JP2745565B2 - How to create curve data representing the shape of an object - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention will be described in the following order.

A Industrial application field B Outline of the invention C Conventional technology (Fig. 6) D Problems to be solved by the invention (Fig. 7) E Means for solving the problems (Figs. 1 to 4) F action (FIGS. 1 to 4) G example (G1) Principle of free curve (FIGS. 2 and 3) (G2) Example of free curve creation (FIGS. 1 to 5) G3) Other Embodiments H Effects of the Invention A Industrial Field of the Invention The present invention relates to a method for creating curve data representing the shape of an object, and is particularly suitable for application to a CAD (computer aided design) type design apparatus. .

The present invention provides a method for creating curve data representing the shape of an object to be designed, using a plurality of nodes and coefficient data representing the length of a control line vector between the plurality of adjacent nodes. Is calculated by calculating a parametric space curve represented by control points satisfying the tangent continuity condition obtained in the above, and creating a free curve passing through a plurality of nodes. A design device can be easily realized.

C. Prior Art This type of design apparatus is used when designing an industrial product, and a method for forming a desired curved surface in an xyz space is disclosed in Japanese Patent Application Laid-Open No. 58-22413.

This method for creating a curved surface is based on sequentially selecting a plurality of adjacent nodes from a number of points designated in the xyz space (these are referred to as nodes) with a radius of curvature within a predetermined error range. It is possible to generate a curved surface approximating a curved surface passing through the designated node as a whole.

However, according to this method, since a surface that can be generated is limited to a surface represented by a quadratic function, a free-form surface having an arbitrary shape (which cannot be defined by a quadratic function) cannot be generated as necessary. It is still insufficient in point.

As a method of solving this problem, a method of generating a free-form surface using successively adjacent nodes using an expression represented by a B-spline function has been proposed. A smooth free-form surface approximating an array can be generated.

That is, for the free curve that constitutes this free-form surface,
As shown in Fig. 6, the designer has seven nodes Is set in the xyz space, a smooth free curve K0 can be generated so as to roughly follow a straight line connecting nodes adjacent to each other, and a point on the smooth free curve K0 can be generated. Is Can be obtained by solving the simultaneous equations

here, Therefore, the expressions (1) to (5) are Which can be transformed as follows: Can be expressed in a matrix format as

D. Problems to be Solved by the Invention However, according to this method, there is a problem that it is difficult to efficiently adapt to the design procedure of the designer when actually designing the shape of an industrial product.

First, since the generated B-spline curve does not pass through the node specified by the designer, there is a disadvantage that the outer dimensions of the generated free curve cannot be predicted at the stage when the designer specifies the node.

In general, when designing an industrial product in practice, as shown in FIG. 7, a cross section is assumed for the main part of the product, and the outer dimensions of the cross section (for example, the outer dimension L _{x1 in the} x direction and the outer dimension L in the y direction). The outer dimension (represented by _Ly1 ) is often given as a basic design condition, and the designer must select nodes so as to satisfy all the conditions for such a cross-sectional shape.

However, since the B-spline function generated as described above with reference to FIG. 6 does not pass through the node specified by the designer, the designer ends up generating a B-spline curve generated by repeatedly specifying the node by trial and error. When the shape and dimensions are displayed on the display and examined, and as a result the design conditions for the external dimensions cannot be satisfied, a complicated operation of resetting the nodes must be repeated.

This means that even if an attempt is made to correct a part of the cross-sectional shape once the design is completed, the local correction cannot be performed, and only the entire correction can be performed.

However, in practice, the design work of the designer usually involves making the outer shape that is being created closer to the shape that the designer imagines by repeating local modifications. , In this regard B
-The method of generating a cross-sectional shape by using a spline curve is inconveniently inconsistent with the design procedure.

Third, the B-spline curve is characterized in that, in principle, it generates a curve that satisfies the condition that the curvature is continuous and the tangent is continuous. For example, the B-spline curve has a small curvature such that it is adjacent to a curved portion having a large curvature. In some cases, even if an attempt is made to generate a curved portion, it cannot be actually generated. If an unreasonable way of specifying a node is used, the generated outer shape curve is deformed to an unpredictable degree (for example, the curved portion K0X in FIG. 7). As shown in FIG. 2).

The present invention has been made in consideration of the above points. For example, when a designer designs a cross-sectional shape, a free curve passing through a plurality of points designated in advance can be generated by a simple design work. It is intended to propose a method of creating a free curve.

