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We propose the space of axis-aligned deformations as the meaningful space for content-aware image retargeting. Such deformations exclude local rotations, avoiding harmful visual distortions, and they are parameterized in 1D. We show that standard warping energies for image retargeting can be minimized in the space of axis-aligned deformations while… (More)

This document contains the proofs and other derivations that were omitted from the paper. Theorem 1: Complex barycentric coordinates k j (z) reproduce similarity transformations, i.e: () () 1 () n j j j k z T z T z = = ∑ where T is a 2D similarity transformation. Proof: Similarity transformations can be represented using a linear polynomial over the complex… (More)

Conformal maps are considered very desirable for planar deformation applications, since they allow only local rotations and scale, avoiding shear and other visually disturbing distortions of local detail. Conformal maps are also orientation-preserving C<sup>∞</sup> diffeomorphisms, meaning they are extremely smooth and prevent unacceptable "foldovers"… (More)

We describe a system for the animation of a skeleton-controlled articulated object that preserves the fine geometric details of the object skin and conforms to the characteristic shapes of the object specified through a set of examples. The system provides the animator with an intuitive user interface and produces compelling results even when presented with… (More)

A space deformation is a mapping from a source region to a target region within Euclidean space, which best satisfies some userspecified constraints. It can be used to deform shapes embedded in the ambient space and represented in various forms -- polygon meshes, point clouds or volumetric data. For a space deformation method to be useful, it should possess… (More)

We present an efficient O(<i>n</i>) numerical algorithm for first-order approximation of geodesic distances on geometry images, where <i>n</i> is the number of points on the surface. The structure of our algorithm allows efficient implementation on parallel architectures. Two implementations on a SIMD processor and on a GPU are discussed. Numerical results… (More)

Conformal maps are widely used in geometry processing applications. They are smooth, preserve angles, and are locally injective by construction. However, conformal maps do not allow for boundary positions to be prescribed. A natural extension to the space of conformal maps is the richer space of quasiconformal maps of bounded confor-mal distortion. Extremal… (More)

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 data in the plane, and in particular for holomorphic maps. We extend and generalize these results by investigating the complex… (More)

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 shape. Current deformation transfer methods can be applied only to shapes which are represented as a single component manifold mesh,… (More)

We present an algorithm for mapping a triangle mesh, which is homeomorphic to a disk, to a planar domain with arbitrary fixed boundaries. The algorithm is guaranteed to produce a globally bijective map when the boundary is fixed to a shape that does not self-intersect. Obtaining a one-to-one map is of paramount importance for many graphics applications such… (More)