Piecewise Linear Approximation for Scientific Data

The visualization of scientific data allows for a faster and better insight in measurements and numerical computations. In order to generate reliable image results, the rendering has to be based on an error control. Since many visualization techniques use linear approximation schemes, we give estimates of the approximation error in arbitrary dimensions. Our results can be considered as generalizations and improvements of already existing estimates for curves and surfaces.

[1]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.

[2]  Marc Levoy,et al.  Efficient ray tracing of volume data , 1990, TOGS.

[3]  Bernd E. Hirsch,et al.  Triangulation of trimmed surfaces in parametric space , 1992, Comput. Aided Des..

[4]  Robert P. Markot,et al.  Surface algorithms using bounds on derivatives , 1986, Comput. Aided Geom. Des..

[5]  Reinhard Klein.  Linear Approximation of Trimmed Surfaces , 1994, IMA Conference on the Mathematics of Surfaces.

[6]  Reinhard Klein.  Polygonalization of algebraic surfaces , 1994 .

[7]  G. Ziegler.  Lectures on Polytopes , 1994 .

[8]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[9]  Marc Levoy,et al.  Display of surfaces from volume data , 1988, IEEE Computer Graphics and Applications.

[10]  William E. Lorensen,et al.  Decimation of triangle meshes , 1992, SIGGRAPH.

[11]  Peter Shirley,et al.  A polygonal approximation to direct scalar volume rendering , 1990, SIGGRAPH 1990.

[12]  Mark Hall,et al.  Adaptive polygonalization of implicitly defined surfaces , 1990, IEEE Computer Graphics and Applications.

[13]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[14]  Lee Westover,et al.  Footprint evaluation for volume rendering , 1990, SIGGRAPH.

[15]  Alan H. Barr,et al.  Accurate triangulations of deformed, intersecting surfaces , 1987, SIGGRAPH.