Physically Based Modeling And Simulation Of 1D Flexible Parts Deformation With Constraints

As an important research topic in the field of CAD and computer graphics, modeling and simulating the deformation of 1D flexible parts are intensively involved in many applications, such as industry product design, virtual surgery, computer animation and so on. Nowadays, the geometrically based deformation models are mature enough, however, these methods cannot meet the requirements of high-fidelity simulation. This paper is about physically based modeling and simulation of 1D flexible parts with constraints.Chapter one is the background about deformation technique. We first introduced computer descriptions of 1D flexible parts and deformation models of geometrically based and physically based. Then numerical methods for solving Euler-Lagrange mechanics equation are also presented.In the second chapter, we build a physics-based dynamic Catmull-Rom spline model with constraints. At the beginning, we analysis the property of Catmull-Rom spline and add aided control points to describe the centerline of 1D flexible parts. Then, to solve the problem of modeling dynamic spline, we propose the formulation of deformation energies and generalized force, so we get Euler-Lagrange equation of the spline. At last, we provide fix-point constraints and smooth constraints equations for dynamic spline with constraints modeling.In the third chapter, aiming at exact deformation and real-time simulation, efficient and stable numerical solutions are given. We propose a stable equation based on Lyapunov theory for updating control points to solve Lagrange equation without constraints. After that, we propose the solution of Lagrange equation with constraints, which can get the real-time deformation of 1D flexible with constraints.In the end, a summary of this paper and future research directions are given.