The Method of Moving Frames for Surface Global Parametrization

This article introduces a new representation of surface global parametrization based on Cartan’s method moving frames . We show that system structure equations , characterizing the local coordinates changes with respect to frame system, completely characterizes set possible cone parametrizations. The discretization this provably provides necessary and sufficient conditions for existence valid mapping. are able derive versatile algorithm parametrization, allowing feature constraints singularities. As first equation is independent coordinate we do not require prior knowledge cuts or positions. So, single non-linear least-square problem enough place quantized cones while minimizing given distortion energy. therefore take full advantage link between geometry topology its metric solve challenging constrained problems.