Unification of distance and volume optimization in surface simplification

A popular method for simplifying a surface is to repeatedly contract an edg e into a vertex and take concomitant actions. In such edge contraction algo rithms, the position of the new vertex plays an important role in preservin g the original shape. Two methods among them are distance optimization and volume optimization. Even though the two methods were independently develop ed by different groups and were regarded as two different branches, we foun d that they are unifiable. In this paper we show that they can be expressed with the same formula, and the only differences are in the weights. We pro ve that volume optimization is actually a distance optimization weighted by the area of triangles adjacent to the contracted edge. (C) 1999 Academic P ress.