Authors: You, L.H., Tang, B.P., You, X.Y. and Zhang, J.J.
In this paper, we present a new method to improve the efficiency of physics-based surface modeling which creates and manipulates surfaces through physics-based curve deformations. The proposed physics-based mathematical model of curve deformations consists of a vector-valued fourth order ordinary differential equation and boundary constraints. An efficient finite difference solution for curve modeling (FDSCM) is developed to solve the mathematical model. The computational efficiency and accuracy from FDSCM are compared to those from the finite difference solution for surface modeling (FDSSM). It is found that FDSCM is more efficient and accurate than FDSSM. The effects of the vector-valued shape control parameters and sculpting forces in the ordinary differential equation together with the boundary tangents in the boundary constraints on curve deformations are investigated. Their strong influences indicate that they are useful shape manipulation tools. With our proposed physics-based curve deformations, we create various geometric models by sweeping a deformed curve or using 2D cross-section curves or 3D feature curves, and manipulate surface shapes by deforming these curves.