Using Radial Basis Functions to Solve Geodesics Equations for Body Measurements

Abstract

For the application of apparel industry, 3D body measurements are the minimal arc length distances between the point couples along the body surface. The calculation of geodesics is nontrivial, and can only be approximated for free-form surfaces, because the computation of geodesics requires solving a set of ordinary differential equations (geodesics equations), which do not exhibit any closed form solution for free-form surfaces. In this article, the method of radial basis function (RBF) is used in solving the geodesics equations based on the bicubic tensor product Bezier patches. This method does not require any mesh to support the localized approximations. The accuracy and efficiency of this meshless collocation method are examined by comparison to the Ritz\u2019s method.