Parameterized surface fitting technique having independent control of fitting and parameterization
First Claim
1. In a 3-D computer graphics system, a computer-implemented method for fitting a smooth surface to an input surface, the method comprising:
- a) dividing the input surface into patches;
b) generating parameterizations of the patches, wherein the parameterizations minimize a discretized higher order energy functional defined on the input surface; and
c) fitting smooth surfaces to the patches, wherein the smooth surfaces are derived from the generated parameterizations, wherein generating the parameterizations and fitting the smooth surfaces are independently controlled.
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Abstract
A method for creating a smooth parameterization and fitting it to an input surface in a 3-D computer graphics system comprises specifying a plurality of boundary curves on the surface that define a patch of the surface. The boundary curves are typically specified using a user-interactive curve editing procedure, but may also be specified automatically. The method then automatically generates a parameterization of the patch such that a discretized higher order energy functional defined on the surface is minimized. The method further comprises the step of fitting a smooth surface to the input surface, where the smooth surface has a parameterization as generated in the previous step. The fitting and parameterization steps are independently controlled to give the user a high degree of flexibility and control over both steps. The method is useful for converting dense irregular polygon meshes into surface models suitable for interactive modification and animation.
233 Citations
20 Claims
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1. In a 3-D computer graphics system, a computer-implemented method for fitting a smooth surface to an input surface, the method comprising:
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a) dividing the input surface into patches;
b) generating parameterizations of the patches, wherein the parameterizations minimize a discretized higher order energy functional defined on the input surface; and
c) fitting smooth surfaces to the patches, wherein the smooth surfaces are derived from the generated parameterizations, wherein generating the parameterizations and fitting the smooth surfaces are independently controlled. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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11. A computer-implemented method for fitting a smooth parameterized surface to an input surface patch, the method comprising:
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a) generating a mapping M into 3 from a parameter space region I in 2 wherein an image surface M(I) substantially coincides with the surface patch, and wherein a parameterization of M minimizes a discretized energy functional defined on the patch; and
b) generating from M a mapping M′
into 3 from the parameter space region I in 2, wherein an image surface M′
(I) approximately fits the surface patch, while a parameterization of M′
substantially coincides with the parameterization of M;
wherein the parameterization of M and the fit of M′
(I) to the surface patch are independently controlled.- View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19, 20)
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Specification