Abstract: In the computer animation and virtual reality applications，both geometric and physical modeling based methods have been widely studied.In this paper，a mass-spring Bezier volume space is constructed through attaching a basic mass-spring lattice to the bounding box of the object.This method is simpler and faster than that utilizes the common mass-spring model which connects the mass points and springs on the object itself，and it is easier to achieve the global deformation.The mass movement meets Lagrange’dynamics equation.This paper adopts a differential equation to express the movement of particles，and uses numerical solution of the system of real time computation，which increases efficiency.At the same time this paper applies a simple soft-objects collision approach on mass-spring model.The experiment shows that the method is simple and effective.

Key words: soft-object, free-form deformation, mass-spring model, collision handling

摘要： 在虚拟现实和计算机动画技术中，基于几何模型和基于物理模型的方法已经得到广泛的研究。利用几何模型和物理模型相结合的方法，将质点弹簧模型加到Bezier网格上，通过控制Bezier网格上的控制点来达到物体的变形，该方法与直接在物体上建立质点弹簧模型的方法相比更加简单、快速，且更加容易达到物体的全局变形。质点的运动满足拉格朗日运动方程，采用了微分方程组来表示质点的运动规律，并给出了用数值求解法对系统进行了的实时计算的求解过程；同时还将一个简单的柔软物体碰撞处理方法应用在质点-弹簧模型中，实验表明该方法简单有效。

关键词: 柔性物体, 自由变形, 质点-弹簧模型, 碰撞处理