Manifold Learning with Orthogonal Geodesic Grids
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2014
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In Reverse Engineering, it is capital to find a parametric trimmed surface which approximates a triangular mesh (2-manifold with border) M in R3 -- This article proposes and implements a quasi isometry f: M -> R2 which allows a parameterization of M -- We consider quasi - developable 2- manifolds M in R3 -- f(p) = (u,w) with (u,w) being the coordinates of p in M under a grid of geodesic curves Ci(u) and Cj(w) on M -- We seek that the geodesic curves Ci(u) and Cj(w) be orthogonal to each other on M -- This means, that the Ci(u) should not cross each other, and each Ci(u) should intersect each Cj(w) in perpendicular manner
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@inproceedings{Ruiz_etal_2014_manif1,
author={O. E. Ruiz and D. A. Acosta and C. Cadavid and R. Ebratt and S. Arroyave and J. Londono.},
title={Manifold Learning with Orthogonal Geodesic Grids.},
booktitle={Virtual Concept International Workshop (VC-IW 2014) in Innovation in Product Design and Manufacture.},
year={2014},
editor={},
volume={},
pages={},
note={ISBN: 978-2-9548927-0-2},
url={},
document_type={Extended Abstract},
address={Medellin, Colombia},
month={March 26-27},
publisher ={},
organization={},
abstract ={In Reverse Engineering, it is capital to find a parametric trimmed surface which approximates a triangular mesh (2-manifold with border) M in R3. This article proposes and implements a quasi isometry f : M -> R2 which allows a parameterization of M. We consider quasi - developable 2- manifolds M in R3. f(p) = (u,w) with (u,w) being the coordinates of p in M under a grid of geodesic curves Ci(u) and Cj(w) on M.We seek that the geodesic curves Ci(u) and Cj(w) be orthogonal to each other on M. This means, that the Ci(u) should not cross each other, and each Ci(u) should intersect each Cj(w) in perpendicular manner.}
}