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A non-stationary subdivision scheme for generalizing trigonometric spline surfaces to arbitrary meshes. (English) Zbl 1069.65557
Summary: We present a non-stationary subdivision scheme for generating surfaces from meshes of arbitrary topology. Surfaces generated by this scheme are tensor product bi-quadratic trigonometric spline surfaces except at the extraordinary points. The scheme can be considered as a adaptation of the Doo-Sabin scheme to the non-stationary case. Convergence of the scheme is based on the convergence of a sequence of subdivision matrices to a variant of Doo-Sabin subdivision matrix.

MSC:
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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