q ₁ + Q ₂ ) δ ² +3 (−Q ₀ + Q ₁ ) δ (15) Δ ² P ₀ = Δ ² P (0) = ΔP (δ) − ΔP (0) = 6 (-Q 0 + 3Q 1 -3Q 2 + Q 3) δ 3 +6 (Q 0 -2Q 1 + Q 2) δ 2 ... (16) Δ 3 P 0 = Δ 3 P (0) = Δ 2 P (δ) −Δ ² P (0) = 6 (−Q ₀ + 3Q ₁ −3Q ₂ + Q ₃ ) δ ³ (17)

[0149] _{t = t j (j = 1~5} ) zeroth-order difference P _j in, first-order difference [Delta] P _j, the second-order differential delta ² P _j and the third-order differential delta ³ P _j is, t = Using the 0th order difference P _j−1 , the 1st order difference ΔP _j−1 , the 2nd order difference Δ ² _Pj−1, and the 3rd order difference Δ ³ P _j−1 at t _j−1 , expressed.

[0150] _{^{Δ 3 P j = Δ 3 P}} j-1 ... (18) Δ 2 P j = Δ 2 P j-1 + Δ 3 P j ... (19) ΔP j = ΔP j-1 + Δ 2 P j ... ( 20) P _j = P _j-1 + ΔP _j (21)

Here, since the point P ₅ is the end point of the cubic Bezier curve, P ₅ = P (1) = Q ₃ from the equation (7). Accordingly, the point P ₅ without calculating on the basis of the forward difference method, can also be calculated by P ₅ = Q _3.

FIG. 18 shows a procedure for calculating six points P _j (j = 0 to 5) on a cubic Bezier curve by the forward difference method.

J is initialized to 0 (step 131), and t
= T zeroth-order difference P ₀ at _0, the first-order difference [Delta] P _0, the second-order differential delta ² P ₀ and the third-order differential delta ³ P _0, respectively, is calculated by equation (13) to (17) (Step 132).

J is incremented (step 133)
), The 0-order difference P _j at t = t _j, the first-order difference ΔP
_j , the second-order difference Δ ² _Pj and the third-order difference Δ ³ _Pj are calculated by equations (18) to (21), respectively (step 134).
).

Until j becomes 5, the processing of steps 133 and 134 is repeated (step 135).

In this way, the 0th-order differences P ₀ , P ₁ , P ₂ , P ₃ , P ₄ and P 0 calculated by the forward difference method
The value of _{5 is} a value representing each of the six points on the cubic Bezier curve. The obtained points P ₀ ,..., P ₅ are temporarily stored in a memory associated with the degree conversion processing 23.

4.2.3 Calculation of unit tangent vector at start point and end point (FIG. 16; step 123)
In order to satisfy the condition that the tangent vectors at the start point and end point of the cubic Bezier curve are preserved in the degree conversion to the quadratic Bezier curve, the unit tangent vector E _{i at} the start point of the cubic Bezier curve and the unit tangent vector at the end point E _f is calculated (see FIG. 17b).

Since the tangent vector at the starting point of the cubic Bezier curve is given by equation (9), its unit tangent vector E _i is expressed by the following equation using the coordinate data of control points Q ₀ and Q ₁ .

[0159]

(Equation 8)

Since the tangent vector at the end point of the cubic Bezier curve is given by the equation (10), the unit tangent vector _Ef is represented by the following equation using the coordinate data of the control points Q ₂ and Q ₃ .

[0161]

(Equation 9)

As described above, the unit tangent vector E _{i at} the start point of the cubic Bezier curve and the unit tangent vector E _{f at the} end point are calculated. The calculated unit tangent vectors E _i and E _f are stored in a memory associated with the degree conversion processing 23.

4.2.4 Calculation of Control Points of Fifth-Order Bezier Curve
16; Step 124) Six parameters t for giving a point on the cubic Bezier curve
_j (j = 0 to 5) and six points P _j on the cubic Bezier curve
Based on (j = 0 to 5) and the two unit tangent vectors E _i and E _f , the tangent vectors at the starting point and the ending point of the cubic Bezier curve are stored, respectively, and have substantially the same shape as the cubic Bezier curve. according to the conditions that must become a kicked, calculates the six control points K _i which defines a fifth-order Bezier curve (i = 0~5) (see FIG. 17c).

In order to satisfy the condition that the fifth-order Bezier curve must have substantially the same shape as the third-order Bezier curve, the fifth-order Bezier curve is divided into six points P _j on the third-order Bezier curve.
(J = 0 to 5) or so as to pass through the vicinity thereof, to determine the six control points of fifth-order Bezier curves K _{i (i} = 0~5).
That is, a point on the fifth-order Bezier curve at t = t _j (expression
In (1), P (t _j ) when n = 5 is set, and 3
So that the error between a point P _j on the next Bezier curve (distance) is minimized, to calculate the control point K _i for (i = 0 to 5).

A point P (t _j ) on the quintic Bezier curve at t = t _j (j = 0 to 5) and a point P _j on the cubic Bezier curve
Is expressed by the following equation.

[0166]

(Equation 10)

In order to make the start point and end point of the quintic Bezier curve coincide with the start point P ₀ and end point P _{5 of the} cubic Bezier curve, respectively, the six controls of the quintic Bezier curve are set so that the following equation is satisfied. determining the point K _{i (i} = 0~5).

[0168]

[Equation 11]

(Equation 12)

By rearranging equation (24) using equations (25) and (26), the following equation is obtained.

[0170]

(Equation 13)

The unit tangent vector at the start point K ₀ of the fifth-order Bezier curve is the same as the unit tangent vector E _{i at} the start point P ₀ of the cubic Bezier curve, and the unit tangent vector at the end point K ₅ of the fifth-order Bezier curve is obtained. There utilizing condition that such be the same as the unit tangent vector E _f at the end P ₅ cubic Bezier curve to determine the control points K ₁ and K ₄ of the fifth-order Bezier curve as follows.

In order to make the unit tangent vector at the start point of the quintic Bezier curve the same as that of the cubic Bezier curve, the control point K ₁ is obtained by extending the unit tangent vector E _i starting from the control point K ₀ . Must be on extension.
When the distance between the control points K ₀ and K ₁ is set as d _i , the control point K ₁ becomes the control point K ₀ , the unit tangent vector E _i and the distance d
It is expressed by the following equation using _i .

K ₁ = K ₀ + d _i E _i (28)

[0174] Similarly, the control point K _4, the control point K ₅
The distance between the K ₄ Place the d _f a, the control point K ₄ is the control point K
₅ , expressed by the following equation using the unit tangent vector E _f and the distance d _f .

K ₄ = K ₅ + d _f E _f (29)

The start point P ₀ and end point P ₅ of the cubic Bezier curve are matched with the start point and end point of the quintic Bezier curve, respectively, and the start point and end point of the quintic Bezier curve are set to control points K ₀ and K ₅ , respectively. The following equation is established from the condition of making them match.

K ₀ = P ₀ (30) K ₅ = P ₅ (31)

The equation (30) is substituted into the equation (28), and the equation (31) is replaced by the equation (29)
Into the control points K ₁ and K _{4 of the} fifth-order Bezier curve.
Are represented by the following equations.

