Numerical Computation Of Geodesic On Implicit Surface

Implicit curves/surfaces enjoys great advantages in geometric modeling, such asjudging the relationship between a point and curves or surfaces and operating intersec-tion of curves and surfaces, and has received more and more attention in recent years.Shape analysis which is a process of extracting useful information from geometricalmodel is a fundamental part of Computer Aided Design or Computer Aided Manipu-lating. Nowadays since shape design attaches more and more importance in productdevelopment, shape analysis becomes increasingly eventful at the same time. Amongthe significant contents is computation of geodesic which is also applied abroad inphysics, engineering technology and robot model and so on. At present, there is notmuch work related to computation of geodesic on implicit surface. N.M.Patrikalakiset al [2002] have given us controlling equations of geodesic on implicit surfaces ,欧阳宏等[2008] have manipulated some numerical cases, but we think that the numericalresult is not satisfying in some sense. Based on previous work, we have improved thecontrolling equation model of geodesic on implicit surfaces at basis of previous people,and converted the nonlinear equations from discrete scheme to nonlinear least squaresproblems, then used Levenberg-Marquardt method to solve it. Moreover, we have pro-posed a superior initialization method to obtain a convergent result. The experimentshows that our algorithm can derive much accurate outcome.