Contour interpolation with bounded dihedral angles

Abstract

In this paper, we present the first nontrivial theoretical bound on the quality of the 3D solids generated by any contour interpolation method. Given two arbitrary parallel contour slices with n vertices in 3D, let α be the smallest angle in the constrained Delaunay triangulation of the corresponding 2D contour overlay, we present a contour interpolation method which reconstructs a 3D solid with the minimum dihedral angle of at least α/8. Our algorithm runs in O(nlogn) time where n is the size of the contour overlay.We also present a heuristic algorithm that optimizes the dihedral angles of a mesh representing a surface in 3D.