Using quadratic simplicial elements for hierarchical approximation and visualization

David F. Wiley; Henry R. Childs; Bernd Hamann; Kenneth I. Joy; Nelson Max

doi:10.1117/12.458802

12 March 2002 Using quadratic simplicial elements for hierarchical approximation and visualization

David F. Wiley, Henry R. Childs, Bernd Hamann, Kenneth I. Joy, Nelson Max

Proceedings Volume 4665, Visualization and Data Analysis 2002; (2002) https://doi.org/10.1117/12.458802
Event: Electronic Imaging, 2002, San Jose, California, United States

Abstract

Best quadratic simplicial spline approximations can be computed, using quadratic Bernstein-Bezier basis functions, by identifying and bisecting simplicial elements with largest errors. Our method begins with an initial triangulation of the domain; a best quadratic spline approximation is computed; errors are computed for all simplices; and simplices of maximal error are subdivided. This process is repeated until a user-specified global error tolerance is met. The initial approximations for the unit square and cube are given by two quadratic triangles and five quadratic tetrahedra, respectively. Our more complex triangulation and approximation method that respects field discontinuities and geometrical features allows us to better approximate data. Data is visualized by using the hierarchy of increasingly better quadratic approximations generated by this process. Many visualization problems arise for quadratic elements. First tessellating quadratic elements with smaller linear ones and then rendering the smaller linear elements is one way to visualize quadratic elements. Our results show a significant reduction in the number of simplices required to approximate data sets when using quadratic elements as compared to using linear elements.

Citation Download Citation

David F. Wiley, Henry R. Childs, Bernd Hamann, Kenneth I. Joy, and Nelson Max "Using quadratic simplicial elements for hierarchical approximation and visualization", Proc. SPIE 4665, Visualization and Data Analysis 2002, (12 March 2002); https://doi.org/10.1117/12.458802

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