Method and apparatus for generating a surface by simulating a ph

Details Method and apparatus for generating a surface by simulating a ph Method and apparatus for generating a surface by simulating a ph

1993-06-25

1996-10-15

Zimmerman, Mark K.

395142, G06T 1700

Patent

active

055662811

ABSTRACT:
In order to generate a display of a surface, an equation or equations are generated corresponding to all or parts of the surface. The equation or equations represent the surface as a physical membrane. Boundary conditions of the surface can thus be specified, and the equation solved using the boundary conditions as outer constraints to generate a display of the surface. A set of points within the boundary of the surface may be specified, which then define inner constraints for the solution of the equation. Where parts of the surface join at a point or line, a further equation can be generated, which further equation represents the area around the join as a physical membrane. Solution of that equation, preserving the boundary of the area around the join, provides a smooth transition between the parts of the surface.

REFERENCES:
patent: 5345546 (1994-09-01), Harada et al.
Bohm et al., "A Survey of Curve and Surface Methods in CAGD", Computer Aided Geometric Design, 1 (1984), pp. 1-60.
"Using Partial Differential Equations to Generate Free-Form Surfaces" (paragraph : "Simple Hull Design"), Computer Aided Design, Bloor, et al, vol. 22, No. 4, May 1990, UK, pp. 202-212.
"On the G.sup.1 Continuity of Piecewise Bezier Surfaces: A review with New Results", Wen-Hui Du et al, Computer Aided Designs, vol. 22, No. 9, Nov. 1990, UK, pp. 556-573.
"Surface Reconstruction Using Deformable Models with Interior and Boundary Constraints", Proceedings Third International Conference on Computer Vision, Wang et al, Nov. 1990, JP, pp. 300-303.
"Connecting Arbitrary Surfaces Under Geometric Constraints", Computers In Industry, Vergeest, vol. 8, No. 1, Feb. 1987, NL, pp. 3-12.

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