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Advection-Based Function Matching on Surfaces
(The Eurographics Association and John Wiley & Sons Ltd., 2016)
A tangent vector field on a surface is the generator of a smooth family of maps from the surface to itself, known as the flow. Given a scalar function on the surface, it can be transported, or advected, by composing it ...
Iterative Closest Conformal Maps between Planar Domains
(The Eurographics Association and John Wiley & Sons Ltd., 2016)
Conformal maps between planar domains are an important tool in geometry processing, used for shape deformation and image warping. The Riemann mapping theorem guarantees that there exists a conformal map between any two ...
An Operator Approach to Tangent Vector Field Processing
(The Eurographics Association and Blackwell Publishing Ltd., 2013)
In this paper, we introduce a novel coordinate-free method for manipulating and analyzing vector fields on discrete surfaces. Unlike the commonly used representations of a vector field as an assignment of vectors to the ...
Spatial Deformation Transfer
(ACM SIGGRAPH / Eurographics Association, 2009)
Much effort is invested in generating natural deformations of three-dimensional shapes. Deformation transfer simplifies this process by allowing to infer deformations of a new shape from existing deformations of a similar ...
As-Killing-As-Possible Vector Fields for Planar Deformation
(The Eurographics Association and Blackwell Publishing Ltd., 2011)
Cartoon animation, image warping, and several other tasks in two-dimensional computer graphics reduce to the formulation of a reasonable model for planar deformation. A deformation is a map from a given shape to a new one, ...
Soft Maps Between Surfaces
(The Eurographics Association and Blackwell Publishing Ltd., 2012)
The problem of mapping between two non-isometric surfaces admits ambiguities on both local and global scales. For instance, symmetries can make it possible for multiple maps to be equally acceptable, and stretching, slippage, ...
Can Mean-Curvature Flow be Modified to be Non-singular?
(The Eurographics Association and Blackwell Publishing Ltd., 2012)
This work considers the question of whether mean-curvature flow can be modified to avoid the formation of singularities. We analyze the finite-elements discretization and demonstrate why the original flow can result in ...