A physical-geometric approach to model thin dynamical structures in CAD systems

The efficient accurate modeling of thin, approximately one-dimensional structures, like cables, fibers, threads, tubes, wires, etc. in CAD systems is a complicated task since the dynamical behavior has to be computed at interactive frame rates to enable a productive workflow. Traditional physical methods often have the deficiency that the solution process is expensive and heavily dependent on minor details of the underlying geometry and the configuration of the applied numerical solver. In contrast, pure geometrical methods are not able to handle all occurring effects in an accurate way. To overcome this shortcomings, we present a novel and general hybrid physical-geometric approach: the structure's dynamics is handled in a physically accurate way based on the special Cosserat theory of rods capable of capturing effects like bending, twisting, shearing, and extension deformations, while collisions are resolved using a fast geometric sweep strategy which is robust under different numerical and geometric resolutions. As a result, fast editable high quality tubes can easily be designed including their dynamical behavior.