A framework for modeling high quality tension-determined surfaces

Many surfaces in nature are determined by the equilibrium of surface tension and external forces, such as air pressure or gravity. Such surfaces, to be called tension-determined surfaces (TDS), are widely used in architectural design and industrial design. A well-known example is the minimal surface which has a zero mean curvature. Existing methods for modeling general TDS, which are normally represented as triangle mesh surfaces, have difficulty in achieving both uniform curvature distribution and high mesh quality. In this paper, we present a novel framework for generating high quality triangular meshes that accurately approximate TDS. While the simultaneous optimization of both surface tension energy and mesh quality is generally infeasible due to conflict, the proposed method resolves the conflict by constraining the two energies into the orthogonal normal and tangent subspaces respectively; to optimize the energies in constrained subspaces, we first project the energy gradients into the subspaces and then combine the projections to drive a stable and convergent optimization process. Experiments show that our method produces better results than previous works in terms of both accuracy of curvature approximation and the mesh quality of the output TDS.