Bounded-distortion Piecewise Mesh Parameterization

3D painting, remeshing, mesh compression, and digital geometry
processing, require finding a low-distortion parameterization
for irregular connectivity triangulations of arbitrary genus
2-manifolds. We present a simple and fast method for computing
parameterizations with strictly bounded distortion. The new method
operates by flattening the mesh onto a region of the 2D plane.
To comply with the distortion bound, the mesh is automatically
cut and partitioned on-the-fly. The method guarantees avoiding
global and local self-intersections, while attempting to reduce
the total length of the introduced seams. To our knowledge,
this is the first method to compute the mesh partitioning and
the parameterization simultaneously and entirely automatically,
while providing guaranteed distortion bounds. Our results on
a variety of objects demonstrate that the method is fast enough
to work with large complex irregular meshes in interactive
applications.