  In machine learning and computer graphics, a fundamental task is the
approximation of a probability density function through a well-dispersed
collection of samples. Providing a formal metric for measuring the distance
between probability measures on general spaces, Optimal Transport (OT) emerges
as a pivotal theoretical framework within this context. However, the associated
computational burden is prohibitive in most real-world scenarios. Leveraging
the simple structure of OT in 1D, Sliced Optimal Transport (SOT) has appeared
as an efficient alternative to generate samples in Euclidean spaces. This paper
pushes the boundaries of SOT utilization in computational geometry problems by
extending its application to sample densities residing on more diverse
mathematical domains, including the spherical space Sd , the hyperbolic plane
Hd , and the real projective plane Pd . Moreover, it ensures the quality of
these samples by achieving a blue noise characteristic, regardless of the
dimensionality involved. The robustness of our approach is highlighted through
its application to various geometry processing tasks, such as the intrinsic
blue noise sampling of meshes, as well as the sampling of directions and
rotations. These applications collectively underscore the efficacy of our
methodology.
