Abstract
We present an interpolating, univariate subdivision scheme which preserves the discrete curvature and tangent direction at each step of subdivision. Since the polygon have a geometric information of some original (in some sense) curve as a discrete curvature, we can expect that the limit curve has the same curvature at each vertex as the control polygon. We estimate the curvature bound of odd vertices and give an error estimate for restoring a curve from sampled vertices on curves.
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Myungjin Jeon received his MS and Ph.D from Seoul National University. His research int-rests include geometric modelling, computer graphics, differential geometry, discrete geometry, e-learning for mathematics.
Dongsoong Han received his MS and Ph.D from Seoul National University. His research interests include computer graphics, Riemannian geometry, mathematics education with thechnology.
Gundon Choi received his MS and Ph.D from Seoul national University. His research interests include CAGD, global analysis on manifolds, de Sitter space in Lorentzian geometry.
Kyeongsu Park received his MS and Ph.D from Seoul National University. His research interests include geometric structures on smooth manifolds, Lorentzian geometry and computer graphics.
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Jeon, M., Han, D., Park, K. et al. Ternary univariate curvature-preserving subdivision. JAMC 18, 235–246 (2005). https://doi.org/10.1007/BF02936568
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DOI: https://doi.org/10.1007/BF02936568