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On approximating contours of the piecewise trilinear interpolant using triangular rational quadratic Bezier patches

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3 Author(s)
Hamann, B. ; Dept. of Comput. Sci., California Univ., Davis, CA, USA ; Trotts, I.J. ; Farin, G.E.

Given a three dimensional (3D) array of function values Fi,j,k 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 C0 continuous surface consisting of rational quadratic surface patches interpolating the triangles in T. We determine the Bezier 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

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Visualization and Computer Graphics, IEEE Transactions on  (Volume:3 ,  Issue: 3 )