POLTHIER K.: Parameterizing singularities of positive integral index

• Main Authors: Matthias Nieser, Konrad Polthier
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: North Pole
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.698.316; http://www.mi.fu-berlin.de/en/math/groups/ag-geom/publications/db/2009-ParameterizingSingularitiesOfPositiveIntegralIndex.pdf

Classical surface parameterization algorithms often place singular-ities in order to enhance the quality of the resulting parameter map. Unfortunately, singularities of positive integral index (as the north pole of a sphere) were not handled since they cannot be described with piecewise linear parameter functions on a triangle mesh. Preprocess-ing is needed to adapt the mesh connectivity. We present an extension to the QuadCover parameterization algorithm [KNP07], which allows to handle those singularities. A singularity of positive integral index can be resolved using bilin-ear parameter functions on quadrilateral elements. This generaliza-tion of piecewise linear functions for quadrilaterals enriches the space of parameterizations. The resulting parameter map can be visualized by textures using a rendering system which supports quadrilateral el-ements, or it can be used for remeshing into a pure quad mesh. 1