Automated design system and automated design program

TECHNICAL FIELD OF THE INVENTION

The present invention relates to computer-aided design and computer-aided design program which transform the shape of a member in the shape of the target function with a curved surface.

BACKGROUND

Today it is clear desire to reduce the processes from planning through design and production to meet customer demand. To improve the efficiency of design and manufacturing processes, the increasing popularity of computer graphics have (CG) and computer-aided design (CAD). To depict shapes having complex shapes with curved lines or curved surfaces, such as cars, appliances, etc., on a computer that has traditionally existed following treatments.

Origin - is solid modeling, where simple shapes called non-derivative elements are contained in a computer, and such operation to combine these shapes to each other, are repeated so as to express complex shapes. Non-derivative element - is, for example, a column, cube, hexagon, torus, sphere and the like, and solid modeling forms are represented by operations on sets of non-derivative elements. Hence, to generate a complex shape, it takes many steps and a lot of precise calculations.

Second - this surface modeling, which uses an algorithm such as the algorithm Bezier, B-spline, Bezier rational, non-uniform rational B-spline (NURBS), etc., in order to perform operations such as cutting or the connection lines or surfaces, and by repeating these operations complex free presented curves or curved surfaces.

Nevertheless, even with a model in which there are no problems from the point of view using the above described solid model or surface model, in some cases, problems may arise in the case where it is used by the downflow of data such as CAM, CAE, and so on. P. This is caused by differences between the support element, which must be supported by machine-generated graphics, and an element of support, which should be supported by other applications, computer graphics, computer-aided design and downflow data and differences in the definition of the form, etc. The model is corrected using this application as a translator which modifies these differences (Japanese Patent Application №№ 2001-250130, Hei 11-65628, Hei 10-69506, Hei 4-134571, Hei 4-117572 and Hei 1-65628) .

Disclosure of invention

However, the above-described correcting operation is extremely inefficient to reduce design and manufacturing processes. The reasons for correction are different in each case, but the point which becomes a problem particularly in the production stage is that the representations of all curved lines and curved surfaces are approximated by Euclidean geometry in a conventional computer graphics or computer aided design. For example, when the cylindrical surface of table saddle type shown in Fig. 6, generated by the sweep operation, a long line appears in the lower part of the slope of the saddle and a short line in the central part of the saddle. Therefore, this sweep operation is a transformation accompanied with graphical and increase the restriction to maintain the continuity of the curved surface generated. However, in the conventional computer graphics or computer aided design of this increase and contraction is not considered, and the internal representation of approximately represented as a cylinder type. Hence, if the model computer graphics and computer-aided design model, which is actually about is represented by a Euclidean geometry is transferred to the CAE, the appearance of errors in it becomes a problem in the production.

The present invention was developed to solve such problems, with the aim of providing computer-aided design and computer-aided design software, which can greatly use the model computer graphics or computer-aided design model and can improve the efficiency of design and manufacturing processes.

CAD system according to the present invention comprises: a device information extraction point sequence, which extracts a plurality of point sequences on a curved surface; a dividing device which generates a curved surface from the point sequences using another computer aided design system, and divides the curved surface into a predetermined number of cells; computing device of the first fundamental form computing coefficients of the first fundamental form defined by a tangent vector which forms a tangent plane of the cell; computing device to the second fundamental form computing coefficients of the second fundamental form defined by the tangent vector and a normal cell; a memory that stores the point sequence information, the coefficients of the first fundamental form and coefficients of the second fundamental form.

Moreover, a CAD system according to the present invention further comprises: the principal curvature computing device which computes a principal curvature of the cell based on the coefficients of the first fundamental form and coefficients of the second fundamental form; a line of curvature computing device which computes a line of curvature showing a principal direction of the cell based on the principal curvature; analysis device characteristic points / characteristic lines, which extracts a point or a line, which is becoming a reference point or a reference line conversion, setting the template changes in one or more characteristic values ​​of the five characteristic value showing a characteristic curve of the surface containing the Gaussian curvature and mean curvature, calculated on based on the principal curvature, the main direction of curvature of the line and the coefficients of the first fundamental form and coefficients of the second fundamental form; and a girth length computing device which computes a girth length based on a curvature computed from the coefficients of the first fundamental form and coefficients of the second fundamental form.

