JP2770315B2 - Object surface shape data creation method - Google Patents

Description

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

A Industrial Field of Use B Summary of the Invention C Prior Art D Problems to be Solved by the Invention E Means for Solving Problems (FIGS. 2 and 3) F Function (FIGS. 2 and 3) Fig. G Example (G1) Principle of Free Curve (Fig. 2) (G2) Example of Free Curve Creation (Figs. 1 to 7) (G3) Other Examples H Effect of the Invention A Industrial BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for creating surface shape data of an object, for example, CAD (computer aided design) or CAM (computer).
In the aided manufacturing, the present invention is suitably applied to a case where the surface shape of an object represented by a generated free curve is deformed.

B. SUMMARY OF THE INVENTION The present invention relates to a method for deforming a detailed surface shape of an object consisting of a plurality of curved segments connected to each other under a tangential continuity condition. The control points are moved in the same direction by the same amount of movement, and two new curve segments are formed while maintaining the tangent continuity condition.

C Prior Art For example, when designing the shape of an object having a free-form surface using a CAD method (geometric modeling), a designer generally uses a plurality of points in a three-dimensional space through which the surface passes (referred to as nodes). Is designated, and a computer calculates a boundary curve network connecting the plurality of designated nodes by using a predetermined vector function, thereby creating a curved surface represented by a so-called wire frame. Thus, a large number of framework spaces surrounded by boundary curves can be formed (such processing is hereinafter referred to as framework processing).

The boundary curve network formed by such framework processing is
It itself represents the rough shape of the surface of the object that the designer intends to design, and a curved surface that can be expressed by a predetermined vector function using the boundary curve surrounding each framework space as an interpolation calculation as the surface shape of the details of the object If it can be done, it is possible to generate a free-form surface (which cannot be defined by a quadratic function) designed by the designer as the surface shape of the object as a whole. Here, the curved surface formed in each frame space forms a detailed surface shape of the object as a basic element constituting the entire curved surface, and this is called a patch.

Conventionally, in a CAD system of this kind, a cubic tensor product of, for example, a Bezier equation or a B-Spline equation, which is easy to calculate, is used as a vector function expressing a boundary curve network. For example, it is considered to be optimal for mathematical expression of a free-form surface having no special feature in shape.

In other words, a free-form surface representing the surface shape of an object that does not have special features in terms of shape is such that when points given in space are projected on the xy plane, the projected points are regularly arranged in a matrix. And the number of projection points is m × n
It is known that when represented by, the framework space can be easily stretched using a quadrilateral patch represented by a cubic Bezier equation.

However, when this conventional mathematical expression is applied to a curved surface having a shape characteristic (for example, a curved surface having a greatly distorted shape), in order to obtain a curved surface that can be used as a surface shape of an object, Since there is a difficulty in the connection method between the patches and it is necessary to execute a high-level mathematical operation process, there has been a problem that the operation process by the computer becomes complicated and enormous, and the operation time becomes long.

As a method for solving this problem, an internal control point that satisfies the condition of continuation of a tangent plane is obtained for a shared boundary of adjacent framework spaces, and a vector function representing a free-form surface determined by the internal control point is obtained. Therefore, a method of stretching a patch with a free-form surface has been proposed (Japanese Patent Application No. 60-277448).
No., Japanese Patent Application No. 60-290849, Japanese Patent Application No. 60-298638, Japanese Patent Application No.
No. 61-15396, Japanese Patent Application No. 61-33412, Japanese Patent Application No. 61-59790
No., Japanese Patent Application No. 61-64560, Japanese Patent Application No. 61-96368, Japanese Patent Application No. 61
-69385).

D Problems to be Solved by the Invention By the way, in practice, the design work of a designer is usually performed by repeating a local correction so as to approach the shape imagined by the designer step by step. Thus, the free-form surface generated as described above is repeatedly corrected so as to approach the shape imaged by the designer.

That is, as a method of correcting such a free-form surface, the designer cuts the free-form surface at a desired cross section on the surface screen, and visually confirms the cross-sectional shape of the free-form surface obtained thereby.
After locally modifying details of a free curve in which a plurality of curve segments each composed of a Bezier curve represented by a cubic Bezier equation representing the cross-sectional shape are connected, a free-form surface is generated again based on the cross-sectional shape. (Japanese Patent Application Nos. 62-276925 and 62-278694).

