Interpolation by piecewise quadric polynomial to scattered data points

Authors:
Shanshan Gao;Caiming Zhang;Li Zhong
Affiliations:
School of Computer Science and Technology, Shandong Economic University, Jinan, Shandong, China;School of Computer Science and Technology, Shandong Economic University, Jinan, Shandong, China;School of Computer Science and Technology, Ludong University, Yantai, Shandong, China
Venue:
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Year:
2006

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Abstract

This paper presents a new method to construct C1 polynomial surface to the scattered data points. The given data points are triangulated into triangle networks, and a C1piecewise quadric interpolant patch is constructed at the adjacent region of each point. For the different cases of the number of adjacent points, two different algorithms are used for determining the patches, respectively. The surface patch on each triangle is constructed by the weighted combination of the three patches corresponding to the vertices of the triangle. All of the surface patches are put together to form the whole surface with C1 continuity. The construction of the surface by the new method is simple, and the surface has the shape suggested by the given data points and is more fairing. Comparison examples are included.