Abstract
We propose a method to approximate a polygonal object by a deformable smooth surface, namely the t-skin defined by Edelsbrunner for all 0< t < 1. We guarantee that they are homeomorphic and their Hausdorff distance is at most ε >0. Such construction makes it possible for fully automatic, smooth and robust deformation between two polygonal objects with different topologies. En route to our results, we also give an approximation of a polygonal object with a union of balls.
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Cheng, Hl., Tan, T. (2005). Approximating Polygonal Objects by Deformable Smooth Surfaces. In: Jȩdrzejowicz, J., Szepietowski, A. (eds) Mathematical Foundations of Computer Science 2005. MFCS 2005. Lecture Notes in Computer Science, vol 3618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549345_22
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DOI: https://doi.org/10.1007/11549345_22
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