Loop and Catmull-Clark are the most famous approximation subdivision schemes,but their limit surfaces do not interpolate the vertices of the given mesh.Progressive-iterative approximation(PIA)is an efficient method fo...Loop and Catmull-Clark are the most famous approximation subdivision schemes,but their limit surfaces do not interpolate the vertices of the given mesh.Progressive-iterative approximation(PIA)is an efficient method for data interpolation and has a wide range of applications in many fields such as subdivision surface fitting,parametric curve and surface fitting among others.However,the convergence rate of classical PIA is slow.In this paper,we present a new and fast PIA format for constructing interpolation subdivision surface that interpolates the vertices of a mesh with arbitrary topology.The proposed method,named Conjugate-Gradient Progressive-Iterative Approximation(CG-PIA),is based on the Conjugate-Gradient Iterative algorithm and the Progressive Iterative Approximation(PIA)algorithm.The method is presented using Loop and Catmull-Clark subdivision surfaces.CG-PIA preserves the features of the classical PIA method,such as the advantages of both the local and global scheme and resemblance with the given mesh.Moreover,CG-PIA has the following features.1)It has a faster convergence rate compared with the classical PIA and W-PIA.2)CG-PIA avoids the selection of weights compared with W-PIA.3)CG-PIA does not need to modify the subdivision schemes compared with other methods with fairness measure.Numerous examples for Loop and Catmull-Clark subdivision surfaces are provided in this paper to demonstrate the efficiency and effectiveness of CG-PIA.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.61872316 and 61932018.
文摘Loop and Catmull-Clark are the most famous approximation subdivision schemes,but their limit surfaces do not interpolate the vertices of the given mesh.Progressive-iterative approximation(PIA)is an efficient method for data interpolation and has a wide range of applications in many fields such as subdivision surface fitting,parametric curve and surface fitting among others.However,the convergence rate of classical PIA is slow.In this paper,we present a new and fast PIA format for constructing interpolation subdivision surface that interpolates the vertices of a mesh with arbitrary topology.The proposed method,named Conjugate-Gradient Progressive-Iterative Approximation(CG-PIA),is based on the Conjugate-Gradient Iterative algorithm and the Progressive Iterative Approximation(PIA)algorithm.The method is presented using Loop and Catmull-Clark subdivision surfaces.CG-PIA preserves the features of the classical PIA method,such as the advantages of both the local and global scheme and resemblance with the given mesh.Moreover,CG-PIA has the following features.1)It has a faster convergence rate compared with the classical PIA and W-PIA.2)CG-PIA avoids the selection of weights compared with W-PIA.3)CG-PIA does not need to modify the subdivision schemes compared with other methods with fairness measure.Numerous examples for Loop and Catmull-Clark subdivision surfaces are provided in this paper to demonstrate the efficiency and effectiveness of CG-PIA.