Furthermore, computer-aided design of the present invention also comprises: a reproducing device which transforms the line of curvature for the girth length in the line direction of curvature with a characteristic point or feature line as a transformation reference, and reproduces point cell or a curved surface.

Moreover, the CAD system of the present invention also comprises: a converting device which extracts a plurality of point sequences on a curved surface from the reproduced cell or curved surface, and converts the point sequences according to a graphical representation algorithm in another computer aided design.

In accordance with the program-aided design of the present invention on the computer executes: a process of extracting information about the point sequence for extracting a plurality of point sequences on a curved surface; dividing process for generating a curved surface from the point sequences using another computer aided design system, and dividing the curved surface into a predetermined number of cells; calculation process of the first fundamental form computing coefficients of the first fundamental form defined by a tangent vector which forms a tangent plane of the cell; calculation process of the second fundamental form computing coefficients of the second fundamental form defined by the tangent vector and a normal cell; and storing process for storing the point sequence information, the coefficients of the first fundamental form and coefficients of the second fundamental form.

Furthermore, in accordance with the program-aided design of the present invention on a computer is also performed: the principal curvature computing process for computing the curvature of the main cell based on the coefficients of the first fundamental form and coefficients of the second fundamental form; a line of curvature computing process for computing a line of curvature showing a principal direction of the cell based on the principal curvature; the process of analysis of the characteristic points / characteristic lines for extracting a point or a line which become a reference point or a reference line of transformation defined patterns changes in one or more characteristic quantities of the five characteristic values ​​showing the characteristics of the curved surface comprising a Gaussian curvature and a mean curvature computed based on principal curvature, the main direction of curvature of the line and the coefficients of the first fundamental form and coefficients of the second fundamental form; and a girth length computing process for computing a girth length based on a curvature computed from the coefficients of the first fundamental form and coefficients of the second fundamental form.

Moreover, in accordance with the program-aided design of the present invention on the computer also operates the playback process for converting a line of curvature for the girth length in the line direction of curvature with a characteristic point or feature line as a transformation reference point and the playback of the cell or a curved surface.

Furthermore, in accordance with the program-aided design of the present invention on a computer perform the conversion process for extracting a plurality of point sequences on a curved surface from the reproduced cell or curved surface, and converting the point sequences according to a graphical representation algorithm in another computer aided design.

Computer graphics system of the present invention comprises: a device information extraction point sequence, which extracts a plurality of point sequences on a curved surface; a dividing device which generates a curved surface from the point sequences using another computer graphics system, and divides the curved surface into a predetermined number of cells; computing device of the first fundamental form computing coefficients of the first fundamental form defined by a tangent vector which forms a tangent plane of the cell; computing device to the second fundamental form computing coefficients of the second fundamental form defined by the tangent vector and a normal cell; and a memory device which stores the point sequence information, the coefficients of the first fundamental form and coefficients of the second fundamental form.

Furthermore, according to the computer graphics program of the present invention is executed on a computer: a process of extracting information about the point sequence for extracting a plurality of point sequences on a curved surface; dividing process for generating a curved surface from the point sequences using another computer graphics system and dividing the curved surface at the predestined Goes number of cells; calculation process of the first fundamental form computing coefficients of the first fundamental form defined by a tangent vector which forms a tangent plane of the cell; calculation process of the second fundamental form computing coefficients of the second fundamental form defined by the tangent vector and a normal cell; and storing process for storing the point sequence information, the coefficients of the first fundamental form and coefficients of the second fundamental form.

The present invention provides the following results.

Since the device information extraction point sequence extracts a plurality of point sequences on a curved surface a dividing device generates a curved surface from the point sequences using another computer graphics system or computer aided design system, and divides the curved surface into a predetermined number of cells; computing device provides a first fundamental form computing coefficients of the first fundamental form defined by a tangent vector which forms a tangent plane of the cell; computing device provides the second fundamental form computing coefficients of the second fundamental form defined by the tangent vector and a normal cell; and a memory stores information about the point sequence, the coefficients of the first fundamental form and coefficients of the second fundamental form, then by adopting the theory of the curved surface, which ensures line continuity freeform / free-form surface, a model computer graphics model or computer-aided design can be widely consuming and efficiency design and manufacturing processes can be improved.

