可变形B样条曲线曲面模型及其有限元求解

可变形模型对于轮廓提取及表面重建具有重要的意义。表面重建及轮廓提取的过程就是可变形模型在模拟外力的作用下朝着目标轮廓变形的过程,基于B样条的可变形模型结合了几何造型中广泛使用的B样条的优点,B样条方法是当前自由曲线和曲面描述中最广为流行的技术,作者从拉格朗日动力学方程出发,推导出可变形B样条曲线曲面模型的动力学方程,在对动力学方程的有限元求解中,对其单元划分及单元矩阵的求解过程进行了研究,通过程序算例,验证了有限元求解的有效性。

Deformable B-spline Curves and Surfaces Model and Its Finite Element Solution

Deformable models are of great importance for contour extraction and surface reconstruction, which cause the deformable models deform to the object contours due to simulated external force.Deformable B spline models can share the merit of the popular used B splie. From the Lagrangian mechanics, the dynamics equation of deformable B spline curve and surface is derived. Its finite element solution is studied including the finite element generation and element matrix calculation. A example is given to verify its validity.