Surface parameterizations are widely applied in computer graphics,medical imaging,and transformation optics.In this paper,we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy fo...Surface parameterizations are widely applied in computer graphics,medical imaging,and transformation optics.In this paper,we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for spherical conformal parameterizations of simply connected closed surfaces of genus-zero.In addition,we give the sparsity structure of the Hessian matrix,which leads to a robust Hessian-based trust region algorithm for the computation of spherical conformal maps.Numerical experiments demonstrate the local quadratic convergence of the proposed algorithm with low conformal distortions.We subsequently propose an application of our method to surface registrations that still maintain local quadratic convergence.展开更多
基金supported by National Natural Science Foundation of China(Grant No.12371377)the Jiangsu Provincial Scientific Research Center of Applied Mathematics(Grant No.BK20233002)supported by Shanghai Institute for Mathematics and Interdisciplinary Sciences(Grant No.SIMIS-ID-2024-LG)。
文摘Surface parameterizations are widely applied in computer graphics,medical imaging,and transformation optics.In this paper,we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for spherical conformal parameterizations of simply connected closed surfaces of genus-zero.In addition,we give the sparsity structure of the Hessian matrix,which leads to a robust Hessian-based trust region algorithm for the computation of spherical conformal maps.Numerical experiments demonstrate the local quadratic convergence of the proposed algorithm with low conformal distortions.We subsequently propose an application of our method to surface registrations that still maintain local quadratic convergence.