[0179] _{K 1 = P 0 + d i} E i ... (32) K 4 = P 5 + d f E f ... (33)

In equation (27), among the terms in Σ, i =
The terms relating to 0, 1, 4 and 5 are taken out of Σ, and the equation (3
Substituting 2) and (33) yields:

[0181]

[Equation 14]

In equation (34), P _j = (x _j , y _j , z _j ),
K _i = (a _i , b _i , c _i ), E _i = (E _{i, x} ,
E _{i, y} , E _{i, z} ) and E _f = (E _{f, x} , E _{f, y} , E
_{f, z} ), the following equation is obtained.

[0183]

(Equation 15)

In Equation (35), the unknowns are d _i , d _f ,
is _{a 2, a 3, b 2} , b 3, c 2 and c _3.

The condition under which the error r is minimized is represented by setting the partial differential values obtained by partially differentiating the error r with each unknown number to 0.

[0186]

(Equation 16)

[Equation 17]

(Equation 18)

[Equation 19]

(Equation 20)

(Equation 21)

(Equation 22)

(Equation 23)

The error r represented by the equation (35) is calculated as unknown d _i
The following equation is obtained by partial differentiation with

[0188]

(Equation 24)

By rearranging equation (44), the following equation is obtained.

[0190]

(Equation 25)

The error r represented by the equation (35) is calculated as unknown d _f
The following equation is obtained by partial differentiation with

[0192]

(Equation 26)

By rearranging equation (46), the following equation is obtained.

[0194]

[Equation 27]

Here, the unit tangent vectors E _i and E _f
Since is a unit vector, the following equation holds.

| E _i | = (E _{i, x} ² + E _{i, y} ² + E _{i, z} ² ) ^1/2 = 1 (48) | E _f | = (E _{f, x} ² + E _{f, y} ² + E _{f, z} ² ) ^1/2 = 1 (49)

[0197] Further, as shown in FIG. 17b, placing the corner at the intersection of the straight line obtained by extending the straight line E _f obtained by extending the unit tangent vector E _i in the opposite direction and θ the following equation holds.

[0198] _{E i · E f = E i} , x E f, x + E i, y E f, y + E i, z E f, z = | E i || E f | cosθ = cosθ ∴ cosθ = E i _{, xEf, x} + _{Ei, yEf , y} + _{Ei, zEf , z} ... (50)

The formulas (42) and (43) are rearranged using the formulas (48), (49) and (50) as follows.

[0200]

[Equation 28]

(Equation 29)

When the error r represented by the equation (35) is partially differentiated by unknown numbers a ₂ , a ₃ , b ₂ , b ₃ , c ₂ and c _{3, the} following equations are obtained.

[0202]

[Equation 30]

(Equation 31)

(Equation 32)

[Equation 33]

(Equation 34)

(Equation 35)

Here, the constant terms in equations (51) to (58) are
By arranging as shown in equations (59) to (61) and rearranging using equations (36) to (43), the equations shown in equations (62) to (69) are obtained.

[0204]

[Equation 36]

(37)

(38)

[Equation 39]

(Equation 40)

[Equation 41]

(Equation 42)

[Equation 43]

[Equation 44]

[Equation 45]

[Equation 46]

Here, the unknowns d _i , d _f , a ₂ , a ₃ ,
b ₂ , b ₃ , c ₂ and c ₃ are represented by vectors as follows.

[0206]

[Equation 47]

When equations (62) to (69) are collectively expressed by a vector equation, A and B are defined as constant matrices.
It can be expressed by the following equation.

AX = B (71)

[0209] The constant matrix A is expressed as follows.

[0210]

[Equation 48]

[Equation 49]

[Equation 50]

A (i, k) represents the element at row i and column k of matrix A, and A ₀ (i, k) represents the element at row i and column k of matrix A ₀ . C
_j (i) represents the element of column i of the matrix C _j , and C _j (k) represents the element of column k of the matrix C _j .

The constant matrix B is expressed as follows.

[0213]

(Equation 51)

(Equation 52)

Since constant matrices A and B are known,
The unknown vector X is calculated by applying Gaussian elimination to the equations represented by (71) to (76). That is, the distance between the control point K ₀ and K ₁ d _i, the control point K ₅ and K ₄
The distance between d _f, and the control point _{K 2 = (a 2, b} 2, c
₂ ) and K ₃ = (a ₃ , b ₃ , c ₃ ) will be calculated.

Specific method (software) for executing Gaussian elimination on a computer (digital computer)
Is generally known and described in, for example, "Scientific and Technical Computation Handbook by Science Corporation UNIX Workstation [Basic C Language Version] pp 148-151".

The control points K ₁ and K ₄ are calculated by the equations (32) and (33) using the calculated distances d _i and d _f , respectively.

FIG. 19 shows a procedure for calculating control points that define a fifth-order Bezier curve.

Hereinafter, this calculation procedure will be described as a process of executing the calculation of the control point data of the fifth-order Bezier curve by a computer. This calculation processing can be partially or entirely realized by a dedicated arithmetic circuit (hardware).

The coordinate data of the start point P ₀ and the end point P ₅ are read from the memory, and the control points K ₀ and K ₅ are calculated by the equations (30) and (31) (step 151).

Parameter t _j (j = 0-5), point P
_j (j = 0 to 5) and unit tangent vectors E _i and E _f are read from the memory, and a constant matrix A is calculated by the equations (72) to (74), and according to the equations (75) and (76) A constant matrix B is calculated (step 152).

An unknown vector X (distances d _i and d _f and control points K ₂ and K ₃ ) is calculated by executing a Gaussian elimination method using the calculated constant matrices A and B (step 153). .

Based on the calculated distances d _i and d _f , the control points K ₁ and K ₄ are calculated by using equations (32) and (33).
Are calculated (step 154).

[0223] As described above, six control points K _i which defines a fifth-order Bezier curve (i = 0 to 5) is calculated.

For example, in the CAD data file shown in FIG.
The coordinate data of the control point shown in 20 is obtained. This element C1
The control points K _{0 to} K ₅ obtained by the degree conversion for
As shown in 21.

4.3 Degree conversion from cubic Bezier curve to quintic Bezier curve (when there is degeneration; part 1) 4.3.1 Approximate calculation of unit tangent vector at start point and end point Control point degenerates at start point of cubic Bezier curve Since Q ₁ = Q ₀ , P (0) /
dt = 0, and the start point definitive unit tangent vector E _i can not be calculated. Similarly, when the control point is degenerate at the end point of the cubic Bezier curve, since Q ₂ = Q ₃ , the equation (1)
0) in P (1) / dt = 0, and the unit tangent vector E _f can not be computed at the end point.

As described above, since the unit tangent vectors E _i and E _{f at the} starting point and the ending point cannot be obtained during the degeneracy, according to the method described in “4.2.4 Calculation of control point of fifth-order Bezier curve” described above. , The control points of the fifth-order Bezier curve cannot be calculated, that is, the third-order Bezier curve cannot be transformed into the fifth-order Bezier curve.

When the control point is degenerated at the start point or end point of the cubic Bezier curve, the unit tangent vector is approximately calculated as follows.

