Bézier tilings of the sphere and their applications in benchmarking multipatch isogeometric methods

In this work, we explore new parametric models of a sphere with rational Bézier patches. The geometry is represented as a spherical tessellation with various topologies. The tiles are degeneracy-free rational Bézier surfaces, obtained using a general composite mapping method. Five novel, topologically distinct tilings are described, four of which have conforming parameterizations. The mesh of the fifth tiling is nonconforming despite having equal interface knot vectors (intrinsic nonconformity). We apply these novel geometries in three case studies that are proposed as benchmark problems for C0- and C1-multipatch IGA methods.