Quasi-isometric mesh parameterization using heat-based geodesics and poisson surface fills
Fecha
2019-01-01
Autores
Mejia-Parra D.
Sánchez J.R.
Posada J.
Ruiz-Salguero O.
Cadavid C.
Título de la revista
ISSN de la revista
Título del volumen
Editor
MDPI AG
Resumen
In the context of CAD, CAM, CAE, and reverse engineering, the problem of mesh parameterization is a central process. Mesh parameterization implies the computation of a bijective map ? from the original mesh M ? R3 to the planar domain ?(M) ? R2. The mapping may preserve angles, areas, or distances. Distance-preserving parameterizations (i.e., isometries) are obviously attractive. However, geodesic-based isometries present limitations when the mesh has concave or disconnected boundary (i.e., holes). Recent advances in computing geodesic maps using the heat equation in 2-manifolds motivate us to revisit mesh parameterization with geodesic maps. We devise a Poisson surface underlying, extending, and filling the holes of the mesh M. We compute a near-isometric mapping for quasi-developable meshes by using geodesic maps based on heat propagation. Our method: (1) Precomputes a set of temperature maps (heat kernels) on the mesh; (2) estimates the geodesic distances along the piecewise linear surface by using the temperature maps; and (3) uses multidimensional scaling (MDS) to acquire the 2D coordinates that minimize the difference between geodesic distances on M and Euclidean distances on R2. This novel heat-geodesic parameterization is successfully tested with several concave and/or punctured surfaces, obtaining bijective low-distortion parameterizations. Failures are registered in nonsegmented, highly nondevelopable meshes (such as seam meshes). These cases are the goal of future endeavors. © 2019 by the authors.