Bijective Composite Mean Value Mappings

We introduce the novel concept of composite barycentric mappings and give theoretical conditions under which they are guaranteed to be bijective. We then focus on mean value mappings and derive a simple procedure for computing their Jacobians, leading to an efficient GPU‐assisted implementation for...

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Bibliographic Details
Published in:Computer graphics forum Vol. 32; no. 5; pp. 137 - 146
Main Authors: Schneider, T., Hormann, K., Floater, M.S.
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.08.2013
Subjects:
Computation
Computer graphics
Computer science
Deformation
G.1.1 [Numerical Analysis]: Interpolation-Interpolation formulas
I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation
Jacobians
Mapping
Pixels
Studies
Three dimensional
Two dimensional
United States > US
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:We introduce the novel concept of composite barycentric mappings and give theoretical conditions under which they are guaranteed to be bijective. We then focus on mean value mappings and derive a simple procedure for computing their Jacobians, leading to an efficient GPU‐assisted implementation for interactively designing composite mean value mappings which are bijective up to pixel resolution. We provide a number of examples of 2D image deformation and an example of 3D shape deformation based on a natural extension of the concept to spatial mappings.
Bibliography:ark:/67375/WNG-JH312B68-M
istex:BC13F05FD3E8E056C0F481EE20E8C4505A78BC7E
ArticleID:CGF12180
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ObjectType-Article-2
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12180