Constrained willmore surfaces

• Published in: ACM transactions on graphics Vol. 40; no. 4; pp. 1 - 17
• Main Authors: Soliman, Yousuf, Chern, Albert, Diamanti, Olga, Knöppel, Felix, Pinkall, Ulrich, Schröder, Peter
• Format: Journal Article
• Language: English
• Published: New York, NY, USA ACM 31.08.2021
• Subjects: Computer graphics; Computing methodologies; Discretization; Mathematical analysis; Mathematical optimization; Mathematics of computing; Mesh geometry models; Numerical analysis; Shape analysis; Shape modeling; geometric flows; willmore surfaces; geometric modeling; conformal geometry; discrete differential geometry; differential coordinates

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 to classic non-linear splines. For surfaces, isometry is too rigid a constraint and instead one asks for...