摘要
给出了求解代数曲面上两点之间测地线的一种算法.在算法中,把决定代数曲面测地线的微分方程组离散为一个非线性方程组,然后采用迭代数值方法求解.为此,给出了一种基于细分的初值生成方法.最后给出了一些数值算例用来验证算法的有效性.
An algorithm for computing the geodesic line between the two points of an algebraic surface was presented. The system of differential equations for a geodesic line on an algebraic surface was discredited into a nonlinear system. Then it was solved numerically based on iterative methods. In order to get a better convergence, a method based on subdivision was designed to specify initial values for the iterations. Examples show the efficiency of our method.
基金
国家自然科学基金(60533060
60473132
10626049)
教育部博士点专项科研基金
高等学校学科创新引智计划(b07033)资助
关键词
代数曲面
测地线
测地曲率
algebraic surface
geodesic line
geodesic curvature
