Multi-Scale Geometry Interpolation

Interpolating vertex positions among triangle meshes with identical vertex‐edge graphs is a fundamental part of many geometric modelling systems. Linear vertex interpolation is robust but fails to preserve local shape. Most recent approaches identify local affine transformations for parts of the mes...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Computer graphics forum Ročník 29; číslo 2; s. 309 - 318
Hlavní autoři: Winkler, T., Drieseberg, J., Alexa, M., Hormann, K.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford, UK Blackwell Publishing Ltd 01.05.2010
Témata:
Affine transformations
Computer graphics
Curvature
Finite element method
Geometry
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Hierarchy and geometric transformations
Image processing systems
Interpolation
Matching
Mathematical analysis
Preserves
Systems development
Transformations
ISSN:0167-7055, 1467-8659
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:Interpolating vertex positions among triangle meshes with identical vertex‐edge graphs is a fundamental part of many geometric modelling systems. Linear vertex interpolation is robust but fails to preserve local shape. Most recent approaches identify local affine transformations for parts of the mesh, model desired interpolations of the affine transformations, and then optimize vertex positions to conform with the desired transformations. However, the local interpolation of the rotational part is non‐trivial for more than two input configurations and ambiguous if the meshes are deformed significantly. We propose a solution to the vertex interpolation problem that starts from interpolating the local metric (edge lengths) and mean curvature (dihedral angles) and makes consistent choices of local affine transformations using shape matching applied to successively larger parts of the mesh. The local interpolation can be applied to any number of input vertex configurations and due to the hierarchical scheme for generating consolidated vertex positions, the approach is fast and can be applied to very large meshes.
Bibliografie:ArticleID:CGF1600
istex:5C39719E26CF32ED45BCC1F745A0C13CEEA1553F
ark:/67375/WNG-M9S6T80Q-Q
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-2
content type line 23
ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2009.01600.x