Smooth Hierarchical Surface Triangulations

We present a new method to produce a hierarchical set of triangle meshes that can be used to blend different levels of detail in a smooth fashion. The algorithms produces a sequence of meshes M0, M1, M2,..., Mn, where each mesh Mi can be transformed to mesh M2+1 through a set of triangle-collapse operations. For each triangle, a function is generated that approximates the underlying surface in the area of the triangle, and it's function serves as a basis for assisting a weight to the triangle in the ordering operation, and for supplying the point to which the triangles are collapsed. This technique allows us to view a triangulated surface model at varying levels of detail while insuring that the simplified mesh approximates the original surface well