When the control point is degenerate at the starting point P ₀ of the cubic Bezier curve, Q ₁ = Q ₀ , and therefore, equation (8)
, The following equation is obtained when Q ₁ = Q ₀ .

[0229]

(Equation 53)

In the equation (8), when t → 0, the first
Since term (t ² term) can be neglected compared to the second term (term t), the coefficient of the second term 6 (-Q ₀ + Q ₂₎ may be considered to represent the tangent vectors. Thus, the unit tangent vector E _i at the start point can be approximated calculated by the following equation using the coordinate data of the control points Q ₀ and Q _2.

[0231]

(Equation 54)

[0232] Also when the control points are degenerated at the end of the cubic Bezier curve, as in the case of the starting point, the unit tangent vector E _f in the end point, the control points Q ₁ and Q ₃
Is approximated by the following equation using the coordinate data of

[0233]

[Equation 55]

In this way, the unit tangent vector E _{i at} the start point of the cubic Bezier curve and the unit tangent vector E _{f at the} end point are approximately calculated.

FIG. 22 shows a processing procedure for order conversion from a cubic Bezier curve to a quintic Bezier curve when the control points are degenerated. In FIG. 22, the same processes as those shown in FIG. 16 are denoted by the same reference numerals, and redundant description will be avoided. Only the processing in step 123A for approximating the unit tangent vector at the start point and end point of the cubic Bezier curve is different from that shown in FIG.

FIG. 23 shows the procedure for calculating the unit tangent vector in step 123A.

It is determined whether or not the control points Q ₀ and Q ₁ match, that is, whether or not the control point is degenerated at the start point (step 161).

When Q ₀ ≠ Q ₁ (N in step 161
O), a unit tangent vector E _i according to equation (22) is calculated using the coordinate data of the control points Q ₀ and Q ₁ because the starting point is not degenerate (step 162).

When Q ₀ = Q ₁ (YE at step 161)
S), using the coordinate data of the control points Q _0, Q ₂ since the start point is degenerate, a unit tangent vector E _i is approximate calculation according to equation (78) (step 163).

It is determined whether or not control points Q ₂ and Q ₃ match, ie, whether or not the control point is degenerate at the end point (step 164).

When Q ₂ ≠ Q ₃ (N in step 164)
O), end point using coordinate data of the control point Q ₂ and Q ₃ because not degenerate, a unit tangent vector E _f is computed according to Equation (23) (step 165).

When Q ₂ = Q ₃ (YE at step 164)
S), the end point by using the coordinate data of the control points Q _1, Q ₃ since degenerate, the unit tangent vector E _f at the end point is an approximate calculation according to equation (79) (step 166).

[0243] As described above, the unit tangent vector E _i at the start point of the cubic Bezier curve, a unit tangent vector E _f at the end point is calculated.

Using the unit tangent vectors E _i and E _f calculated in this way, even if the control points are degenerated, 3
The order Bezier curve can be transformed into a fifth-order Bezier curve.

For example, in the CAD data file shown in FIG. 20, when the degree conversion is performed on the element C22 whose starting point is degenerated, the coordinate data shown in FIG. 24 is obtained. Control points K ₀ to
K ₅ is as shown in FIG. 25. As can be seen from FIGS. 25 and 24, in the fifth-order Bezier curve of the element C22, the start points K ₀ and K _{1 in the} same manner as the third-order Bezier curve before the degree conversion.
Remains degenerated.

4.4 Degree conversion from cubic Bezier curve to quintic Bezier curve (when there is degeneration; part 2) If the control point is degenerated at the start point or end point of the cubic Bezier curve, the above-mentioned “4.33. As described in “Degree conversion from next-order Bezier curve to fifth-order Bezier curve (when there is degeneracy; part 1)”, the cubic Bezier curve is converted to a fifth-order Bezier curve by approximating the unit tangent vector at the degenerate point.
The degree can be converted to a next-order Bezier curve.

However, when the control point is degenerate at the start point of the cubic Bezier curve (Q ₀ = Q ₁ ), of the obtained control points K _i (i = 0 to 5) of the quintic Bezier curve, The control points K ₁ and K ₀ have the same value or almost the same value, and degeneration remains after conversion. The same applies when the control point is degenerate at the end point of the cubic Bezier curve (Q ₂ = Q ₃ ).

FIG. 26 shows a processing procedure of order conversion that can eliminate degeneration of control points. 26, the same processes as those shown in FIG. 22 are denoted by the same reference numerals, and detailed description will be omitted. In FIG. 26, the processing in step 124A is added. In this process, in step 121, the parameters t set at equal intervals on the axis of the parameter t
_j (j = 0 to 5) is used to eliminate control point degeneration.
Recalculate.

4.4.1 Recalculation of Parameter The parameter t _j is obtained by normalizing the length from the start point P ₀ of the cubic Bezier curve to the point P _j on the curve by using the total length from the start point P ₀ to the end point P _5. Is recalculated.

By recalculating the parameter t _j , the control point K _j (j
= 0 to 5) can be dispersed almost uniformly. This makes it possible to eliminate the degeneration of the control point K _j after the degree conversion.

Referring to FIG. 27, the cubic Bezier curve is approximated as a circle passing through three points P _j , P _{j + 1} and P _{j + 2} (j = 0 to 3).

A vector representing each of the straight line segment P _j P _{j + 1} , the straight line segment P _{j + 1} P _{j + 2,} and the straight line segment P _j P _{j + 2} is
Putting u, v and w, these vectors are expressed by the following equations.

U = (x _{j + 1} −x _j , y _{j + 1} −y _j , z _{j + 1} −z _j ) (80) v = (x _{j + 2} −x _j , y _{j + 2} − y _j , z _{j + 2} −z _j ) (81) w = (x _{j + 2} −x _{j + 1} , y _{j + 2} −y _{j + 1} , z _{j + 2} −z _{j + 1} ) (( 82)

A radius R of a circle passing through the three points P _j , P _{j + 1} and P _{j + 2} is expressed by the following equation using vectors u, v and w.

[0255]

[Equation 56]

[0256] arc P _j P arc length of _{j + 1} L _{2j + 1} and arcs P _{j + 1}
The arc length L _{2j + 2} of P _{j + 2} is given by the following equation.

L _{2j + 1} = 2R · arcsin (| u | / 2R) (84) L _{2j + 2} = 2R · arcsin (| w | / 2R) (85)

The arc lengths L _{1 to} L ₈ are calculated while incrementing j by 1 from 0 to 3.

The point P when the cubic Bezier curve is approximated to a circle
Length M _j (j = 1 to ₀₎ from ₀ to point P _j (j = 1 to 5)
5) is calculated by the following equation.