However, when a designer modifies a free-form surface using such a technique, it swells any part of the free-form curve, which is a cross-sectional shape, by a very small amount without excessively deforming it from the original curve shape. There are times when you want to correct or check the shape of the free curve by making it concave or concave.

In such a case, conventionally, for each curve segment of the free curve, the nodes and internal control points are moved in an arbitrary direction to deform the curve shape for each curve segment, and then the adjacent curve segment is re-formed. By re-setting the internal control points so as to satisfy the tangent continuity condition, curve segments adjacent to each other must be smoothly connected to form a new curve, which is a very complicated design for the designer There was a problem that work was required.

The present invention has been made in view of the above points, and proposes a free curve creation method capable of smoothly deforming the free curve while maintaining the atmosphere of the original free curve with a simple operation of the designer. Things.

E Means for Solving the Problems In order to solve such problems, the present invention uses a computer to generate a large number of nodes representing the rough shape of an object. Of the adjacent nodes, the vector function is calculated by sequentially specifying the positions between the nodes by the parameters u and v sequentially specified at predetermined intervals, thereby obtaining the position vector data at the positions between the nodes. To obtain a plurality of curve segments representing the detailed surface shape of the object.
In the method of creating surface shape data of an object for creating surface shape data for K _SG1N and K _SG2N (K _SG2N and K _SG3N ),
Control points in each curve segment such that the tangent vectors at the nodes between two adjacent curve segments are equal and the tangent vectors are collinear. By setting the position vector data of the surface shape data of an object representing a plurality of curve segments connected under the condition of tangent continuity with each other, when changing the surface shape data of the object, a plurality of curve segments
A first step (SP1) for selecting one of K _SG1N , K _SG2N (K _SG2N , K _SG3N ) and a selected curve segment K
One node of _SG1 And a second step SP2 of selecting the selected node, and moving the selected node in a predetermined direction by a predetermined amount to obtain position vector data of a new node. To obtain the position vector data representing the selected node Vector data that gives a predetermined amount of movement in a predetermined direction with respect to And the selected node In the same direction and the same amount of movement as the predetermined direction and the predetermined amount of movement. A new curve segment K from the surface shape data of the curve segment selected based on the new node and control point position vector data, and a third step SP4 of obtaining the new control point position vector data by moving _A fourth step SP6 for obtaining surface shape data representing a new detailed surface shape of _SGIN , and _performing the same processing for K _SG2 and K _SG3 other than the selected curve segment K _SG1 among the plurality of curve segments. By executing the process, surface shape data representing a new detailed surface shape is generated while substantially maintaining the condition of tangent continuation.

In order to deform the detailed surface shape of an object consisting of multiple curved segments connected under the condition of tangential continuity with each other,
A node shared by the two curve segments and a control point adjacent to the node are moved by the same amount of movement in the same direction to form two new curve segments while maintaining the condition of tangent continuity. This makes it possible to easily create surface shape data of an object obtained by smoothly deforming the portion of the detailed surface shape while maintaining the atmosphere of the detailed surface shape of the original object.

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

(G1) Principle of Free Curve Creation In this embodiment, the free curve is composed of nodes set at arbitrary intervals as shown in FIG. K _SG (K _SG1 , K _SG2 , K
_SG3 ) is connected. This curve segment K _SG is 3
Using the following Bezier equation, Parametric space curve represented by Is represented by

Where t is one of the nodes From the other node in the direction along the curve segment K _SG Is a parameter that changes from value 0 to value 1 as represented by the following equation: 0 ≦ t ≦ 1 (2)

Thus, the curve segment K _SG represented by the cubic Bezier equation is converted to a node by the shift operator E. 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 With the relationship Therefore, by expanding the equation (1) and substituting the relation of the equation (4), the following equation is obtained. , And as a result, the equation (3) is obtained.

Thus, each curve segment K _SG1 , K _SG2 ,
K _SG3 has two nodes and control points based on equation (3). And each curve segment K _SG1 ,
K _SG2, K by representing a free curve using _SG3, nodes and control points respectively representing each curve segment K _SG1, K _SG2, K _SG3 Can be used to represent a free curve.

(G2) Embodiment of Free Curve Creation This embodiment is, as shown in FIG. 2, composed of three curve segments K _SG1 and K _SG1 connected under tangential continuity conditions.
It is intended to create a free curve that swells upward smoothly on any part of the free curve including _SG2 and _KSG3 while maintaining the atmosphere of the original shape.

