JP2737127B2 - Object surface shape data creation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field] The present invention relates to a method for generating surface shape data of an object,
It is optimal for use in three-dimensional shape modeling in CAM. [Summary of the Invention] Two points based on control point information of each surface element are defined in a space between two distant surface elements on the external curved surface of the object, and
Using the point as a control point, a cubic Bezier curve is generated between the boundary end points of each pixel, and the 3rd-order Bezier curve is similarly generated between the boundary end points on the other side of each pixel.
A next Bezier curve is generated, and each curve is set as a boundary line (side) of a surface element to be interpolated, so that a target contour surface can be easily and quickly obtained by removing and interpolating the surface element. This is a method for creating surface shape data of an object. [Prior art] CAD that handles data of three-dimensional free-form surfaces inside a computer and generates NC data (tool path data) for automatically processing the final product or die with an NC machine tool from these data / CAM system is being put to practical use. When dealing with object curved surfaces such as product outlines in a computer, Bzier has properties that are favorable for design such as good controllability of the shape (easy modification and modification) and easy calculation.
A parametric expression format using an expression or a B-spline expression is often used. The three-dimensional model is
It is represented as a set of surface elements (patches) composed of line elements that can be calculated by these equations. [Problems to be Solved by the Invention] In the process of designing a free-form surface of an object, if one surface element (curved surface patch) is deleted because the shape is not as intended, the process returns to the initial stage of shape design. There must be.
Therefore, a procedure of generating a boundary steel (a set of patches) composed of curves again and generating a curved surface is taken, which is very troublesome. In view of this problem, an object of the present invention is to generate (interpolate) a new patch that is geometrically and positionally consistent (continuous) from adjacent patches of a deleted patch. [Means for Solving the Problems] The method for generating surface shape data of an object according to the present invention uses a computer to calculate a surface between surface elements S ₁ and S ₂ as detailed surface shapes of two objects that are separated from each other. To interpolate the element,
A S _1, S ₂ the surface elements data representing the detail surface shape of the object so as to continuously connected, that is, the surface shape creation method of an object that generates patch data, while in contact with the surface elements S ₃ to be interpolated in the end point P ₁ of the boundary line C ₃ of the surface elements S _1, and the other to form a vector of vectors and reverse through the control points around the endpoints, the length, corresponding to this point and the point P ₁ Face element
A fraction of the distance between the end point P ₂ of S _2, the boundary line C of the first process of obtaining the end points as the control points Q _1, the other surface elements S ₂ in contact with the surface element S ₃ in ₄ of the end point P _2, control points by performing the same processing as the first step corresponding to the control point Q ₁
A second process of obtaining the Q _2, the point P _1, P ₂ and an end point, the point Q _1, Q ₂
Using these point vector data as control points, 3
Performing a third process of generating a next Bezier curve data C _1, the boundary line C _3, C ₄ of the other end point P _3, P ₄ relates to the aforementioned first to third step, the point P _3, P ₄ A _{fourth step} of generating cubic Bezier curve data C ₂ using the vector data of the points Q ₃ and Q ₄ corresponding to the points Q ₁ and Q ₂ as control points, A fifth step of using the cubic Bezier curve data C _{1 to} C ₄ as boundary data to generate bicubic Bezier surface data S ₃ having the curves C _{1 to} C ₄ as four sides, Face element
When the surface element between S ₁ and S ₂ is deleted, the above-mentioned surface element S ₃ is interpolated from the surface element S ₁ and S ₂ so as to interpolate the new surface element S ₃ which is tangentially continuous and smoothly connected in shape and position. It is characterized by generating bicubic Bezier surface data. In the above, the control points and endpoints of the Bezier curve are treated as position vectors, and these control points, endpoints and boundary lines, curves,
Surfaces are treated as data. [Operation] An interpolated surface element composed of a Bezier surface is directly generated by using the control points and the end points of the four sides constituting each of two separated surface elements on the free-form surface. The separated surface element and the interpolated surface element match in terms of position and shape, and are tangently connected and smoothly connected. EXAMPLES illustrating one method of interpolating a surface elements S _1, a new interpolation area element S ₃ between S ₂ in Figure 1. FIG. 2 shows a flowchart of the generation procedure. In this example, the surface elements S ₁ and S ₂ are each formed by a quadrilateral, and each side is represented by a cubic Bezier curve represented by four control points P _{0 to} P ₃ as shown in FIG. ing. Tensor expression of cubic Bezier curve, R (t) = (1 -t + tE) 3 P 0 = (1-t) 3 P 0 +3 (1-t) 2 EP 0 +3 (1-t) t 2 E 2 P + t ³ E ³ P ₀ (1) t is a parameter that takes a value of 0 to 1 between both end points P ₀ and P ₃ (node). E is a shift operator indicating each control point, where P ₁ = EP ₀ , P ₂ = E ² P ₀ , and P ₃ = E ³ P ₀ . A quadrilateral surface element is a bicubic Bezier equation using 16 control points 1 to 16 as shown in FIG. 4, using u and v as parameters, S (u, v) = (1−u + uE) ³ ( 1−v−vF) ³ P ₀₀ ... (2) First, as shown in FIGS. 1 and 2, extends from one corner (control point or end point) P ₁ of surface elements S ₁ in step S1, P ₁
