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An Optimization Approach to Improving Collections of Shape Maps
(The Eurographics Association and Blackwell Publishing Ltd., 2011)
Finding an informative, structure-preserving map between two shapes has been a long-standing problem in geometry processing, involving a variety of solution approaches and applications. However, in many cases, we are given ...
Cross-Collection Map Inference by Intrinsic Alignment of Shape Spaces
(The Eurographics Association and John Wiley and Sons Ltd., 2014)
Inferring maps between shapes is a long standing problem in geometry processing. The less similar the shapes are, the harder it is to compute a map, or even define criteria to evaluate it. In many cases, shapes appear as ...
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 ...
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, ...
A Complex View of Barycentric Mappings
(The Eurographics Association and Blackwell Publishing Ltd., 2011)
Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two-dimensional ...
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 ...
Functional Fluids on Surfaces
(The Eurographics Association and John Wiley and Sons Ltd., 2014)
Fluid simulation plays a key role in various domains of science including computer graphics. While most existing work addresses fluids on bounded Euclidean domains, we consider the problem of simulating the behavior of an ...