Sphere control based Delaunay refinement tetrahedralization algorithm for soft tissue

In this paper, we propose a novel conforming sphere control Delaunay refinement tetrahedralization algorithm. It takes isosurface of soft tissue as an input, and arbitrarily small input angles are allowed. Unlike previous sphere control methods, this algorithm is simpler to implement. It only computes the controlling ball of sharp vertex whose concept is also redefined in order to induce the calculation work. We present a strict proof for the convergence of this algorithm. Further more, the radius-edge ratio of most output tetrahedral are bounded by a constant.