The central processing unit (CPU) of the free-curve creation device, in accordance with the instructions of the designer, executes the curve deformation processing program shown in FIG.
By executing the SP0, Yotsute the method shown in Figure 3, first of the three curve segment _{K SG1, K SG2, K SG3} 1
The shape of the curve segment _KSG1 was changed, and
As shown in FIG. 7, the second and third curve segments K
Curve deformation processing program SP0 for _SG2 and K _SG3
, The curve shape including the three curve segments K _SG1 , K _SG2 , and K _SG3 as a whole _swells smoothly upward while maintaining the atmosphere of the original shape under the condition of tangent continuation. It is designed so that a free curve can be created.

That the CPU, the input connexion step SP1 to curve deformation processing program SP0, and waits a specified curve segment K _SG to perform transformation process from the designer.

Here, the designer uses, for example, a mouse or the like, and as shown in FIG. 2, three curve segments K _SG1 ,
Among K _SG2, K _SG3, when moving the cursor on the first curve segment K _SG1 to be Kurutsuku mouse, CPU in the next step SP2, the first curve segment K _SG1 specified by the designer, deformation Nodes that serve as processing criteria Wait for your choice.

In this state, the designer uses the mouse to _move one node on the first curve segment KSG1. If you move the cursor to and click the mouse, the CPU
Is the node in the next step SP3 Wait for the designer to specify whether to use the input value of the movement vector or to specify it on the display screen as the movement direction and movement distance.

If a negative result is obtained (that is, this means that the designer sets the moving direction and the moving distance on the display screen), the CPU proceeds to the next step SP4 and specifies the moving direction and the moving distance from the designer. Wait for.

In this state, the designer visually checks the display screen,
Node using mouse When you stop the cursor at the position where you want to move the mouse and click the mouse, the CPU displays the movement vector that is the specified result on the display screen. Is displayed, and proceed to the next step SP6.

If the CPU obtains an affirmative result in step SP3 described above (that is, this means that the designer inputs the moving direction and the moving distance as vector information from, for example, a keyboard or the like), the CPU proceeds to step SP5 and outputs from the designer. Wait for the specification of the moving direction and moving distance.

In this state the designer is a node When the position where you want to move is input as vector information from a keyboard or the like, the CPU displays the movement vector that is the specified result on the display screen. Is displayed, and proceed to the next step SP6.

In this step SP6, the CPU returns to the node selected in step SP2 as shown in FIG. Control point adjacent to In the direction of movement specified by the designer New node that is moved only Is calculated, and subsequently, the nodes are calculated using the method described above with respect to the expressions (1) to (6). Control point A new first curve segment K _SG1N is obtained by calculation.

Subsequently CPU displays a new first curve segment K _SG1N with One Motomema by calculation in the next step SP7 on the display screen as shown in FIG. 4, at next step SP8, whether the end of the curve deformation processing If a positive result is obtained here (indicating that the designer has instructed the end of the curve deformation processing), the CPU proceeds to the next step SP9.
And ends the curve deformation processing program SP0.

If a negative result is obtained in step SP9 (this indicates that the designer has instructed to continue the curve deformation process), the CPU returns to step SP1 described above, and returns to steps SP2-SP3-SP4-SP5-SP5-. Execute the processing of SP6-SP7.

In this way, the CPU executes the processing loop of the curve deformation processing program SP0 once according to the instruction from the designer, thereby maintaining the atmosphere of the shape of the original first curve segment _KSG1 , A new first curved segment _KSG1N can be created by _expanding this smoothly upward.

In the case designer of this embodiment, as shown in Figure 4, in a state where the first curve segment K _SG1N new is displayed on the display screen, the adjacent first curve segment K _SG1 original Select the second curve segment K _SG2 and select the original first
Node of curve segment K _SG1 of And specify the above-mentioned node Moving direction and moving distance If a value equal to is used, as shown in FIG. 5, while maintaining the atmosphere of the shape of the original second curve segment K _SG2 like the new first curve segment K _SG1N , A new second curved segment _KSG2N can be created by _expanding this smoothly upward.

Furthermore, the second and third curve segments K _SG2 and K _SG3
Similarly, as described above, as shown in FIGS. 6 and 7, the second and third curve segments _KSG2 and _KSG3
The second and third curve segments _KSG2N and _KSG3N can be created by _{smoothly expanding} the shape upward while maintaining the atmosphere of the shape of.

