|Title||On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bezier Patches
|in||IEEE Transactions on Visualization and Computer Graphics|
Bernd Hamann, Isaac J. Trotts, Gerald Farin |
|Keyword(s)||Approximation, contour, isosurface, marching cubes, rational Bézier curve, rational Bézier surface, triangular patch, triangulation, trilinear interpolation, visualization|
Given a three-dimensional (3D) array of function values Fijk 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 Co-continuous surface consisting of rational-quadratic surface patches interpolating the triangles in T. 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.