Also, since it provided on the principal curvature computing device which computes a principal curvature of the cell based on the coefficients of the first fundamental form and coefficients of the second fundamental form; a line of curvature computing device which computes a line of curvature showing a principal direction of the cell based on the principal curvature; analysis device characteristic points / characteristic lines, which extracts a point or a line, which is becoming a reference point or a reference line conversion, setting the template changes in one or more characteristic values ​​of the five characteristic value showing a characteristic curve of the surface containing the Gaussian curvature and mean curvature, calculated on based on the principal curvature, the main direction of curvature of the line and the coefficients of the first fundamental form and coefficients of the second fundamental form; and the computing device the length of coverage, which calculates the length of coverage based on a curvature computed from the coefficients of the first fundamental form and coefficients of the second fundamental form, the model computer graphics or computer aided design, analyzed by the theory of curved surface can be reproduced and transformed into a different model of computer graphics or computer-aided design.

Moreover, as provided by the playback device, which converts the line of curvature for the girth length in the line direction of curvature with a feature point or feature line as a reference point conversion and reproduces cell or a curved surface, the model computer graphics or computer aided design analyzed theory curved surface It can be reproduced.

In addition, because it provides a conversion device which extracts a plurality of point sequences on a curved surface of the reproduced cell or a curved surface and converts the point sequences according to the algorithm graphical representation to another computer graphics or computer-aided design, the model computer graphics or computer aided design, analyzed the theory of curve surface can be transformed into a different model of computer graphics and computer-aided design.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 - is a block diagram showing a configuration of computer aided design of an embodiment of the present invention.

FIG. 2 - an explanatory diagram showing a situation for dividing a curved surface and the reference cell mxn fundamental vectors su and sv.

FIG. 3 - is an explanatory diagram showing planes in which extend tangential unit vector t and the unit normal vector n.

FIG. 4 - is a flowchart of a method showing a flow of processing from the free-form surface analysis to data transfer program by one analysis.

FIG. 5 - is an explanatory diagram showing a direction change of curvature.

FIG. 6 - is an explanatory diagram showing classifications of mean curvature and Gaussian curvature.

FIG. 7 - is an explanatory diagram showing isoclinal orthogonal lines.

FIG. 8 - is an explanatory diagram showing principal curvature extremum lines.

FIG. 9 - is an explanatory diagram showing an extremum lines isoclinal parties Gaussian curvature distribution.

FIG. 10 - an explanatory diagram showing lines of curvature.

EMBODIMENTS

Below is a description of an embodiment of computer aided design system of the present invention is illustrated by drawings. FIG. 1 - is a block diagram showing a configuration of computer aided design system of the present embodiment. CAD system of this embodiment comprises: a CPU, for example, a central processing unit (CPU), etc. (not shown), a memory device, e.g., ROM, RAM, etc. (not shown), the data base 10, the processing section 11 in the graphic display, the display section 12, display section 13 and communication section (not shown).

1 The CPU reads a program analysis, program transformation 2 and 3 playback program stored in the ROM, and executes a series of processes related to the analysis, conversion and playback of free-form surface. RAM - a semiconductor memory in which the CPU primarily stores data.

1 analysis program - a program that the CPU executes the process of reading the data of 20 actual measurement values ​​of the three-dimensional shape of the object by means of automated testing (CAT), etc., or other format data 21 computer-aided design (graphic data represented, for example, by model surfaces, such as the volume model, Bezier, B-spline, rational bezier, or NURBS), creating a table 30 point sequence information, the table 31 of coefficients of the first fundamental form, and the table 32 of coefficients of the second fundamental form, and then store them in the database 10.

Table 30 point sequence information comprises point sequence information (u, v) to the curved surface expressed in parametric form:

(Equation 1)

<IMG>

as shown in FIG. 2. For example, assuming that u = 0, 1 / m, 2 / m, ... m-1 / m (m - natural number) and v = 0, 1 / n, 2 / n, ... n -1 / n (n - natural number), the curved surface shown in FIG. 2, is divided into cell mx n. In this case, the point sequence information (u, v) are mn data sequences from cell identifiers ID1 to IDmn.

