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Least Squares Conformal Maps for Automatic Texture Atlas Generation
, 2002
"... A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded charts are packed in texture space. Existing texture atlas methods for triangulated surfaces suffer from ..."
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Cited by 323 (6 self)
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A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded charts are packed in texture space. Existing texture atlas methods for triangulated surfaces suffer from several limitations, requiring them to generate a large number of small charts with simple borders. The discontinuities between the charts cause artifacts, and make it difficult to paint large areas with regular patterns.
Periodic Discrete Conformal Maps.
, 1998
"... this article we study a discrete geometry which is the simplest example for both theories. Following [1, 3] we will define a discrete conformal map (DCM) to be a map z : Z ..."
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Cited by 3 (2 self)
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this article we study a discrete geometry which is the simplest example for both theories. Following [1, 3] we will define a discrete conformal map (DCM) to be a map z : Z
TWISTING BEHAVIOUR OF CONFORMAL MAPS
"... This paper is devoted to the study of different types of twisting points of conformal maps. We define the sets of gyration, spiral and oscillation points and we prove, in the case that f is conformal almost nowhere, that the above sets have Hausdorff dimension one. Also we define points of bounded r ..."
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This paper is devoted to the study of different types of twisting points of conformal maps. We define the sets of gyration, spiral and oscillation points and we prove, in the case that f is conformal almost nowhere, that the above sets have Hausdorff dimension one. Also we define points of bounded
Curvature Flow in Conformal Mapping
 COMPUTATIONAL METHODS AND FUNCTION THEORY VOLUME 3 (2003), NO. 1, 325–347
, 2003
"... We use a simple example to introduce a notion of curvature flow in the conformal mapping of polyhedral surfaces. The inquiry was motivated by experiments with discrete conformal maps in the sense of circle packing. We describe the classical theory behind these flows and demonstrate how to modify t ..."
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We use a simple example to introduce a notion of curvature flow in the conformal mapping of polyhedral surfaces. The inquiry was motivated by experiments with discrete conformal maps in the sense of circle packing. We describe the classical theory behind these flows and demonstrate how to modify
Effective masses and conformal mappings
, 1993
"... Let Gn, n ∈ N, denote the set of gaps of the Hill operator. We solve the following problems: 1) find the effective masses M ± n, 2) compare the effective mass M ± n with the length of the gap Gn, and with the height of the corresponding slit on the quasimomentum plane (both with fixed number n and t ..."
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Cited by 27 (15 self)
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and their sums) 3) consider the problems 1), 2) for more general cases (the Dirac operator with periodic coefficients, the Schrödinger operator with a limit periodic potential). To obtain 1) 3) we use a conformal mapping corresponding to the quasimomentum of the Hill operator or the Dirac operator.
Geodesic Warps by Conformal Mappings
"... In recent years there has been considerable interest in methods for diffeomorphic warping of images, with applications e.g. in medical imaging and evolutionary biology. The original work generally cited is that of the evolutionary biologist D’Arcy Wentworth Thompson, who demonstrated warps to defor ..."
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Cited by 1 (0 self)
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to deform images of one species into another. However, unlike the deformations in modern methods, which are drawn from the full set of diffeomorphism, he deliberately chose lowerdimensional sets of transformations, such as planar conformal mappings. In this paper we study warps of such conformal mappings
of a Theory of Conformal Mapping
"... Few analytical techniques are better known to students of applied mathematics than conformal mapping. It is the classical method for solving problems in continuum mechanics, electrostatics, and other fields involving the twodimensional Laplace and Poisson equations. To employ the method, one needs ..."
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Few analytical techniques are better known to students of applied mathematics than conformal mapping. It is the classical method for solving problems in continuum mechanics, electrostatics, and other fields involving the twodimensional Laplace and Poisson equations. To employ the method, one needs
Conformal mapping of rectangular heptagons
"... Abstract. A new effective approach to calculating the direct and inverse conformal mapping of rectangular polygons onto a halfplane is put forward; it is based on the use of Riemann theta functions. Bibliography: 14 titles. Keywords: ChristoffelSchwarz integral, Riemann surface, Jacobian, Siegel ..."
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Abstract. A new effective approach to calculating the direct and inverse conformal mapping of rectangular polygons onto a halfplane is put forward; it is based on the use of Riemann theta functions. Bibliography: 14 titles. Keywords: ChristoffelSchwarz integral, Riemann surface, Jacobian, Siegel
Genus zero surface conformal mapping and its application to brain surface mapping
 IEEE Transactions on Medical Imaging
, 2004
"... Abstract—We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic oneforms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces, our algorithm can find a unique mapping betwe ..."
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Cited by 188 (78 self)
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Abstract—We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic oneforms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces, our algorithm can find a unique mapping
of a Theory of Conformal Mapping
"... Few analytical techniques are better known to students of applied mathematics than conformal mapping. It is the classical method for solving problems in continuum mechanics, electrostatics, and other fields involving the twodimensional Laplace and Poisson equations. To employ the method, one need ..."
Abstract
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Few analytical techniques are better known to students of applied mathematics than conformal mapping. It is the classical method for solving problems in continuum mechanics, electrostatics, and other fields involving the twodimensional Laplace and Poisson equations. To employ the method, one
Results 1  10
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