Flattenable Mesh Surface Fitting on Boundary CurvesSource: Journal of Computing and Information Science in Engineering:;2008:;volume( 008 ):;issue: 002::page 21006Author:Charlie C. Wang
DOI: 10.1115/1.2906695Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper addresses the problem of fitting flattenable mesh surfaces in R3onto piecewise linear boundary curves, where a flattenable mesh surface inherits the isometric mapping to a planar region in R2. The developable surface in differential geometry shows the nice property. However, it is difficult to fit developable surfaces to a boundary with complex shape. The technique presented in this paper can model a piecewise linear flattenable surface that interpolates the given boundary curve and approximates the cross-tangent normal vectors on the boundary. At first, an optimal planar polygonal region is computed from the given boundary curve B∊R3, triangulated into a planar mesh surface, and warped into a mesh surface in R3, satisfying the continuities defined on B. Then, the fitted mesh surface is further optimized into a flattenable Laplacian (FL) mesh, which preserves the positional continuity and minimizes the variation of cross-tangential normals. Assembled set of such FL mesh patches can be employed to model complex products fabricated from sheets without stretching.
keyword(s): Surface fitting ,
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contributor author | Charlie C. Wang | |
date accessioned | 2017-05-09T00:27:17Z | |
date available | 2017-05-09T00:27:17Z | |
date copyright | June, 2008 | |
date issued | 2008 | |
identifier issn | 1530-9827 | |
identifier other | JCISB6-25988#021006_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/137618 | |
description abstract | This paper addresses the problem of fitting flattenable mesh surfaces in R3onto piecewise linear boundary curves, where a flattenable mesh surface inherits the isometric mapping to a planar region in R2. The developable surface in differential geometry shows the nice property. However, it is difficult to fit developable surfaces to a boundary with complex shape. The technique presented in this paper can model a piecewise linear flattenable surface that interpolates the given boundary curve and approximates the cross-tangent normal vectors on the boundary. At first, an optimal planar polygonal region is computed from the given boundary curve B∊R3, triangulated into a planar mesh surface, and warped into a mesh surface in R3, satisfying the continuities defined on B. Then, the fitted mesh surface is further optimized into a flattenable Laplacian (FL) mesh, which preserves the positional continuity and minimizes the variation of cross-tangential normals. Assembled set of such FL mesh patches can be employed to model complex products fabricated from sheets without stretching. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Flattenable Mesh Surface Fitting on Boundary Curves | |
type | Journal Paper | |
journal volume | 8 | |
journal issue | 2 | |
journal title | Journal of Computing and Information Science in Engineering | |
identifier doi | 10.1115/1.2906695 | |
journal fristpage | 21006 | |
identifier eissn | 1530-9827 | |
keywords | Surface fitting | |
tree | Journal of Computing and Information Science in Engineering:;2008:;volume( 008 ):;issue: 002 | |
contenttype | Fulltext |