The parameterization of surfaces is a cornerstone to various
applications in computer graphics such as texture mapping,
resampling, and simulation. We introduce new linear operators for
generating mappings of low parametric distortion. Given an
initial mapping from the parametric plane onto a surface mesh, we
establish a secondary map of the plane onto itself that mimics the
initial one. The resulting low-distortion parameterization is
smooth as it stems from solving a quasi-harmonic equation. Our
parameterization method is robust and independent of (the quality
of) the initial map. In fact, for most cases the methods converges
from a simple projection on the least squares plane even for complex
models.