2011
DOI: 10.1007/978-3-642-19867-0_5
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Smooth 2D Coordinate Systems on Discrete Surfaces

Abstract: Abstract. We introduce a new method to compute conformal parameterizations using a recent definition of discrete conformity, and establish a discrete version of the Riemann mapping theorem. Our algorithm can parameterize triangular, quadrangular and digital meshes. It can be adapted to preserve metric properties. To demonstrate the efficiency of our method, many examples are shown in the experiment section.

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