Computer Graphics, 26, 2, July 1992 Functional Optimization for Fair Surface Design Henry I! Moreton Carlo H. Skquin Computer Science Division University of California, Berkeley Abstract This paper presents a simple-to-use mechanism for the creation of complex smoothly shaped surfaces of any genus or topological type. The surfaces are specified through interpolated geometric constraints consisting of positions and, optionally, surface normals and surface curvatures. From a designer s point of view, this is a very natural way to specify a desired shape, whether free-form or technical. Nonlinear optimization techniques are then used to minimize a fairness functional based on the variation of curvature. This functional produces very high quality surfaces with predictable, intuitive behavior, while generating, where possible, simple shapes, such as cylinders, spheres, or tori, which are commonly used in geometric modeling. While easy to use, this optimization-based approach is computationally quite demanding. With more efficient optimization algorithms and with the ever increasing processing power available on every desk-top, the techniques described here will provide the basis for a new class of practical interactive geometric modeling tools. Figure 1. A suitcase comer. (a) illustrates the specifkatlon with normal and curvature constraints. (b) illustrates the resulting blend. 1
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Functional optimization for fair surface design
Moreton, Henry P.; Séquin, Carlo H.
Follow ACM SIGGRAPH Computer Graphics
, Volume 26 (2)
Association for Computing Machinery – Jul 1, 1992
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