The table 31 of coefficients of the first fundamental form comprises coefficients of the first fundamental form E, F and G, derived from the following equations. If u and v, discussed above, have a functional relationship, then s (u, v) denotes a curved line on the curved surface, the partial derivative ds / du = su means tangential vector curve u = constant, and the partial derivative ds / dv = sv mean curve tangent vector v = constant. Under these conditions, the fundamental vectors su and sv forms a tangent plane of the curved surface. Furthermore, the vector ds, connecting two points on a curved surface from s (u, v) to s (u + du, v + dv), is represented as:

(Equation 2)

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Thus the square of the absolute value of ds is represented by:

(Equation 3)

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The above coefficients of the first fundamental form defined from the fundamental vector of the curved surface by the following equation:

(Equation 4)

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The above coefficients of the first fundamental form E, F and G are uniquely determined for the respective cells in this manner. Table 31 coefficients of the first fundamental form retains the values ​​for the corresponding cell identifiers ID1 to IDmn.

Furthermore, combining the above equation 3 and equation 4 gives:

(Equation 5)

<IMG>

Table 32 coefficients of the second fundamental form comprises coefficients of the second fundamental form L, M and N, deduced from the following equations. Assuming that ω - is the angle between the fundamental vectors and su su, then their inner product F, and the absolute value H of the vector product of the fundamental vectors is represented as follows using the coefficients of the first fundamental form:

(Equation 6)

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(Equation 7)

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Then using this calculated value H unit normal vector n on the curved surface is represented as:

(Equation 8)

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Furthermore, as shown in FIG. 3, the beam lines tangential vectors at the point P on the curved surface is located on this tangent plane, and their unit tangent vector t is represented by the following equation:

(Equation 9)

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The plane defined by t and n, as shown in FIG. 3 is called a normal plane.

The curvature k at the point P on the plane of the normal section is called the normal curvature. Differentiation t for the arc length s on a plane normal section provides:

(Equation 10)

<IMG>

Multiplication of both equations on the normal vector and the introduction of the following coefficients of the second fundamental form:

(Equation 11)

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gives:

(Equation 12)

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The above coefficients of the second fundamental form L, M and N are uniquely determined for the respective cells in this manner. Table 32 coefficients of the second fundamental form retains the values ​​for the corresponding cell identifiers ID1 to IDmn.

If equation 5 is substituted into Equation 12 yields the following equation.

(Equation 13)

<IMG>

From the foregoing, the normal curvature is computed from the coefficients of the first fundamental form and coefficients of the second fundamental form.

Program 2 conversion - is a program that executes on a computer a process of reading the information required for the free-form surface of the table 30, the point sequence information, the table 31 of coefficients of the first fundamental form, and the table 32 of coefficients of the second fundamental form, then creating data free-form surface and convert them into a form that can interpret different application-aided design.

Program 3 playback, similarly to program 2 reading - is a program that executes on a computer a process of reading the information required for the free-form surface of the table 30, the point sequence information, the table 31 of coefficients of the first fundamental form, and the table 32 of coefficients of the second fundamental form, then creating data free-form surface and the output processing section 11 on the graphical display.

Database 10 stores the above data table 30, the point sequence information, the table 31 of coefficients of the first fundamental form, and the table 32 of coefficients of the second fundamental form, and writes in the output result of the analysis program 1 in association with an identifier of the cell, as described below.

Processing section 11 performs graphic display processing on the output results of the graphic display of the playback program, and other computer-aided design.

Section 12 of the display shows the output results processing section 11 on the graphic display.

Output section 13 outputs the output results of the processing section 11 on the display in communication section, other recording media, etc. Section transmits data such as the point sequence information, the coefficients of the first fundamental form and coefficients of the second fundamental form stored in the database 1, the data to other clients or servers via a network such as a LAN, the Internet, etc.

The following describes a sequence of processing flows related to the analysis, conversion, and reproduction by means of free-form surface CAD system of the present embodiment, with respect to the drawings. FIG. 4 - is a flowchart of a method showing a flow of processing from the free-form surface analysis to data transfer program by one analysis.

With the help of user actions CPU receives command data analysis for actual measurement values ​​of 20 or 21 different data format CAD 1 reads a program from the ROM and the analysis takes the process of analyzing the free-form surface. First, the CPU performs a process of extracting a plurality of point sequences on a curved surface such as a two-dimensional NURBS surface, bicubic surface, and the like contained in data 20 and actual measurement value data 21 else aided design format. After that, a curved surface is generated from this point sequence using the other computer aided design system (step S1 in FIG. 4) and the curved surface is divided into a predetermined number of the cell mn, as shown in FIG. 2, after which the relevant parts of the cell are standardized by the fundamental vectors su and sv. Point sequence information (u, v), generated during the standardization is written in the table 30, the point sequence information contained in the database 10, in association with the identifier of the cell.

