Robust curve embedding in inconsistent surface meshes

We present a numerically robust algorithm for augmenting inconsistent meshes and polygon soups with curves defined on a mesh proxy. Unlike prior approaches, which transfer only vertex positions to the proxy, our method represents input edges on the proxy by geodesic paths and merges them with proxy-defined edge paths such as UV seams. This enables reliable detection of intersections between geodesic paths and proxy seams and avoids explicit edge-edge intersection tests, which makes the construction stable even on poorly conditioned meshes. We demonstrate the method in texture transfer, where projected input faces are cut along UV seams of the proxy so that the reconstructed result mesh reproduces the proxy seam layout explicitly and avoids distortions that previous approaches could only mitigate heuristically. To construct this result mesh, we first build an overlay curve network consisting of geodesic segments and proxy seam edges, and then reconstruct a manifold mesh aligned with the input mesh. Our experiments show that this reconstruction removes seam artifacts and reduces the associated high-distortion outliers of prior heuristic methods. Beyond UV seams, the construction can be used more generally to transfer proxy-defined curves onto disjoint meshes, such as collections of NURBS patches.