Feature-Aligned Parametrization in Penner Coordinates

Abstract
Parametrization is a key element of many geometric modeling tasks. Seamless parametrization,
in particular, is needed as a starting point for many algorithms for quadrangulation and
conversion to high-order patches, as well as for the construction of seamless texture maps
and displacement maps.
Seamless parametrizations are difficult to compute robustly, in part because, in general, it is not known
if one exists for a given mesh connectivity or for a particular configuration of singularities. Recently,
Penner-coordinate-based methods that allow for connectivity changes have been shown to achieve a
perfect success rate on a widely used dataset (Thingi10k).
However, previously proposed Penner coordinate methods do not support sharp feature alignment or
soft alignment with preferred directions on the surface, both of which are important for practical
applications, especially those involving models with sharp features.
In this paper, we extend Penner coordinates to surfaces with sharp features to which the parametrization
needs to be aligned. Our algorithm extends the holonomy signature description of seamless parametrizations
to surfaces with marked feature curves. We describe sufficient conditions for obtaining feasible solutions
and describe a two-phase method to efficiently enforce feature constraints or minimize residual errors when
solutions are unattainable. We demonstrate that the resulting algorithm works robustly on the Thingi10k
dataset with automatic feature labeling, and the resulting seamless parametrizations can be optimized,
quantized, and quadrangulated, completing the quad mesh generation pipeline.
Paper
- Official ACM Digital Library Article [Coming soon]
- arXiv Article [Coming soon]
- Paper PDF
Downloads
- Code [Coming soon]
- Data [Coming soon]
Results

Example of a feature aligned seamless parametrizations computed with our method and corresponding quadrangulation.