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TitleOn Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bezier Patches (Article)
inIEEE 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
Volume3
Number3
Pages215--227
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Abstract Given a three-dimensional (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 Co-continuous surface consisting of rational-quadratic surface patches interpolating the triangles in T. We determine the Bézier control points of a single rational-quadratic surface patch based on the coordinates of the vertices of the underlying triangle and the gradients and Hessians associated with the vertices.