Abstract
In this paper a method is presented to fair the limit surface of a subdivision algorithm around an extraordinary point. The eigenvalues and eigenvectors of the subdivision matrix determine the continuity and shape of the limit surface. The dominant, sub-dominant and subsub-dominant eigenvalues should satisfy linear and quadratic equality- and inequality-constraints to guarantee continuous normal and bounded curvature globally. The remaining eigenvalues need only satisfy linear inequality-constraints. In general, except for the dominant eigenvalue, all eigenvalues can be used to optimize the shape of the limit surface with our method.
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Ginkel, I., Umlauf, G. (2007). Tuning Subdivision Algorithms Using Constrained Energy Optimization. In: Martin, R., Sabin, M., Winkler, J. (eds) Mathematics of Surfaces XII. Mathematics of Surfaces 2007. Lecture Notes in Computer Science, vol 4647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73843-5_11
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DOI: https://doi.org/10.1007/978-3-540-73843-5_11
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