Then, the CPU executes processing of differential geometric analysis. Those. it performs processing for computing the coefficients of the first fundamental form E, F and G, given by fundamental vectors su and sv, which form the tangent plane of the cell. The computed coefficients of the first fundamental form E, F and G, similarly to the point sequence information, are written in the table 31 of coefficients of the first fundamental form, contained in the database 10, in association with the identifier of the cell. Furthermore, CPU performs a process of calculating the coefficients of the second fundamental form L, M and N, the fundamental vectors defined su and sv and the unit normal vector n of the cell. The computed coefficients of the second fundamental form L, M and N, similarly to the coefficients of the first fundamental form E, F and G, are written in the table 32 of coefficients of the second fundamental form, contained in the database 10, in association with the identifier of the cell.

Furthermore, CPU performs processing for computing an integrable condition which is a condition where the differential equation representing the above described cell, continuously in the respective cell boundaries, in other words, a condition where this differential equation has a unique solution.

Now, the coordinates (u, v) of a curved surface as described above, are replaced by (u1, u2), and the set point p (u1, u2). If a curved line formed by fixing u2 and moving u1, called a curve u1, and a curved line formed by fixing u1 and moving u2, called a curve u2, assuming that p (u1, u2) on the curved surface - is the starting point , then the tangent vector along the curve u1 and u2 curved line can be calculated as follows:

(Equation 14)

<IMG>

Then, the unit normal vector n can be calculated from e1 and e2 as follows:

(Equation 15)

<IMG>

Thus, three vectors {e1, e2, n} are defined for the respective points on the curved surface.

For the respective points first fundamental quantities E, F and G are defined as follows:

(Equation 16)

<IMG>

Then, a first fundamental tensor (gij, i, j = 1, 2) is defined as follows:

(Equation 17)

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In addition, four numerical combination gij, i, j = 1, 2, are defined as follows.

(Equation 18)

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Moreover, for the respective points of the second fundamental quantities L, M and N are defined as follows:

(Equation 19)

<IMG>

Then, a second fundamental tensor (hij, i, j = 1, 2) is defined as follows:

(Equation 20)

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Now, if the dynamic coordinate system {e1, e2, n} is differentiated by the coordinates (u1, u2) curved surface obtained by structural equations of a curved surface shown by the following two equations (Gaussian equation 21 and Weingarten's equation 22):

(Equation 21)

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(Equation 22)

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(Equation 23)

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Equation 23 shows where the Christoffel symbol.

Integrable condition of the structure equations 21 and 22 is shown by the following two equations (Equation 24 Gauss equation and the equation Mainardi-Codazzi equation 25):

(Equation 24)

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(Equation 25)

<IMG>

(Equation 26)

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where the equation 26 shows the curvature tensor Reimann-Christoffel.

In the case where the first fundamental tensor (gij, i, j = 1, 2) and the second fundamental tensor (hij, i, j = 1, 2) are used as a function of the coordinates (u1, u2) of the curved surface, and they satisfy the above equation Gauss and Codazzi-Mainardi equation, the shape of the surface having the gij and hij, uniquely determined (in accordance with the fundamental theory of Bonn). Consequently, the appropriate cells are continuous C2.

The CPU performs the arithmetic processes and calculates the above integrable condition (step S2).

Next, the CPU executes the process of analyzing the lines of curvature, the process of analyzing the characteristic lines and the process of converting the curvature / girth length (step S3). First, principal curvatures k1 and k2 are calculated in the cell based on the coefficients of the first fundamental form E, F and G and the coefficients of the second fundamental form L, M and N by the line of curvature analyzing process (step S4).

That is first calculated above extremum curvature k1. The form of the normal section of the plane, which is the intersection of the normal plane and curved surface varies with the direction of the touch and also changes the normal curvature. This form is returned to the initial condition when the normal half-plane rotated. Now, assuming that:

(Equation 27)

<IMG>

and overwriting k as a function of k (γ) of γ, we get:

(Equation 28)

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From this quadratic equation γ, for dk (γ) / dγ = 0, k (γ) becomes a peak. Then, if the equation 15 is differentiated in this condition for an extremum and γ k, and rewritten as,

<IMG>

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(Equation 29)

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received. Then, if it is substituted in equation 16,

(Equation 30)

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