Length-preserved natural boundary for intrinsic parameterization

This paper proposes a fast approach to generate length-preserved natural boundary for intrinsic parameterization. Given a triangular mesh with disklike topology, we compute an optimal boundary for its parameterization. An optimal boundary is expected to be length-preserved with the length of every triangular edge on the boundary is invariant before and after parameterization; also, the boundary is requested to be natural where the inner angle is close to the angle excess at every boundary vertex on the given mesh. Computation of a length-preserved natural boundary is formulated as a constrained non-linear optimization problem, the procedure of solving which is in general very time-consuming. Here, we speed up the optimization by adopting the scheme of sequential linearly constrained programming. It is shown at the end of this paper that our length-preserved natural boundary could greatly improve the speed and quality of the original intrinsic parameterization.