Error-bounded reduction of triangle meshes with multivariate data

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Abstract
Interactive visualization is complicated by the complexity of the objects being visualized. Sampled or computed scientific data is often dense, in order to capture high frequency components in measured data or to accurately model a physical process. Common visualization techniques such as isosurfacing on such large meshes generate more geometric primitives than can be rendered in an interactive environment. Geometric mesh reduction techniques have been developed in order to reduce the size of a mesh with little compromise in image quality. Similar techniques have been used for functional surfaces (terrain maps) which take advantage of the planar projection. We extend these methods to arbitrary surfaces in 3D and to any number of variables defined over the mesh by developing a algorithm for mapping from a surface mesh to a reduced representation and measuring the introduced error in both the geometry and the multivariate data. Furthermore, through error propagation, our algorithm ensures that the errors in both the geometric representation and multivariate data do not exceed a user-specified upper bound.

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