Dynamic Ball B-Spline Curves

A ball B-spline curve (BBSC) is a skeleton-based 3D geometric representation, which can represent 3D tubular objects with varying radius, such as trunks, plants, and blood vessels. To enhance the ability of BBSC, we propose a physics-based generalization of BBSC called dynamic BBSC (D-BBSC), which can describe the deformation behavior of a BBSC over time. We provide the mathematical expression of D-BBSC and prove its several mathematical properties. We derive the equations of motion of D-BBSC based on Lagrangian mechanics and investigate the equations of motion when it is under linear geometric constraints. Additionally, a D-BBSC physical simulation system based on the finite difference method (FDM) is implemented and several experimental results are demonstrated. The D-BBSC can be applied to simulate the elastic behavior of 3D tubular objects with varying radius in entertainment applications.