M ₁ = L ₁ (86) M ₂ = L ₁ + (L ₂ + L ₃ ) / 2 = M ₁ + (L ₂ + L ₃ ) / 2 (87) M ₃ = L ₁ + (L) _{2 + L 3) / 2 +} (L 4 + L 5) / 2 = M 2 + (L 4 + L 5) / 2 ... (88) M 4 = L 1 + (L 2 + L 3) / 2 + (L 4 + L 5) _{/ 2 + (L 6 + L} 7) / 2 = M 3 + (L 6 + L 7) / 2 ... (89) M 5 = L 1 + (L 2 + L 3) / 2 + (L 4 + L 5) / 2 + (L ₆ + L ₇ ) / 2 + L ₈ = M ₄ + L ₈ (90)

In the above equations (86) to (90), (L ₂ + L
₃₎ / 2 represents the length of the curve from the point P ₁ on the cubic Bezier curve to the point P _2, the arc P ₁ P ₂ when placed with j = 0
The arc length L ₂ of an average value of the arc length L ₃ of the arc P ₁ P ₂ when placed with j = 1. Similarly, (L ₄ + L ₅ ) / 2 represents the length of the curve from the point P ₂ to the point P ₃ on the cubic Bezier curve, and the arc length L of the arc P ₂ P ₃ when j = 1 is set. _Four
When an average value of the arc length L ₅ of the arc P ₂ P ₃ when put and _{j = 2, (L 6 +} L 7) / 2 is from the point P ₃ on the cubic Bezier curve to the point P ₄ It represents the length of the curve and is the average value of the arc length L ₆ of the arc P ₃ P ₄ when j = 2 and the arc length L ₇ of the arc P ₃ P ₄ when j = 3.

The recalculation of the parameter t _j is calculated from the points P ₀ to P
The length M _j (j of the cubic Bezier curve up to _j (j = 0 to 5)
= 1 to 5), since it is possible to normalize by the total length M _5, the calculation is represented by the following equation.

T ₀ = 0 (91) t ₁ = M ₁ / M ₅ (92) t ₂ = M ₂ / M ₅ (93) t ₃ = M ₃ / M ₅ (94) t ₄ = M ₄ / M ₅ (95) t ₅ = 1 (96)

Thus, a new parameter t
_j (j = 0 to 5) is obtained.

FIG. 28 shows the procedure of the parameter recalculation processing in step 124A.

J is initialized to 0 (step 171), and
Points P _j , P _{j + 1} and P _{j + 2} are selected (step 17)
2). Equations (80), (8)
The vectors u, v, and w are calculated by (1) and (82) (step 173).

Using the calculated vectors u, v and w, the radius R of a circle passing through the three points P _j , P _{j + 1} and P _{j + 2} is calculated by equation (83) (step 174). Using equations (84) and (85) using the calculated radius R and the vectors u and w, the arc length L _{2j + 1} and the arc P of the arc P _j P _{j + 1} are obtained.
The arc length L _{2j + 2 of j + 1} P _{j + 2} is calculated (step 17).
Five).

While incrementing j (step 17)
7) Steps 172 to 175 are repeated until j exceeds 3. If j = 3, from point P ₀ to point P _j
This means that the calculation of the arc lengths L _{2j + 1} and L _{2j + 2} necessary for calculating the length M _j up to (j = 1 to 5) has been completed.

When j becomes 4 (NO in step 176), the length M _j (j = 1 to 5) from the point P ₀ to the point P _j is calculated by the equation (86).
Calculated from (90) (step 178). The calculated length M _j to each point P _j is calculated as 3 from the point P ₀ to the point P _5.
By normalizing with the total length (length M ₅ ) of the next Bezier curve (Equations (91) to (96)), a new parameter t _j (j
= 0 to 5) (step 179).

As described above, the parameter t _j (j =
0-5) are recalculated.

[0271] Figure 26, in the process of step 124, the control point of the fifth-order Bezier curve using the recalculated parameters _{t j K i (i = 0~5} ) is calculated in step 124A.

For example, in the CAD data file shown in FIG. 13, when the degree conversion is performed on the element C22 whose starting point is degenerated, the coordinate data shown in FIG. 29 is obtained. The control points of the element C22 after the degree conversion are as shown in FIG. As can be seen by comparing FIG. 25 and FIG. 30,
The control point of the fifth-order Bezier curve of the element C22 is determined by the parameter t _j
Before the recalculation, the starting point remains degenerated as shown in FIG. 25, but after the recalculation, as shown in FIG.
Degeneracy is eliminated, six control points K ₀ ~K ₅ appearing in separate locations.

4.5 Order Conversion from nth-Order Bezier Curve to mth-Order Bezier Curve The above-described conversion from a third-order Bezier curve to a fifth-order Bezier curve is generally applied to order conversion from an nth-order Bezier curve to an mth-order Bezier curve. can do. Here, n and m are integers of 3 or more.

The order conversion includes conversion from lower order to higher order (n
<M) or conversion from higher order to lower order (n> m), or conversion of the same order (n = m).

The conversion from the lower order to the higher order is, for example, a case where a data file is transmitted from the simple CAD system to the CAD system for design support. The conversion from a higher order to a lower order is, for example, a case of transmitting a data file from a CAD system for design support to a simple CAD system. The same conversion is performed when the degeneration of the control point is eliminated.

The conversion from the n-th order Bezier curve to the m-order Bezier curve will be described.

When order conversion is performed from the n-th order Bezier curve to the m-th order Bezier curve, (n + 1) control points Q _i (i = 0,
,.., N) and (m + 1) control points K _i (i
= 0, 1,..., N,..., M).

Since the n-th order Bezier curve is converted to the m-th order Bezier curve, (m + 1) points on the n-th order Bezier curve are required. (M + 1) parameters t _j (j = 0 to m)
Is calculated at regular intervals of 1 / m between 0 and 1 by the following formula.

T _j = j / m (97)

When a point on the n-th order Bezier curve at t = t _j is set as P _j , the point P _j is represented by the following equation from the equation (1).

[0281]

[Equation 57]

Using equation (98), (m + 1) points P _j (j
= Since the amount of computation and calculates the coordinates of 0 to m) is required to be time consuming, may the coordinates of the point P _j calculated by the forward difference method from the point P ₀ in order. This forward difference method is similar to the case of the degree conversion from the cubic Bezier curve to the quintic Bezier curve.

(M + 1) points P _j on the n-th order Bezier curve
The coordinates of (j = 0 to m) are calculated, and the length M _j (j = 1 to m) from the starting point P ₀ of the n-th order Bezier curve to each point P _j is approximately calculated. The parameter t is obtained by normalizing the length M _j (j = 1 to m−1) to each point P _j (j = 1 to m−1) calculated by approximation using the total length M _m of the nth-order Bezier curve.
Recalculate _j (j = 0 to m). Recalculation of this parameter is the same as in the case of the degree conversion from the cubic Bezier curve to the quintic Bezier curve.

When the control point is not degenerate at the start point or end point of the nth-order Bezier curve, the unit tangent vectors E _i and E _{f at} the start point and end point respectively correspond to the control point Q _0.
And the coordinate data of Q ₁ and Q _n−1 and Q _n are calculated by the following equation.

[0285]

[Equation 58]

[Equation 59]

Since Q ₀ = Q ₁ when the control point is degenerate at the start point of the n-th order Bezier curve, the unit tangent vector E _{i at} the start point of the n-th order Bezier curve is obtained by dividing the control points Q ₀ and Q ₂ . And is given by the following equation.

