Computational Geometry Using Control Geometry Having At Least Two Dimensions
First Claim
1. A method for determining a blended geometric object, comprising:
- providing, for each of a plurality of parameterized geometric objects Si, i=1, . . . , N, N≧
2, a mapping fSi from a parametric space, PS, to a common geometric space GS containing the Si wherein (A1) and (A2) hold;
(A1) at least one of the plurality of parameterized geometric objects, Si0, has a dimension greater than or equal to 2;
(A2) for each Si there is a portion Pi of Si wherein fSi is continuous at points of fSi−
1(Pi);
computing, a function S at each of a plurality of points q in PS, for obtaining a corresponding point S(q) in GS, wherein (B1) and (B2) hold;
(B1) S(q) is dependent upon and at least one fSj(q) for j≠
i0, and wherein and (B2) S is continuous at fdisplaying a representation of said corresponding points S(q) as a representation of a geometric object that blends between Si0 and Sj.
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Accused Products
Abstract
A method and system for computer aided design (CAD) is disclosed for designing geometric objects. The present invention interpolates and/or blends between such geometric objects sufficiently fast so that real time deformation of such objects occurs while deformation data is being input. Thus, a user designing with the present invention obtains immediate feedback to input modifications without separately entering a command for performing such deformations. The present invention utilizes novel computational techniques for blending between geometric objects, wherein weighted sums of points on the geometric objects are used in deriving a new blended geometric object. The present invention is particularly useful for designing the shape of surfaces. Thus, the present invention is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft. Additionally, the present invention provides for efficient animation via repeatedly modifying surfaces of an animated object such as a representation of a face.
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Citations
6 Claims
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1. A method for determining a blended geometric object, comprising:
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providing, for each of a plurality of parameterized geometric objects Si, i=1, . . . , N, N≧
2, a mapping fSi from a parametric space, PS, to a common geometric space GS containing the Si wherein (A1) and (A2) hold;
(A1) at least one of the plurality of parameterized geometric objects, Si 0 , has a dimension greater than or equal to 2;
(A2) for each Si there is a portion Pi of Si wherein fS i is continuous at points of fSi −
1(Pi);
computing, a function S at each of a plurality of points q in PS, for obtaining a corresponding point S(q) in GS, wherein (B1) and (B2) hold;
(B1) S(q) is dependent upon and at least one fS j (q) for j≠
i0, and whereinand (B2) S is continuous at f displaying a representation of said corresponding points S(q) as a representation of a geometric object that blends between Si 0 and Sj. - View Dependent Claims (2, 3, 4, 5, 6)
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Specification