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Tech Forums => 3DTech News Around The Web => Topic started by: JeGX on June 27, 2018, 10:16:35 AM

This distribution contains code for constructing and registering conformal spherical parametrizations of watertight, genuszero surfaces. Specifically, it provides implementations for:
 Computing a conformal parametrization over the sphere
 Centering the parametrization with respect to Möbius inversions
 Tessellating the conformal parametrization to a regular equirectangular grid
 Performing fast spherical correlation to find the rotation/reflections that best aligning two centered parametrizations
 Using the registered parametrizations to compute dense correspondences from a source mesh to a target
Link: https://github.com/mkazhdan/MoebiusRegistration
Conformal parameterizations over the sphere provide highquality maps between genus zero surfaces, and are essential for applications such as data transfer and comparative shape analysis. However, such maps are not unique: to define correspondence between two surfaces, one must find the Möbius transformation that best aligns two parameterizations—akin to picking a translation and rotation in rigid registration problems. We describe a simple procedure that canonically centers and rotationally aligns two spherical maps. Centering is implemented via elementary operations on triangle meshes in R3, and minimizes area distortion. Alignment is achieved using the FFT over the group of rotations. We examine this procedure in the context of spherical conformal parameterization, orbifold maps, nonrigid symmetry detection, and dense pointtopoint surface correspondence.
Link: http://www.cs.jhu.edu/~misha/MyPapers/SGP18.pdf
(http://www.ozone3d.net/public/jegx/2018q2/mobiusregistration.jpg)