Quasi-isometric mesh parameterization using heat-based geodesics and poisson surface fills
| dc.citation.journalTitle | Mathematics | eng |
| dc.contributor.author | Mejia-Parra D. | |
| dc.contributor.author | Sánchez J.R. | |
| dc.contributor.author | Posada J. | |
| dc.contributor.author | Ruiz-Salguero O. | |
| dc.contributor.author | Cadavid C. | |
| dc.contributor.department | Universidad EAFIT. Departamento de Ingeniería Mecánica | spa |
| dc.contributor.researchgroup | Laboratorio CAD/CAM/CAE | spa |
| dc.date.accessioned | 2021-04-16T21:59:59Z | |
| dc.date.available | 2021-04-16T21:59:59Z | |
| dc.date.issued | 2019-01-01 | |
| dc.description.abstract | 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. | eng |
| dc.identifier | https://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=9857 | |
| dc.identifier.doi | 10.3390/math7080753 | |
| dc.identifier.issn | 22277390 | |
| dc.identifier.other | WOS;000482856500100 | |
| dc.identifier.other | SCOPUS;2-s2.0-85071185884 | |
| dc.identifier.uri | http://hdl.handle.net/10784/29550 | |
| dc.language | eng | |
| dc.publisher | MDPI AG | |
| dc.relation.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85071185884&doi=10.3390%2fmath7080753&partnerID=40&md5=a35aee1b885b50c247c9fbd70fec1731 | |
| dc.rights | https://v2.sherpa.ac.uk/id/publication/issn/2227-7390 | |
| dc.source | Mathematics | |
| dc.subject.keyword | Geodesic maps | eng |
| dc.subject.keyword | Heat transfer analysis | eng |
| dc.subject.keyword | Mesh parameterization | eng |
| dc.subject.keyword | Poisson fills | eng |
| dc.title | Quasi-isometric mesh parameterization using heat-based geodesics and poisson surface fills | eng |
| dc.type | info:eu-repo/semantics/article | eng |
| dc.type | article | eng |
| dc.type | info:eu-repo/semantics/publishedVersion | eng |
| dc.type | publishedVersion | eng |
| dc.type.local | Artículo | spa |