Fast Algorithm for Generating Frame Fields on Surfaces

The frame field has important applications in mesh generation and finite element analysis.In the past,the method of generating frame field took much time.This paper presents a new technique for generating frame fields fast.Given a triangular mesh,first,Riemann metrics can be defined at each point by the second fundamental tensor of the surface.Then,the anisotropic frame field is regarded as an isotropic field in the sense of this Riemann metrics,and an isotropic field in the sense of the Riemann metric is obtained.In addition,in order to accelerate the solving process,this paper also constructs a multi-resolution hierarchical structure,and using the Gauss-Seidel iterative method to solve the optimization problems in each layer which improves the speed of generating frame field.This algorithm is compared with the previous methods,which show that this algorithm not only improves the speed of generating the frame field,but also makes the generated frame field and curvature closer in trend.