Moebius Geometry Processing

The mainstream approaches in digital geometry processing utilize triangular (simplicial) meshes, discretize differential quantities using finite-element function spaces, and describe transformations with piecewise affine maps. I will describe how Moebius geometry provides an original alternative to discrete differential geometry, by using circles as its basic elements, and describing quantities like conformality and regularity through the invariant cross-ratio. This theory allows for various applications, such as polygonal (non-triangular) mesh deformation, interpolation, and symmetric realization of unconventional mesh patterns.