[0287]

[Equation 60]

When the control point is degenerate at the end point of the n-th order Bezier curve, Q _n = Q _{n -1} . Therefore, the unit tangent vector E _{f at} the end point of the n-th order Bezier curve is _{equal to the} control points Q _n and Q _n It is given by the following equation using _-2 .

[0289]

[Equation 61]

The m-th order Bezier curve is a point P on the n-th order Bezier curve.
_j (j = 0 to m) or a point on the m-th order Bezier curve and a point P
The error r from _j is expressed by the following equation.

[0291]

(Equation 62)

Since the start point and end point of the m-th order Bezier curve coincide with the start point P ₀ and end point P _m of the n-th order Bezier curve, the following equation is obtained.

[0293]

[Equation 63]

[Equation 64]

By substituting equations (104) and (105) into equation (103), the following equation is obtained.

[0295]

[Equation 65]

The starting point P ₀ and the ending point P _{m of the} m-th order Bezier curve
Respectively correspond to the control points K ₀ and K _m , so that the following equation holds.

K ₀ = P ₀ (107) K _m = P _m (108)

[0298] the distance between the control point K ₀ and K ₁ Place and d _i,
The distance between the control point K _m and K _m-1 put the d _f. Under the condition that the unit tangent vector E _{i at the} start point and the unit tangent vector E _{f at the} end point are stored, respectively, the control points K ₁ and K _m-1 of the _m-th order Bezier curve are expressed by the following equations, respectively.

[0299] _{K 1 = K 0 + d i} E i ... (109) K m-1 = K m + d f E f ... (110)

Equations (107) and (108) are respectively replaced by equation (10)
Substituting into (9) and (110) gives the following equation.

[0301] _{K 1 = P 0 + d i} E i ... (111) K m-1 = P m + d f E f ... (112)

By substituting equations (111) and (112) into equation (106), the following equation is obtained.

[0303]

[Equation 66]

Further, P _j = (x _j , y _j , z _j ), K
_{i = (a i, b i} , c i), E i = (E i, x, E i, y,
E _{i, z} ) and E _f = (E _{f, x} , E _{f, y} , E _{f, z} )
By using (113), the following equation is obtained.

[0305]

[Equation 67]

In equation (114), the unknowns are d _i , d _f ,
_{a 2, a 3, ...,} a m-2, b 2, b 3, ..., b m-2, c
_2, c _3, ..., a c _m-2. In the same manner as the conversion from the cubic Bezier curve to the quintic Bezier curve, the error r in the equation (112) is partially differentiated by each unknown and set to 0, and the vector equation obtained by them is subjected to Gaussian elimination. To obtain the unknown.

Thus, the distances d _i and d _f ,
A control point K ₂ ~K _m-2 is obtained. Using the obtained distance d _i and d _f, the equation (109) and (110), the control points K ₁ and K _m-1 is obtained. Control points K ₀ and K
_m is obtained from equations (107) and (108).

The above description includes the approximation calculation of the unit tangent vector and the recalculation of the parameters.
If the control points are not degenerated, those processes can be omitted.

As described above, (n) of the n-th order Bezier curve
By calculating (m + 1) control points K _{0 to} K _m of the _m- th order Bezier curve from +1) control points Q _{0 to} Q _n , the order conversion from the n-th order Bezier curve to the m-th order Bezier curve can be performed. Done.

[0310] 5. Drawing of Bezier Curve As described above, data representing a quintic Bezier curve was obtained in the CAD system 20 for design support. A process of drawing a Bezier curve on a CRT display screen using this data will be described.

5.1 Hardware Configuration FIG. 31 shows an outline of a hardware configuration of the CAD system 20 for design support.

The CAD system 20 for design support is constituted by a computer system as described above,
It has 30. This CPU 30 has a hard disk
Driver 31, FD (floppy disk) driver 32,
A RAM 33, an input device 34, a VRAM 35, a display control circuit 36, and the like are connected via a necessary interface (not shown).

The hard disk driver 31 writes data (including programs) to the hard disk 31A or reads data from the hard disk 31A. The hard disk 31A stores the CAD data base 22 described above.
(See FIG. 1). Further, the CAD data conversion processing 21, the degree conversion processing 23,
A program for controlling the CPU 30 to be executed by the U30 is stored in the hard disk 31A.

The FD driver 32 writes data to the FD 32A or reads data from the FD 32A. C
The AD database 22 may be realized by the FD 32A. A computer program such as CAD data conversion processing 21, degree conversion processing 23, and display processing may be stored in the FD 32A.

The RAM 33 temporarily stores data generated in the CAD data conversion processing 21 and the degree conversion processing 23,
Used as work memory for other purposes.

The input device 34 includes a keyboard, a mouse, and the like, and is used to input commands and data for a series of operations in the CAD system 20 for design support.

The VRAM 35 is used as a bit map memory, and stores data representing an image (a product design drawing as shown in FIG. 30) to be displayed on the CRT display device 37 on the display surface of the CRT display device 37. It is stored for each pixel.

Under the control of the CPU 30, the display control circuit 36 generates and outputs a video signal for displaying a graphic representing a product on the CRT display device 37 based on the image data stored in the VRAM 35.

5.2 Processing for Displaying Bezier Curve The Bezier curve P (t) is expressed by the following equation (1) and equation (2): n = 5
And can be expressed by the following equation (control point symbol Q
the _i replaced by K _i).

[0320] P (t) = (1-5t + 10t 2 -10t 3 + 5t 4 + t 5) K 0 +5 (t-4t 2 + 6t 3 -4t 4 + t 5) K 1 +10 (t 2 -3t 3 + 3t 4 + t 5 ^{_{) K 2 +10 (t 3 -2t}} 4 + t 5) K 3 +5 (t 4 -t 5) K 4 + t 5 K 5 (0 ≦ t ≦ 1) ... (115)

As an example of the converted fifth-order Bezier curve, FIG.
Considering a curve C1 shown in FIG. 30, the control point K _i (i
= 0 to 5) is shown in FIG. 29 (CRVE1 data) and is as follows.

K ₀ = (K _{0, x} , K _{0, y} , K _{0, z} ) = (136.1315,248.0133,0.0) K ₁ = (136.1315,248.3959,0.0) K ₂ = (129.0745,266.662,0.0) K ₃ = (117.4764,268.6526,0.0) K ₄ = (109.691,269.6551,0.0) K ₅ = (99.8779,269.6551,0.0)

The fifth-order Bezier curve represented by the equation (115) is represented by C
FIG. 32 shows a display processing procedure by the CPU 30 for displaying on the RT display device 37. For the sake of simplicity, a description will be given of a process of displaying a quintic Bezier curve represented by data without performing enlargement, reduction, or translation processing on the data representing the quintic Bezier curve. Further, in the coordinate data shown in FIG. 29, since the Ζ coordinates are all 0.0, they are displayed on a two-dimensional plane.

In the display processing of the Bezier curve, the coordinates of the Bezier curve are calculated according to the formula (115) while changing the parameter t in small increments, and a straight line is drawn between two adjacent coordinates. Therefore, the smaller the change of the parameter t is, the more the curve is represented by more straight lines, so that a smoother curve can be displayed.

