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ABSTRACT
<p><b>Abstract</b>—Given a three-dimensional (3D) array of function values <it>F</it><sub><it>i</it>, <it>j</it>,<it>k</it></sub> on a rectilinear grid, the marching cubes (MC) method is the most common technique used for computing a surface triangulation <tmath>${\cal T}$</tmath> approximating a contour (isosurface) <it>F</it>(<it>x</it>, <it>y</it>, <it>z</it>) = <it>T</it>. We describe the construction of a <it>C</it><super>0</super>-continuous surface consisting of rational-quadratic surface patches interpolating the triangles in <tmath>${\cal T}.$</tmath> 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.</p>
INDEX TERMS
Approximation, contour, isosurface, marching cubes, rational Bézier curve, rational Bézier surface, triangular patch, triangulation, trilinear interpolation, visualization.
CITATION

G. E. Farin, B. Hamann and I. J. Trotts, "On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bézier Patches," in IEEE Transactions on Visualization & Computer Graphics, vol. 3, no. , pp. 215-227, 1997.
doi:10.1109/2945.620489
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