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 algorithm produces a sequence of meshes M-0, M-1, M-2, ..., M-n, where each mesh M-i can be transformed to mesh Mi+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 this function serves as a basis for assigning 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.