In this case, two curved segments K _SG1 and K _SG2 (K _SG2 and K _SG3 ) connected to each other under the condition of tangential continuity
Nodes shared by each other About the same direction and the same amount of movement , So that two new curve segments are maintained while maintaining the condition of tangent continuity.
K _SG1N and K _SG2N (K _SG2N and K _SG3N ) can thus be formed, and thus a plurality of curve segments K _SG1 , K _SG2 , K _SG3 as a whole
It is possible to create a free curve that swells smoothly upward in any part of the curved shape including, while maintaining the atmosphere of the original shape.

According to the above method, the node shared by the two curve segments connected under the condition of the tangent continuity and the control point adjacent to the node are moved by the same amount of movement in the same direction, and the condition of the tangent continuity is obtained. By forming two new curve segments while maintaining the condition, it is possible to create a free curve in which the free curve smoothly expands upward while maintaining the atmosphere of the original curve shape. .

Also, if this new free curve is moved by the same amount of movement with its sign inverted, it can be easily returned to the original shape of the free curve, and if it is moved by the amount of movement in the negative direction, A new free curve in which the free curve is smoothly recessed can be created while maintaining the atmosphere of the curved shape.

Thus, by repeating the above-described free curve creation method, the curve shape as a whole can be arbitrarily changed by a minute amount without changing the detailed shape of each curve segment by a complicated operation. In doing so, 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 curve segment represented by a cubic Bezier equation is set on an arbitrary plane, but the order of the mathematical equation is not limited to this. The fourth or higher order may be used.

(2) In the above-described embodiment, the case where the curve segment represented by the Bezier equation is extended has been described. However, the present invention is not limited to this. For example, a spline equation, a Coons equation, a Forgason equation, etc. May be used.

H Advantageous Effects of the Invention As described above, according to the present invention, when deforming the detailed surface shape of an object consisting of a plurality of curve segments connected under a tangential continuity condition, the nodes shared by the two curve segments And by moving the control points adjacent to the node by the same amount of movement in the same direction to form two new curved segments while maintaining the condition of tangent continuity, the detailed surface of the original object can be formed. Surface shape data of an object in which the detailed surface shape portion is smoothly deformed can be easily created while maintaining the shape atmosphere.

[Brief description of the drawings]

FIG. 1 is a flowchart showing one embodiment of the present invention, and FIG.
FIG. 3 is a schematic diagram for explaining a curved segment, FIG. 3 is a schematic diagram for explaining a deformation of a first curved segment, FIG.
FIG. 7 to FIG. 7 are schematic diagrams used to describe a process of deforming a free curve composed of first to third curve segments. K _SG1 , K _SG2 , K _SG3 …… original curve segment, K _SG1N , K
_SG2N , K _SG3N …… new curve segment,

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int.Cl. ⁶ , DB name) G06T 17/00 JICST file (JOIS)

Claims (1)

(57) [Claims] A computer is used to sequentially designate a position between adjacent nodes among a plurality of nodes representing a rough shape of an object at predetermined intervals by using a parameter. By calculating a vector function, the position vector data at the position between the nodes is obtained, and thereby the surface shape data of a plurality of curve segments representing the detailed surface shape of the object is generated. In the method, by setting position vector data of control points in each curve segment such that tangent vectors at nodes between two adjacent curve segments are equal to each other and the tangent vectors are collinear, Surface shape data of an object representing multiple curved segments connected under continuous conditions A first step of selecting one of the plurality of curve segments when changing the surface shape data of the object;
And a second step for selecting one node of the selected curve segment; and moving the selected node in a predetermined direction by a predetermined amount to obtain position vector data of a new node. In addition, while calculating direction vector data that gives a predetermined amount of movement in the predetermined direction with respect to the position vector data representing the selected node, the position vector data of the control point next to the selected node, A third step of obtaining the position vector data of a new control point by moving in the same direction and the same amount of movement as the predetermined direction and the predetermined movement amount, and based on the position vector data of the new node and the control point. Obtaining surface shape data representing a new detailed surface shape for a new curve segment from the surface shape data of the selected curve segment. A fourth step of executing a similar process on the plurality of curve segments other than the selected curve segment to thereby obtain a new detailed surface shape while substantially maintaining the tangent continuity condition. A method for generating surface shape data of an object, characterized by generating surface shape data representing the following.