First, the equation (115) is calculated with t = 0,
The coordinates of the starting point P (0) are obtained. X of the point P (0), y, coordinates P _x, and P _y (step 181).

Next, assuming that t + Δt (= t), equation (115)
Is calculated, and the coordinates of a point P (t + Δt) on the Bezier curve defined by t + Δt are obtained. This point P (t + Δ
The x and y coordinates of t) are defined as P _{x + Δ} and P _{y + Δ} (step 18).
2). Δt may be appropriately determined according to the resolution (or magnification) of the image. For example, Δt = 0.02.

The two points (P _x , P
_y ) to a point (P _{x + Δ} , P _{y + Δ} ) (CRT
Display a straight line on the display screen of the display device 37) (Step
183).

When data representing the coordinates of two points is given, hardware for drawing a straight line between them is known. If the display control circuit 36 includes this hardware, straight line drawing can be achieved by giving the calculated two coordinate data to this hardware. An example in which the processing of step 183 is realized by software will be described later.

P _{x + Δ} is set as P _x , and P _{y + Δ} is set as P _y (step 184).

Thereafter, the flow returns to step 182, where t + Δ
t is set as a new t, and P is again calculated using a new parameter (t + Δt) obtained by adding Δt to the new t.
_{x + Δ} and _{Py + Δ} are calculated.

The processing of steps 182 to 184 is repeated until t = 1.0.

In the case of a three-dimensional Bezier curve, the display can be performed in the same manner. In this case, the calculation according to the formula (115) is also performed for the Ζ coordinate. If a coordinate point in a three-dimensional space is photographed on a two-dimensional plane, data for display can be obtained.

When displaying a Bezier curve by enlarging, reducing or translating it, the coordinate data (data shown in FIG. 29) in the CAD data file is subjected to an operation for enlarging, reducing or translating. Then, the display processing shown in FIG. 32 may be performed. In particular, in the case of enlargement or reduction, the change Δt of the parameter t is changed to be appropriate. For example, when the enlargement magnification is increased, it is preferable to decrease the variation Δt.

[0334] Not only display on the screen of the CRT display device 37 but also drawing of a Bezier curve using another output device (for example, a printer) is possible.

The processing for displaying a straight line by software (step 183) will be described.

The resolution or resolution (number of pixels) of the display screen of the CRT display device 37 is determined according to the device. Figure 33
Schematically shows the structure of the CRT display screen, where the lattice points are the centers of the pixels. When displaying a straight line connecting two points (P _x , P _y ) and (P _{x + Δ} , _{Py + Δ} ) separated by one pixel pitch or more, a straight line connecting these two points (indicated by a chain line) ) Illuminate the pixels (shown by hatching) through which they pass.

FIG. 34 shows a straight line display processing routine. Since this routine is already known, it will be briefly described. Two points (P _x , P _y ), (P _{x + Δ} ,
P _{y + Δ} ). An equation representing a straight line connecting these two points is created.

The parameter I determines a position on the X-axis which is a basis for calculation for obtaining a pixel to be displayed. (If the scale of the coordinates of the display screen and the scale of the coordinates of the data match, the pixel on the display screen is stepped by one in the X-axis direction by I). This parameter I is set to 1 (step 191).

On the basis of the above equation of the straight line, the parameter I to be set is to be displayed (to be lit).
Find the coordinates (x, y) of the pixel on the screen (step 193)
). There are one pixel and two pixels to be displayed.

If the pixel thus obtained is within the display screen (YES in step 194), the pixel is illuminated (step 195). If the obtained pixel is not in the display screen, the display of the pixel is not performed.

Thereafter, the parameter I is incremented (if P _{x + Δ} > P _x ) or decremented (P _x
> _{Px + Δ} ) (step 196) and step 192
Return to

Steps 193 to 196 are repeated until the parameter I becomes larger than (P _{x + Δ−} P _x ) (step 192).

The process of illuminating the pixel on the display screen (step 195) is achieved by setting the bit of the storage location corresponding to the pixel to 1 on the VRAM 35 (for monochrome display). Under the control of the display control circuit 36, the bit map image data in the VRAM 35 is reflected on the display screen of the CRT display device 37.

Generally, a bit map memory is a display device.
There are storage locations corresponding to each of the 37 pixels. CPU30
Writes the image data to be displayed in a storage location corresponding to the pixel on the display screen. In the case of color display, one pixel of image data is generally composed of a plurality of bits of three primary colors R.I. G. FIG. It consists of B data. In the case of gray display, one pixel of image data is composed of a plurality of bits of image data, and in the case of black and white display, the image data is represented by one bit per pixel.

The black-and-white bit map display will be briefly described with reference to FIG.

The size of the display screen is 640 × 480 pixels. XY coordinates are set with the origin at the upper left of the screen (x
= 0 to 639, y = 479).

The start address of the VRAM 35 (bit map memory) is assumed to be A0000. 8-bit data (that is, display data for 8 pixels) can be stored in a storage location designated by one address. The addresses of the VRAM 35 are set so as to increase in the order of horizontal and vertical scanning of the screen.

The position of each pixel on the display screen is
Corresponding to the bit position in the storage location specified by the address of For example, (x, y) =
The point P at (0, 12) corresponds to the fifth bit in the address A0001 in the VRAM 35.

When the data of the pixel on the display screen to be displayed is obtained, the CPU 30 calculates the address of the VRAM 35 corresponding to the pixel and the bit position in the address,
Write 1-bit data "1" to the bit position. This is the process in step 195 in FIG.

[Brief description of the drawings]

FIG. 1 is a functional block diagram showing a software configuration of a simple CAD system and a CAD system for design support.

FIGS. 2A and 2B are diagrams illustrating how to draw a cubic Bezier curve in which a control point is not degenerated on a simple CAD system. FIG. 2A shows a state in which a start point is specified, and FIG. (C) shows the state where the end point is specified, and (D) shows the state where the tangent at the end point is specified.

FIG. 3 is a diagram for explaining how to draw a cubic Bezier curve with degenerated control points on a simple CAD system;
Indicates a state in which a start point is specified, (B) indicates a state in which an end point is specified, and (C) indicates a state in which a tangent at the end point is specified.

FIG. 4 shows an example of a product illustration drawn by a simple CAD system.

FIG. 5 shows an example of an EPSF data file.

FIG. 6 shows an example of an EPSF data file.

FIG. 7 shows an example of an EPSF data file.

FIG. 8 is a diagram in which some graphic elements are emphasized in the illustration shown in FIG. 4;

FIG. 9 shows an example of an IGES data file.

FIG. 10 shows an example of an IGES data file.

FIG. 11 shows an example of an IGES data file.

FIG. 12 is a flowchart showing an overall procedure of an order conversion process in the CAD system for design support.

FIG. 13 shows an example of a CAD data file.

FIG. 14 is displayed on a CAD system for design support.
Shows the product represented by the CAD data file.

FIG. 15 shows control points for some graphic elements in the figure showing the product of FIG. 14;

FIG. 16 is a flowchart showing a procedure of order conversion processing from a cubic Bezier curve to a quintic Bezier curve.

