
Title  On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular RationalQuadratic Bezier Patches
(Article) 
in  IEEE Transactions on Visualization and Computer Graphics 
Author(s) 
Bernd Hamann, Isaac J. Trotts, Gerald Farin 
Keyword(s)  Approximation, contour, isosurface, marching cubes, rational Bézier curve, rational Bézier surface, triangular patch, triangulation, trilinear interpolation, visualization 
Year 
1997

Volume  3 
Number  3 
Pages  215227 
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BibTeX  
Abstract 
Given a threedimensional (3D) array of function values Fijk on a rectilinear grid, the marching cubes(MC) method is the most common technique used for computing a surface triangulation T approximating a contour (isosurface) F(x,y,z)=T. We describe the construction of a Cocontinuous surface consisting of rationalquadratic surface patches interpolating the triangles in T. We determine the Bézier control points of a single rationalquadratic surface patch based on the coordinates of the vertices of the underlying triangle and the gradients and Hessians associated with the vertices.
