Abstract: Control nets of splines are embedded graphs whose node x y z values scale basis functions and whose edges define adjacency and support of the functions. The talk will illustrate this concept and focus on a new family of Polyhedral-net splines (PnS) the generalizes classical tensor-product (quad-grid layout) splines: By allowing non-grid patterns in the control net, PnS enables the modeling and parameterization of well-shaped free-form surfaces. As the talk demonstrates, the PnS surfaces have everywhere, except where not wanted, baked-in differentiability, for example curvature continuity; and PnS are compatible with industrial design standards allowing interplay with tools ranging from Blender to the NURBS step format. Moreover, the same PnS functions can be leveraged for engineering analysis. The talk will show how to solve the (second order) heat equation or the (fourth order, time-dependent) Cahn-Hilliard process on PnS free-form surface with PnS elements
Host: K. Hormann