Triangular mesh parameterization with trimmed surfaces
| dc.citation.journalTitle | International Journal On Interactive Design And Manufacturing | eng |
| dc.contributor.author | Ruiz, O.E. | |
| dc.contributor.author | Mejia, D. | |
| dc.contributor.author | Cadavid, C.A. | |
| dc.contributor.department | Universidad EAFIT. Departamento de Ingeniería Mecánica | spa |
| dc.contributor.researchgroup | Laboratorio CAD/CAM/CAE | spa |
| dc.date.accessioned | 2021-04-16T21:59:55Z | |
| dc.date.available | 2021-04-16T21:59:55Z | |
| dc.date.issued | 2015-04-28 | |
| dc.description.abstract | Given a 2-manifold triangular mesh M subset of R-3, with border, a parameterization of M is a FACE or trimmed surface F = {S, L-0, ... , L-m. F is a connected subset or region of a parametric surface S, bounded by a set of LOOPs L-0, ... , L-m such that each L-i subset of S is a closed 1-manifold having no intersection with the other L-j LOOPs. The parametric surface S is a statistical fit of the mesh M. L-0 is the outermost LOOP bounding F and L-i is the LOOP of the i-th hole in F (if any). The problem of parameterizing triangular meshes is relevant for reverse engineering, tool path planning, feature detection, redesign, etc. State-of-art mesh procedures parameterize a rectangular mesh M. To improve such procedures, we report here the implementation of an algorithm which parameterizes meshes M presenting holes and concavities. We synthesize a parametric surface S subset of R-3 which approximates a superset of the mesh M. Then, we compute a set of LOOPs trimming S, and therefore completing the FACE F = {S, L-0, ... , L-m. Our algorithm gives satisfactory results for M having low Gaussian curvature (i.e., M being quasi-developable or developable). This assumption is a reasonable one, since M is the product of manifold segmentation pre-processing. Our algorithm computes: (1) a manifold learning mapping phi : M -> U subset of R-2, (2) an inverse mapping S : W subset of R-2 -> R-3, with W being a rectangular grid containing and surpassing U. To compute phi we test IsoMap, Laplacian Eigenmaps and Hessian local linear embedding (best results with HLLE). For the back mapping (NURBS) S the crucial step is to find a control polyhedron P, which is an extrapolation of M. We calculate P by extrapolating radial basis functions that interpolate points inside phi(M). We successfully test our implementation with several datasets presenting concavities, holes, and are extremely non-developable. Ongoing work is being devoted to manifold segmentation which facilitates mesh parameterization. | eng |
| dc.identifier | https://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1701 | |
| dc.identifier.doi | 10.1007/s12008-015-0276-1 | |
| dc.identifier.issn | 19552513 | |
| dc.identifier.issn | 19552505 | spa |
| dc.identifier.other | WOS;000364009400005 | |
| dc.identifier.other | SCOPUS;2-s2.0-84945437192 | |
| dc.identifier.uri | http://hdl.handle.net/10784/29522 | |
| dc.language | eng | |
| dc.publisher | Springer-Verlag France | |
| dc.relation.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-84945437192&doi=10.1007%2fs12008-015-0276-1&partnerID=40&md5=07f29541c91ef8edd0b33d6b48b539dc | |
| dc.rights | https://v2.sherpa.ac.uk/id/publication/issn/1955-2513 | |
| dc.source | International Journal On Interactive Design And Manufacturing | |
| dc.subject.keyword | Triangular mesh parameterization | eng |
| dc.subject.keyword | Trimmed surface | eng |
| dc.subject.keyword | Manifold learning | eng |
| dc.subject.keyword | NURBS | eng |
| dc.subject.keyword | RBFs | eng |
| dc.title | Triangular mesh parameterization with trimmed surfaces | 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 |