Periodic discrete conformal maps

On Discrete Conformal Seamless Similarity Maps

An algorithm for the computation of global discrete conformal parametrizations with prescribed global holonomy signatures for triangle meshes was recently described in [Campen and Zorin 2017]. In this paper we provide a detailed analysis of convergence and correctness of this algorithm. We generalize and extend ideas of [Springborn et al. 2008] to show a connection of the algorithm to Newton’s ...

Quasiconformal distortion of projective transformations and discrete conformal maps

We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circumcircle preserving piecewise projective interpolation between discretely con...

Computation of Quasi-Conformal Surface Maps Using Discrete Beltrami Flow

The manipulation of surface homeomorphisms is an important aspect in 3D modeling and surface processing. Every homeomorphic surface map can be considered as a quasiconformal map, with its local non-conformal distortion given by its Beltrami differential. As a generalization of conformal maps, quasiconformal maps are of great interest in mathematical study and real applications. Efficient and ac...

Conformal Maps and Minimal Surfaces

Conformal maps in periodic dynamo flows and in stretch-twist suppression on Riemannian manifolds

Examples of conformal dynamo maps have been presented earlier [Phys Plasmas 14(2007)] where fast dynamos in twisted magnetic flux tubes in Riemannian manifolds were obtained. This paper shows that conformal maps, under the Floquet condition, leads to coincidence between exponential stretching or Lyapunov exponent, conformal factor of fast dynamos. Unfolding conformal dynamo maps can be obtained...