10 April 2018 Quadratic polynomial interpolation on triangular domain
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Proceedings Volume 10615, Ninth International Conference on Graphic and Image Processing (ICGIP 2017); 1061546 (2018) https://doi.org/10.1117/12.2302956
Event: Ninth International Conference on Graphic and Image Processing, 2017, Qingdao, China
Abstract
In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.
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Ying Li, Ying Li, Congcong Zhang, Congcong Zhang, Qian Yu, Qian Yu, } "Quadratic polynomial interpolation on triangular domain", Proc. SPIE 10615, Ninth International Conference on Graphic and Image Processing (ICGIP 2017), 1061546 (10 April 2018); doi: 10.1117/12.2302956; https://doi.org/10.1117/12.2302956
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