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

摘要

Given a three dimensional (3D) array of function valuesnFi,j,k on a rectilinear grid, the marching cubes (MC) methodnis the most common technique used for computing a surface triangulationnT approximating a contour (isosurface) F(x, y, z)=T. We describe thenconstruction of a C0 continuous surface consisting ofnrational quadratic surface patches interpolating the triangles in T. Wendetermine the Bezier control points of a single rational quadraticnsurface patch based on the coordinates of the vertices of the underlyingntriangle and the gradients and Hessians associated with the vertices