Multiresolution analysis of arbitrary meshes,
M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and
W. Stuetzle. , Siggraph 1995, pg 173-182. This paper discusses more
than just parameterization, but they do introduce a harmonic map
parameterization as a sub-problem. Hence, this has become the paper to
cite for a harmonic mapping of a mesh to the plane. This is
essentially an edge-based method, which tries to minimize the square
of the norm of the gradient of change in u and v.
- This mapping may fold.
- This mapping requires the boundary to be fixed.
- This can be phrased as a linear least-squares problem, this time
by placing constraints on the edges, which are then turned into
weights as in Floater . The edge weights
are based on the ratio of the adjacent edge lengths to the area of the
two adjacent faces.
- This can also be thought of as placing springs on the edges to
get them to be certain lengths.
- Since a triangle's side lengths completely determine its angles,
this method also tries to make a conformal map, albeit indirectly.