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

B Hamann, IJ Trotts, GE Farin - IEEE Transactions on …, 1997 - ieeexplore.ieee.org
B Hamann, IJ Trotts, GE Farin
IEEE Transactions on Visualization and Computer Graphics, 1997ieeexplore.ieee.org
Given a three dimensional (3D) array of function values F/sub i, 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 C/sup 0/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 …
Given a three dimensional (3D) array of function values F/sub i,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 C/sup 0/ 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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