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

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 7 approximating a contour (isosurface) F(x, y, z) = T. We describe the construction of a C 0 -continuous surface consisting of rational-quadratic surface patches interpolating the triangles in 7. 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.