17A and 17B are diagrams for explaining order conversion from a cubic Bezier curve to a quintic Bezier curve. FIG. 17A illustrates four control points defining a cubic Bezier curve and six control points on the cubic Bezier curve. (B) shows two unit tangent vectors at a start point and an end point, and (C) shows six control points defining a degree-converted fifth-order Bezier curve.

FIG. 18 is a flowchart showing a processing procedure for calculating a point on a cubic Bezier curve.

FIG. 19 is a flowchart illustrating a processing procedure for calculating six control points that define a fifth-order Bezier curve.

FIG. 20 shows an example of a CAD data file obtained by order-converting a cubic Bezier curve without degeneration.

FIG. 21 shows control points of a Bezier curve obtained by performing degree conversion on a cubic Bezier curve without degeneration.

FIG. 22 is a flowchart showing a processing procedure for order conversion from a cubic Bezier curve to a quintic Bezier curve when control points are degenerated at the start point or end point of the cubic Bezier curve.

FIG. 23 is a flowchart showing a processing procedure for calculating a unit tangent vector at a start point and an end point when a control point is degenerated at a start point or an end point of a cubic Bezier curve.

FIG. 24 shows an example of a CAD data file obtained by performing degree conversion on a degenerate cubic Bezier curve.

FIG. 25 shows control points of a fifth-order Bezier curve obtained by performing degree conversion on a degenerate cubic Bezier curve.

FIG. 26 is a flowchart illustrating a procedure of order conversion processing from a cubic Bezier curve to a quintic Bezier curve when control points are degenerated at the start point or end point of the cubic Bezier curve.

FIG. 27 is a diagram illustrating recalculation of a parameter that gives a point on a fifth-order Bezier curve.

FIG. 28 is a flowchart showing a procedure of recalculation processing of a parameter that gives a point on a fifth-order Bezier curve.

FIG. 29 shows a CAD data file obtained by order-converting a cubic Bezier curve into a quintic Bezier curve.

FIG. 30 shows a product shape represented by a CAD data file obtained by order-converting a cubic Bezier curve into a quintic Bezier curve.

FIG. 31 is a block diagram illustrating a hardware configuration of a CAD system for design support.

FIG. 32 is a flowchart showing a procedure of processing for displaying a Bezier curve.

FIG. 33 shows how a straight line is drawn on the display screen.

FIG. 34 is a flowchart showing a processing procedure for drawing a straight line.

FIG. 35 shows a relationship between coordinates on a display screen and data of a storage location of a bit map memory.

[Explanation of symbols]

 10 Simple CAD system 11 EPSF data base 12 IGES data conversion processing 20 CAD system for design support 21 CAD data conversion processing 22 CAD data base 23 Order conversion processing

────────────────────────────────────────────────── ─── Continuation of the front page (56) References Fujio Yamaguchi Shape processing by computer display published by Nikkan Kogyo Shimbun [II] pp. 37-42 "5.1.8 Increase in degree of curved surface segment of BEZIER" Transactions of the Japan Society of Mechanical Engineers C 56 531 pp. 3123-3129 Masaaki Yokoyama et al. "Error Analysis of Specified Surface Approximation by BE SIER Surface" (58) Fields investigated (Int. Cl. ⁶ , DB name) G06F 17/50 G06T 11/20 JICST file (JOIS)

Claims (9)

