This paper presents a new approach to construct C1 continuous surfaces on N-sided regions. For C0 continuous surfaces on N-sided regions their smoothed surfaces are constructed by the integral smoothing operation with...This paper presents a new approach to construct C1 continuous surfaces on N-sided regions. For C0 continuous surfaces on N-sided regions their smoothed surfaces are constructed by the integral smoothing operation with displaced integrals. The final smoothed surfaces are C1 continuous with the original surfaces on the boundary.展开更多
Area-preserving parameterization is now widely applied,such as for remeshing and medical image processing.We propose an efficient and stable approach to compute area-preserving parameterization on simply connected ope...Area-preserving parameterization is now widely applied,such as for remeshing and medical image processing.We propose an efficient and stable approach to compute area-preserving parameterization on simply connected open surfaces.From an initial parameterization,we construct an objective function of energy.This consists of an area distortion measure and a new regularization,termed as the Tutte regularization,combined into an optimization problem with sliding boundary constraints.The original area-preserving problem is decomposed into a series of subproblems to linearize the boundary constraints.We design an iteration framework based on the augmented Lagrange method to solve each linear constrained subproblem.Our method generates a high-quality parameterization with area-preserving on facets.The experimental results demonstrate the efficacy of the designed framework and the Tutte regularization for achieving a fine parameterization.展开更多
文摘This paper presents a new approach to construct C1 continuous surfaces on N-sided regions. For C0 continuous surfaces on N-sided regions their smoothed surfaces are constructed by the integral smoothing operation with displaced integrals. The final smoothed surfaces are C1 continuous with the original surfaces on the boundary.
基金supported by Anhui Center for Applied Mathematics,the NSF of China (No.11871447)the special project of strategic leading science and technology of CAS (No.XDC08010100)the National Key Research and Development Program of MOST of China (No.2018AAA0101001).
文摘Area-preserving parameterization is now widely applied,such as for remeshing and medical image processing.We propose an efficient and stable approach to compute area-preserving parameterization on simply connected open surfaces.From an initial parameterization,we construct an objective function of energy.This consists of an area distortion measure and a new regularization,termed as the Tutte regularization,combined into an optimization problem with sliding boundary constraints.The original area-preserving problem is decomposed into a series of subproblems to linearize the boundary constraints.We design an iteration framework based on the augmented Lagrange method to solve each linear constrained subproblem.Our method generates a high-quality parameterization with area-preserving on facets.The experimental results demonstrate the efficacy of the designed framework and the Tutte regularization for achieving a fine parameterization.
