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United States Patent  [ii] Patent Number: 4,821,214
Sederberg  Date of Patent: Apr. 11,1989
 COMPUTER GRAPHICS METHOD FOR
CHANGING THE SHAPE OF A GEOMETRIC
MODEL USING FREE-FORM
 Inventor: Thomas W. Sederberg, Orem, Utah
 Assignee: Brigham Young University, Provo, Utah
 Appl. No.: 853,010
 Filed: Apr. 17,1986
 Int. CI.* :. G06F 15/62
 U.S. CI 364/522; 340/720;
 Field of Search 364/512, 518-522;
 References Cited
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(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
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