Computer graphics method for changing the shape of a geometric model using ...

[54] COMPUTER GRAPHICS METHOD FOR

CHANGING THE SHAPE OF A GEOMETRIC
MODEL USING FREE-FORM
DEFORMATION

[75] Inventor: Thomas W. Sederberg, Orem, Utah

[73] Assignee: Brigham Young University, Provo, Utah

[21] Appl. No.: 853,010

[22] Filed: Apr. 17,1986

[51] Int. CI.* :. G06F 15/62

[52] U.S. CI 364/522; 340/720;

364/521

[58] Field of Search 364/512, 518-522;

340/720, 723

[56] References Cited

U.S. PATENT DOCUMENTS

4,275,449 6/1981 Aish 364/512

4,549,275 10/1985 Sukonick 364/521

4,609,993 9/1986 Shimizu 364/522

4,685,070 8/1987 Flinchbaugh 364/522

OTHER PUBLICATIONS

M. S. Casale et al., "An Overview of Analytic Solid Modeling," IEEE Computer Graphics and Applications, pp. 45 to 56 (Feb. 1985).

Farouki et al., "A Hierarchy of Geometric Forms,"
IEEE CG & A, pp. 51 to 78 (May 1985).
M. E. Mortenson, "Geometric Modeling," Chapter 4,
Sections 1-5, pp. 240 to 259 (1985).
Rockwood et al., "Blending Surfaces in Solid Model-
ling," (1985).

C. Hoffman et al., "Automatic Surface Generation in
Computer Aided Design," paper from Department of
Computer Science, Cornell University, pp. 1 to 21
(1985).

A. E. Middleditch et al., "Blend Surfaces for Set Theoretic Volume Modeling Systems," Computer Graphics, vol. 19, No. 3, pp. 161 to 170 (1985). T. W. Sederberg, "Piecewise Algebraic Surface Patches," Computer Aided Geometric Design 2, pp. 53 to 59 (1985).

A. H. Barr, "Global and Local Deformations of Solid

-46

Y

Primitives," Computer Graphics, vol. 18, No. 3, pp. 21 to 30 (1984).

E. S. Cobb, "Design of Sculptured Surfaces Using the B-Spline Representation," Department of Computer Science, The University of Utah (1984). W. Bohm et al., "A Survey of Curve and Surface Methods in CAGD", Computer Aided Geometric Design 1, pp. 1 to 60 (1984).

(List continued on next page.)

Primary Examiner—Gary V. Harkcom

Assistant Examiner—H. R. Herndon

Attorney, Agent, or Firm—Workman, Nydegger Jensen

A method of using a computer graphic system for freeform deformation of geometric models. The method is based on the use of a control-point grid which is imposed on the model and which can then be moved by a system designer to specify a deformation to a particular region of the model. Displacement of control points on the grid provides the designer with an intuitive appreciation for the resulting affect in terms of deformation on the specified region of the geometric model. The free-form deformation of the model is accomplished I through the use of a trivariate vector rational polyno: mial in which the displaced control points represent coefficients of the polynomial. The method provides a powerful and highly flexible technique that can be adapted and used in the environment of virtually any presently known solid modeling system, such as CSG or B-rep. The method can be used to deform surface primitives of any type or degree, such as planes, quadrics, parametric surface patches or implicitly defined surfaces. Single or successive deformations can be applied both globally and locally, and local deformations can be imposed using the method of the present invention with any desired degree of derivative continuity. It is also possible to use the method of the present invention to deform a solid geometric model in such a way that its volume is preserved.

17 Claims, 11 Drawing Sheets 40

OTHER PUBLICATIONS

T. Varady et al., "Design Techniques for the Definition
of Solid Objects with Free-Form Geometry," Com-
puter Aided Geometric Design 1, pp. 207 to 225 (1984).
A. A. G. Requicha et al., "Solid Modeling: Current
Status and Research Directions," IEEE Computer
Graphics & Applications, pp. 25 to 35 (1983).
A. A. G. Requicha et al., "Solid Modeling: A Historical
Summary and Contemporary Assessment," IEEE
Computer Graphics & Applications, pp. 9 to 24 (1982).
J. A. Brewer et al., "Visual Interaction with Over-

hauser Curves and Surfaces," Computer Graphics, vol.

II, No. 2, pp. 132 to 137 (1977).

R. E. Parent, "A System for Sculpting 3-D Data,"

Computer Graphics, vol. 11, No. 2, pp. 138 to 147

(1977).

P. Bezier et al., "Mathematical and Practical Possibilities of Unisurf," Computer Aided Geometric Design, pp. 127 to 152 (1974).

M. A. Sabin et al., "Interrogation Techniques for Parametric Surfaces," Computer Graphics '70 Conference, (1970).