Geometric Curve Modeling with Sobolev Gradients
نویسنده
چکیده
The Sobolev gradient method is a powerful tool for geometric modeling. We treat the problem of constructing fair curves by minimizing a fairness measure subject to geometric constraints. The measure might include curve length, curvature, torsion, and/or variation of curvature. The constraints may include specified values, tangent vectors, and/or curvature vectors. We may also require periodicity in the case of closed curves, or nonlinear inequalities representing shape-preservation criteria. The curve is represented by discrete vertices and divided difference approximations to derivatives with respect to arc length. A Sobolev gradient method is then particularly effective for minimizing the functional.
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