Constrained willmore surfaces

Smooth curves and surfaces can be characterized as minimizers of squared curvature bending energies subject to constraints. In the univariate case with an isometry (length) constraint this leads classic non-linear splines. For surfaces, is too rigid a instead one asks for Willmore (squared mean curvature) energy conformality constraint. We present efficient algorithm (conformally) constrained using triangle meshes arbitrary topology or without boundary. Our conformal class based on discrete notion equivalence meshes. The resulting optimization problem solved efficiently competitive gradient descent method together appropriate Sobolev metrics. represented either through point positions differential coordinates. latter enable realization abstract metric initial immersion. A versatile toolkit extrinsic geometry processing, suitable construction manipulation smooth results inclusion additional point, area, volume