【摘要】 曲面的变分设计方法在构造高质量的曲面方面显示出了明显的优越性.通过对Greiner所提出的三阶能量泛函进行变分,得到相应的Euler-Lagrange方程,并构造了一个新的六阶梯度流.采用类差分法对所构造的几何流进行数值求解,并用其解决几何设计中的各种问题,包括曲面处理、N-边洞填补方面以及曲面恢复等.实验结果表明,文中所构造的几何流确能产生高质量的曲面.更多还原

【Abstract】 Physics and geometry based variational techniques for surface construction have been shown its remarkable superiority on designing high quality surfaces.We derive an Euler-Lagrange equation from the geometric invariant curvature integral functional which was proposed by Greiner.Using this Euler-Lagrange equation,we construct a sixth-order geometric flow,which is solved numerically by a divided-difference-like method.The proposed equation is applied to solve several surface modeling problems,including surface blending,N-sided hole filling and surface recovery.The illustrative examples show that this flow yields high quality surfaces.更多还原