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.