English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Surface mapping plays an important role in geometric processing. They induceboth area and angular distortions. If the angular distortion is bounded, themapping is called a {\it quasi-conformal} map. Many surface maps in ourphysical world are quasi-conformal. The angular distortion of a quasi-conformalmap can be represented by Beltrami differentials. According to quasi-conformalTeichm\"uller theory, there is an 1-1 correspondence between the set ofBeltrami differentials and the set of quasi-conformal surface maps. Therefore,every quasi-conformal surface map can be fully determined by the Beltramidifferential and can be reconstructed by solving the so-called Beltramiequation.  In this work, we propose an effective method to solve the Beltrami equationon general Riemann surfaces. The solution is a quasi-conformal map associatedwith the prescribed Beltrami differential. We firstly formulate a discreteanalog of quasi-conformal maps on triangular meshes. Then, we propose analgorithm to compute discrete quasi-conformal maps. The main strategy is todefine a discrete auxiliary metric of the source surface, such that theoriginal quasi-conformal map becomes conformal under the newly defined discretemetric. The associated map can then be obtained by using the discrete Yamabeflow method. Numerically, the discrete quasi-conformal map converges to thecontinuous real solution as the mesh size approaches to 0. We tested ouralgorithm on surfaces scanned from real life with different topologies.Experimental results demonstrate the generality and accuracy of our auxiliarymetric method.

Computing Quasiconformal Maps on Riemann surfaces using Discrete Curvature Flow