(57) [Claims] 1. A design system comprising a first CAD system and a second CAD system, wherein the first CAD system includes a first data file and first conversion means. The first data file is a collection of data representing an illustration of a product having a curve; the first data file includes control point data defining a cubic Bezier curve representing the curve; The first conversion means converts the first data file into a common data file having a data format common to a plurality of types of CAD systems, and the second CAD system performs the second conversion. And a CAD data base, wherein the second converting means converts the common data file transmitted from the first CAD system into the second data file. C
CA with data format specific to AD system
The CAD data base stores the converted CAD data file including control point data defining a cubic Bezier curve. In the design system, the second CAD system further includes data conversion means for converting control point data defining a cubic Bezier curve into control point data defining a quintic Bezier curve; Display control means for displaying an image representing a product on a display device based on the CAD data file. The data conversion means includes a CAD data file stored in the CAD data base.
Bezier curve extracting means for extracting data representing a cubic Bezier curve from a file, a sixth parameter for determining six first parameters for giving six points on the cubic Bezier curve at regular intervals within a predetermined range. (1) parameter determining means, six points on the cubic Bezier curve using the six first parameters determined by the first parameter determining means and control point data defining the cubic Bezier curve A coordinate determining means for determining coordinate data representing a cubic Bezier curve; two unit tangent vectors representing gradients at each of a start point and an end point of a cubic Bezier curve are determined using control point data defining a cubic Bezier curve; A tangent vector determining means which is determined by approximation when the control point is degenerate at the start point or the end point of the Bezier curve; a cubic Bezier determined by the coordinate determining means Using the coordinate data representing the six points on the line, six points corresponding to the length of the cubic Bezier curve from the starting point of the cubic Bezier curve to each point are used.
Parameter determining means for determining the second parameters, six second parameters determined according to the length of the cubic Bezier curve, and six parameters on the cubic Bezier curve. Based on the coordinate data representing a point and the two unit tangent vectors at the start and end points of the cubic Bezier curve, the gradients at the start and end points of the cubic Bezier curve are stored, and Control point determining means for determining control point data defining a fifth-order Bezier curve so as to pass through the point or the vicinity thereof, wherein the display control means defines a fifth-order Bezier curve converted by the data converting means; Means for creating data for displaying a product based on CAD data including control point data, and means for expanding the display data on a bit map memory For example, an image of the product to be reflected by the display data developed in the bit map memory is displayed on the display device, CAD system. 2. A CAD data base storing a CAD data file containing control point data defining a cubic Bezier curve, and a control defining a quintic Bezier curve using the control point data defining the cubic Bezier curve. Data conversion means for converting the data into point data; and display control means for displaying an image representing a product on a display device based on the CAD data file converted by the data conversion means. CAD data stored in the database
Bezier curve extracting means for extracting data representing a cubic Bezier curve from a file, a sixth parameter for determining six first parameters for giving six points on the cubic Bezier curve at regular intervals within a predetermined range. (1) parameter determining means, six points on the cubic Bezier curve using the six first parameters determined by the first parameter determining means and control point data defining the cubic Bezier curve A coordinate determining means for determining coordinate data representing a cubic Bezier curve; two unit tangent vectors representing gradients at each of a start point and an end point of a cubic Bezier curve are determined using control point data defining a cubic Bezier curve; A tangent vector determining means which is determined by approximation when the control point is degenerate at the start point or the end point of the Bezier curve; a cubic Bezier determined by the coordinate determining means Using the coordinate data representing the six points on the line, six points corresponding to the length of the cubic Bezier curve from the starting point of the cubic Bezier curve to each point are used.
Parameter determining means for determining the second parameters, six second parameters determined according to the length of the cubic Bezier curve, and six parameters on the cubic Bezier curve. Based on the coordinate data representing a point and the two unit tangent vectors at the start and end points of the cubic Bezier curve, the gradients at the start and end points of the cubic Bezier curve are stored, and Control point determining means for determining control point data defining a fifth-order Bezier curve so as to pass through the point or the vicinity thereof, wherein the display control means defines a fifth-order Bezier curve converted by the data converting means; Means for creating data for displaying a product based on CAD data including control point data, and means for expanding the display data on a bit map memory For example, an image of the product to be reflected by the display data developed in the bit map memory is displayed on the display device, CAD system. 3. A design system comprising a first CAD system and a second CAD system, wherein the first CAD system includes a first data file and first conversion means. The first data file is a collection of data representing an illustration of a product having a curve; the first data file includes control point data defining an nth-order Bezier curve representing the curve; The first conversion means converts the first data file into a common data file having a data format common to a plurality of types of CAD systems, and the second CAD system performs the second conversion. And a CAD data base, wherein the second converting means converts the common data file transmitted from the first CAD system into the second data file. C
CA with data format specific to AD system
The CAD data base stores the converted CAD data file including control point data that defines an nth-order Bezier curve. In the design system, the second CAD system further includes data conversion means for converting control point data defining an nth-order Bezier curve into control point data defining an mth-order Bezier curve, and data converted by the data conversion means. Display control means for displaying an image representing a product on a display device based on the CAD data file. The data conversion means includes a CAD data file stored in the CAD data base.
Bezier curve extracting means for extracting data representing an nth-order Bezier curve from a file, (m + 1) first parameters giving (m + 1) points on the nth-order Bezier curve at regular intervals within a predetermined range First parameter determining means, which is determined by the first parameter determining means (m
(M +) on the n-th order Bezier curve using (+1) first parameters and control point data defining the n-th order Bezier curve.
1) coordinate determining means for determining coordinate data representing points; two unit tangent vectors representing gradients at each of a starting point and an ending point of an nth-order Bezier curve are obtained by using control point data defining an nth-order Bezier curve; A tangent vector determining means for determining the control point at the start point or the end point of the nth-order Bezier curve when the control point is degenerate, and (m + 1) points on the nth-order Bezier curve determined by the coordinate determining means Is used to determine (m + 1) second parameters corresponding to the length of the nth-order Bezier curve from the start point of the nth-order Bezier curve to each point using the coordinate data representing
And (m + 1) second parameters determined according to the length of the nth-order Bezier curve, coordinate data representing (m + 1) points on the nth-order Bezier curve, Based on the two unit tangent vectors at the start point and end point of the nth-order Bezier curve, the gradient at the start point and the end point of the nth-order Bezier curve is preserved, and the gradient is passed at or near a point on the nth-order Bezier curve. Further comprising control point determining means for determining control point data defining an m-dimensional Bezier curve, wherein the display control means comprises: CAD data containing control point data defining the m-dimensional Bezier curve converted by the data conversion means. Means for creating data for displaying a product based on the data, and means for expanding the display data on a bit map memory. And products of the image reflected by the display data expanded on the memory is displayed on the display device, CAD system. 4. A CAD data base storing a CAD data file containing control point data defining an n-th order Bezier curve, and a control for defining the m-th order Bezier curve using the control point data defining the n-order Bezier curve. Data conversion means for converting the data into point data; and display control means for displaying an image representing a product on a display device based on the CAD data file converted by the data conversion means. CAD data stored in the database
Bezier curve extracting means for extracting data representing an nth-order Bezier curve from a file, (m + 1) first parameters giving (m + 1) points on the nth-order Bezier curve at regular intervals within a predetermined range First parameter determining means, which is determined by the first parameter determining means (m
(M +) on the n-th order Bezier curve using (+1) first parameters and control point data defining the n-th order Bezier curve.
1) coordinate determining means for determining coordinate data representing points; two unit tangent vectors representing gradients at each of a starting point and an ending point of an nth-order Bezier curve are obtained by using control point data defining an nth-order Bezier curve; A tangent vector determining means for determining the control point at the start point or the end point of the nth-order Bezier curve when the control point is degenerate, and (m + 1) points on the nth-order Bezier curve determined by the coordinate determining means Is used to determine (m + 1) second parameters corresponding to the length of the nth-order Bezier curve from the start point of the nth-order Bezier curve to each point using the coordinate data representing
And (m + 1) second parameters determined according to the length of the nth-order Bezier curve, coordinate data representing (m + 1) points on the nth-order Bezier curve, Based on the two unit tangent vectors at the start point and end point of the nth-order Bezier curve, the gradient at the start point and the end point of the nth-order Bezier curve is preserved, and the gradient is passed at or near a point on the nth-order Bezier curve. Further comprising control point determining means for determining control point data defining an m-dimensional Bezier curve, wherein the display control means comprises: CAD data containing control point data defining the m-dimensional Bezier curve converted by the data conversion means. Means for creating data for displaying a product based on the data, and means for expanding the display data on a bit map memory. And products of the image reflected by the display data expanded on the memory is displayed on the display device, CAD system. 5. An n-dimensional Bezier file, which is a file of basic data required to display data representing an image on a bit map memory in order to display an image representing a product, In a CAD system having a CAD data base for storing a CAD data file including control point data defining a curve, control point data defining an nth-order Bezier curve is converted into control point data defining an mth-order Bezier curve. A data conversion device that converts the CAD data stored in the CAD data base
Bezier curve extracting means for extracting data representing an nth-order Bezier curve from a file, wherein (m + 1) parameters for giving (m + 1) points on the nth-order Bezier curve are set within a predetermined parameter range. The first parameter determining means for determining at equal intervals by (1), the first parameter determining means (m
Coordinate determining means for determining coordinate data representing (m + 1) points on the nth-order Bezier curve using +1) parameters and control point data defining the nth-order Bezier curve; start point of the nth-order Bezier curve And a tangent vector determining means for determining two unit tangent vectors representing gradients at each of the end points using control point data defining an n-dimensional Bezier curve, and (m + 1) points on the n-dimensional Bezier curve. Based on the given (m + 1) parameters, coordinate data representing (m + 1) points on the nth-order Bezier curve, and two unit tangent vectors at the start point and end point of the nth-order Bezier curve, respectively. , Preserve the gradients at the start and end points of the n th order Bezier curve, and pass
A data conversion device for a Bezier curve in a CAD system, comprising: control point determining means for determining control point data defining a next Bezier curve. 6. The data according to claim 5, wherein said tangent vector determining means approximates and determines a unit tangent vector when a control point is degenerated at a start point or an end point of an nth-order Bezier curve. Conversion device. 7. The n determined by the coordinate determining means.
Using coordinate data representing (m + 1) points on the next-order Bezier curve, determining (m + 1) parameters corresponding to the length of the n-th order Bezier curve from the starting point of the n-th order Bezier curve to each point. And the control point determining means, instead of the parameters determined at equal intervals by the first parameter determining means, the length of the n-th order Bezier curve by the second parameter determining means. 7. The data conversion device according to claim 6, wherein the control point data is determined by using a parameter determined according to the control point data. 8. The apparatus further comprises means for creating data for displaying a product based on CAD data including control point data defining an m-dimensional Bezier curve, and expanding the display data on a bit map memory. 6. The data conversion device according to claim 5, wherein an image of the product reflected by the data developed on the bit map memory is displayed on a display device. 9. The data conversion device according to claim 5, wherein n = 3 and m = 5.