Means for solving problem E G Example Hereinafter, an example of the present invention will be described in detail with reference to the drawings.

(G1) Free curve principle 0 ≦ t ≦ 1 (15) A parameter that changes from a value 0 to a value 1 as represented by (15).

Thus, the curve segment K _SG represented by the cubic Bezier equation is converted to a node by the shift operator E. Two control points between By specifying, each point on the curve segment K _SG is Position vector from the origin O of xyz space by the expansion formula of It is expressed as

Where the shift operator E is the control point on the curve segment K _SG For i = 0, 1, 2,... (18) Therefore, by expanding equation (14) and substituting the relationship of equation (17), , And as a result, equation (16) is obtained.

Are obtained by substituting the value of the parameter t and t = 0 and 1 into Is represented by

By the way, each such curve segment _KSG1 , _KSG2 ,
The connection at each node of the free curve formed by connecting _KSG3 is generally not smooth.

In this way, each curve segment K _SG1 , K _SG2 , K _SG3
Can be connected to form a smooth free curve as a whole.

(G2) Embodiment of Creating a Free Curve This embodiment is to create a smooth free curve passing through a plurality of points designated by a designer.

The central processing unit (CPU) of the design device, according to the instructions of the designer, executes the free curve creation processing program shown in FIG.
By executing SP1, according to the method shown in FIGS. 2 and 3, a plurality of points designated by the designer are set as nodes, and the tangent continuity condition is satisfied between the nodes at the nodes. By sequentially forming two curve segments, a smooth free curve passing through a plurality of points as a whole can be created.

That is, the CPU enters the free curve creation processing program SP1, and in the next step SP2, sets the internal variable i to the value “0”.
Is set and initialized. In the next step SP3, the internal variable i is incremented, and in the next step SP4, a point, that is, a node It is determined whether or not the input is a coordinate value input in the xyz space.

If a negative result is obtained here, the CPU proceeds to the next step SP5, where a node is picked up from the designer by picking up a point. Waiting for the designation, the designer moves the cursor while referring to the display using, for example, a mouse, and clicks the mouse. Is specified, the process proceeds to the next step SP7.

If an affirmative result is obtained in step SP4, the CPU proceeds to step SP6, where the node based on the coordinate value from the designer is used. When the designer inputs the coordinate value numerically from the keyboard etc., the node corresponding to this coordinate value Is displayed on the display, and then the process proceeds to the next step SP7.

In this step SP7, the CPU Is determined based on the instruction from the designer, and if a negative result is obtained, the process returns to step SP3 and executes steps SP4-SP5 (SP6) to execute the node. Continues the specified input processing of.

If a positive result is obtained in step SP7, the CPU proceeds to the next step SP8, stores the value of the internal variable i in the internal register n, and then proceeds to the next step SP9.

In this step SP9, the CPU determines each node in the final free curve. Waiting for the specification of the coefficient α indicating the tension between them, when the designer inputs the coefficient α from the keyboard or the like, the flow proceeds to the next step SP10.

In step SP10, the CPU sets the internal variable i to the value "0".
Is set, in step SP11, this internal variable i
Is incremented, and the routine goes to the next step SP12.

The length of a chord vector consisting of a straight line l _i-1 (in this case, a straight line l ₀ ) and a chord vector consisting of a straight line l _i (in this case, a straight line l ₁ ) is expressed by a numerical value from the designer. It is calculated by dividing by the input coefficient α.

In this step SP14, the CPU (In this case, the node Waiting for the specification of the direction of the control line vector from the designer, and when the direction of the control line vector is input by, for example, picking up a point on the display with a mouse or inputting a coordinate value, the above equation (26) and The node as in equation (27) Is divided by the coefficient α numerically input from the designer, and the length of the string vector (in this case, composed of straight lines l ₀ and l ₄ )
Calculate the magnitude of the control line vector, and use this to specify the nodes specified at both ends Control point (in this case, the control point Is calculated).

Next, the CPU executes the node specified and input from the designer. And the control points calculated in steps SP12 and SP14 described above. Is used to create the above-described cubic free-form Bezier free-form curve for equations (14) to (19), display the free-form curve on the display, and proceed to the next step SP16.

In this step SP16, in step SP9, the CPU determines whether or not to change the value of the coefficient α specified by the designer from the input from the designer. If a negative result is obtained, the CPU proceeds to step SP17. To
The free curve creation processing program SP1 ends.

