Non-Parametric Shape Design of Free-Form Shells Using Fairness Measures and Discrete Differential Geometry

A non-parametric approach is proposed for shape design of free-form shells discretized into triangular mesh. The forms curvatures are used computing the fairness measures surface. defined as area offset surface and generalized form Gauss map. Gaussian curvature mean computed using angle defect cotangent formula, respectively, in field discrete differential geometry. Optimization problems formulated minimizing various with specified boundary conditions. piecewise developable can be obtained without a priori assignment internal boundary. Effectiveness method generating shapes demonstrated numerical examples.