Let the unit vector in the opposite direction to the vector a (control edge vector) to the control point P ₁ ′ of the edge of the surface element S ₁ connected to n be n ₁ . In step S2, the end point P ₁ of the corners of the surface elements S ₁ and surface elements
Obtains a linear distance l ₁ between the end point P ₂ of the opposite corners of S _2, in the next step S3, the addition of l _1/3 n ₁ to the point P _1, the termination new control points Q ₁ And Incidentally, well divisor of l ₁ is determined appropriately, 3 to 5 preferred. In step S4, the step S1~ for surface elements S ₂
It performs the same processing as S3, obtain a new control point Q _2. In step S5, the end of the points P _1, P _2, obtaining the cubic Bezier curve C ₁ for the control points Q _1, Q _2. Similarly, the surface elements S _1, the end point P of the other corner points of the S _{2 3,} P ₄ in step S6, performs the steps S1 to S4, to obtain new control points Q _3, Q _4, the point P _3, the P ₄ is an end, obtaining a cubic Bezier curve C ₂ for the control point Q _3, Q _4. Such a curve C _1, C ₂ made in the generation bicubic Bezier curved surface S ₃ to surface elements S _1, the original boundary of the S ₂ C _3, C _4, respectively four sides as the interpolated surface element (Step S7). Note that the control points 6, 7, 10, and 11 inside the surface element in FIG. 4 can be determined by setting the twist vector at the four corners to zero or setting the amount corresponding to the curvature to zero. Feature of the process generating the interpolation area element, as shown in Figure 5, even when interpolating surface Motokan that has become uneven, is that the curved surface S ₃ which leads naturally generated. In each of the corners P _{1 to} P ₄ of the interpolated surface element S ₃ , the tangent is continuous. [Effects of the Invention] According to the present invention, it is possible to generate an interpolated curved surface that conforms geometrically and positionally to each surface between two distant surface elements, satisfies the condition of tangent continuity, and is smoothly connected. In the case of deleting one surface element of a geometric model consisting of a set of surface elements and interpolating this with a new surface element, it is possible to partially generate a Bezier surface without returning to the initial stage of model design. In addition, the degree of freedom and efficiency of shape model design can be significantly improved.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram showing an interpolated surface element generation method according to an embodiment of the present invention, FIG. 2 is a flowchart showing the procedure, and FIG. 3 shows a Bezier curve and its control points. FIG. 4 is a diagram showing one plane element of a Bezier curve composed of 16 control points, and FIG. 5 is a diagram showing a state of interpolating between plane elements having a step. In the reference numerals used in the drawings, S ₁ , S ₂ ... Surface element S ₃ ... Interpolated surface element P _{1 to} P ₄ ... Control points (end points) Q _{1 to} Q _4. Vector.

Claims (1)

(57) [Claims] Utilizing computer to interpolate the surface elements between surface elements S _1, S ₂ as two objects detail surface topography present away to continuously connecting the surface element S _1, S ₂ a surface shape creating method of an object to generate surface elements data representing such objects details surface shape, in the end point P ₁ of the boundary line C ₃ of the one surface elements S ₁ of which is in contact with the surface elements S ₃ to be interpolated , Forming a vector in the opposite direction to the vector passing through the control points around the end point, the length of which is the number of distances between the point P ₁ and the end point P ₂ of the other surface element S ₂ corresponding to this point A _{first step} of determining the end point as a control point Q ₁ , and an end point P ₂ of a boundary line C ₄ with the other surface element S ₂ in contact with the surface element S ₃
In, the first process and by performing the same processing and a second process of obtaining the control point Q ₂ to which corresponding to the control point Q _1, the point P _1, P ₂ and end points, control points Q _1, Q ₂ Cubic Bezier curve data C ₁ using vector data of these points as points
A third step of generating the first and second end points P ₃ and P ₄ on the other side of the boundary lines C ₃ and C ₄ .
The third process is performed, and the points P ₃ and P ₄ are set as end points, and the above points Q ₁ and Q ₂
A fourth process of generating the cubic Bezier curve data C ₂ by using the vector data of these points the Q _3, Q ₄ point corresponding as control points, the three-dimensional Bezier curve data C ₁ -C ₄ using the boundary data, and a fifth process of generating a bicubic Bezier surface data S ₃ to four sides of the curve C ₁ -C _4, surface elements between the surface element S _1, S ₂ Is deleted,
S _1, S shape and location and smoothly to a new lead of the surface element S ₃ object surface shape data and generates the bicubic Bezier curved surface data to interpolate from ₂ tangent How to make.