When the CPU obtains an affirmative result in step SP16, it returns to step SP9 and waits for designation of a new coefficient α. Based on the coefficient α thus designated, the above-mentioned steps SP10-SP11-SP12-SP13 are executed. The processing loop of -SP14-SP15 is executed to create a free curve based on the newly designated coefficient α.

When the value of the coefficient α is sequentially changed to, for example, α = 3, 4, 6, and 8, the designer specifies the coefficient α as shown in FIGS. 5 (A), (B), (C) and (D). point Can be used as a node to deform the shape of the free curve in an atmosphere in which the tension gradually increases.

According to the above method, a parametric space curve represented by a plurality of nodes and control points satisfying the condition of tangent continuity obtained between the plurality of adjacent nodes is calculated. Is created, a free curve that smoothly passes through a plurality of points designated in advance can be created by a simple operation of the designer as a whole.

Further, according to the above-described method, by dividing the distance between adjacent nodes by an arbitrary coefficient to calculate the magnitude of the control line vector, even if the distance between the nodes is extremely different, the free line created Unnatural feelings such as wavy curves can be effectively prevented, and by changing this coefficient in various ways, the shape of the free curve can be deformed in an atmosphere where the tension increases and decreases at multiple points as nodes, and thus Therefore, the usability of the designer in model creation, free curve design, and the like can be significantly improved.

(G3) Other Embodiments (1) In the above-described embodiment, a case has been described in which a free curve is created that passes points sequentially designated by the designer based on the input order. May be changed after the input of "?", And a free curve may be created by giving the passing order to points that already exist in the design work process of the designer.

By doing so, the degree of freedom in the design of the designer can be improved, and a user-friendly design device can be realized.

(2) In the above-described embodiment, the magnitude of the control line vector is calculated based on the distance between the contacts including the control line vector and the coefficient input from the designer. The present invention is not limited to this, and various changes may be made. Further, if necessary, a means for separately inputting the magnitude of an arbitrary control line vector may be added.

(3) In the above-described embodiment, a case has been described in which a curve segment represented by a cubic Bezier equation is set in the xzy space. However, the degree of the mathematical equation is not limited to this, and may be fourth or higher.

H Advantageous Effects of the Invention As described above, according to the present invention, the tangent continuity condition obtained by using the plurality of nodes and the coefficient data representing the length of the control line vector between the plurality of adjacent nodes is satisfied. By repeatedly calculating a parametric space curve represented by the control points for a plurality of nodes and creating a free curve passing through the plurality of nodes, the designer can easily perform the entire operation with a simple operation. It is possible to create a free curve that smoothly passes through a plurality of nodes specified in advance.

[Brief description of the drawings]

FIG. 1 is a flow chart showing one embodiment of the present invention, and FIG.
FIG. 3 is a schematic diagram illustrating the principle of a free curve, FIG. 3 is a schematic diagram illustrating the connection of curve segments under the condition of tangent continuity, and FIG. FIG. 5 is a schematic diagram showing a difference in the result of creating a free curve due to a difference in coefficient α, FIG. 6 is a schematic diagram showing a free curve created by a conventional method, and FIG. FIG. 3 is a schematic diagram for explaining a problem.

 ────────────────────────────────────────────────── ─── Continuation of front page (56) References JP-A-63-8880 (JP, A) JP-A-62-221073 (JP, A) IPSJ Graphics and CAD Symposium, December 1984 , PP. 51-62 Proc. Of the 1988 Autumn Meeting of the Japan Society of Precision Engineering, Proc. 459−460

Claims (1)

(57) [Claims] 1. Using a central processing unit of a design apparatus,
A curve data creation method for creating curve data representing the shape of an object based on roughly set nodes, comprising inputting data on coordinates of a plurality of nodes so as to provide a plurality of points in a three-dimensional space. A first step to be displayed, a second step to store a variable value relating to the number of times data relating to the coordinates of the node has been input in a register, and a coefficient line representing the length of the control line vector, to obtain a tangent continuation. A third step of calculating control point data that satisfies the following condition between the plurality of adjacent nodes; and a parametric space curve using the data on the coordinates of the plurality of nodes and the control point data. And a fourth step of generating the curve segment data, wherein the fourth step is repeated a number of times based on the variable value stored in the register. By executing, curve data creation method of representing the shape of an object, characterized in that so as to generate a curve data representing the shape of an object passing through the plurality of nodes.