Effective Derivation of Similarity Transformations for Implicit Laplacian Mesh Editing

Laplacian coordinates as a local shape descriptor have been employed in mesh editing. As they are encoded in the global coordinate system, they need to be transformed locally to reflect the changed local features of the deformed surface. We present a novel implicit Laplacian editing framework which...

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Vydáno v:Computer graphics forum Ročník 26; číslo 1; s. 34 - 45
Hlavní autoři: Fu, Hongbo, Kin-Chung Au, Oscar, Tai, Chiew-Lan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford, UK Blackwell Publishing Ltd 01.03.2007
Témata:
configuration-independent
Coordinate transformations
Editing
I.3.5 Computer Graphics: Computational Geometry and Object Modeling Boundary Representations
Laplace transforms
Laplacian
mesh deformation
mesh merging
Studies
ISSN:0167-7055, 1467-8659
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Shrnutí:Laplacian coordinates as a local shape descriptor have been employed in mesh editing. As they are encoded in the global coordinate system, they need to be transformed locally to reflect the changed local features of the deformed surface. We present a novel implicit Laplacian editing framework which is linear and effectively captures local rotation information during editing. Directly representing rotation with respect to vertex positions in 3D space leads to a nonlinear system. Instead, we first compute the affine transformations implicitly defined for all the Laplacian coordinates by solving a large sparse linear system, and then extract the rotation and uniform scaling information from each solved affine transformation. Unlike existing differential‐based mesh editing techniques, our method produces visually pleasing deformation results under large angle rotations or big‐scale translations of handles. Additionally, to demonstrate the advantage of our editing framework, we introduce a new intuitive editing technique, called configuration‐independent merging, which produces the same merging result independent of the relative position, orientation, scale of input meshes.
Bibliografie:ArticleID:CGF940
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2007.00940.x