In this paper,we propose a stochastic geometric iterative method(S-GIM)to approximate the high-resolution 3Dmodels by finite loop subdivision surfaces.Given an input mesh as the fitting target,the initial control mesh...In this paper,we propose a stochastic geometric iterative method(S-GIM)to approximate the high-resolution 3Dmodels by finite loop subdivision surfaces.Given an input mesh as the fitting target,the initial control mesh is generated using the mesh simplification algorithm.Then,our method adjusts the control mesh iteratively to make its finite loop subdivision surface approximate the input mesh.In each geometric iteration,we randomly select part of points on the subdivision surface to calculate the difference vectors and distribute the vectors to the control points.Finally,the control points are updated by adding the weighted average of these difference vectors.We prove the convergence of S-GIM and verify it by demonstrating error curves in the experiment.In addition,compared with existing geometric iterative methods,S-GIM has a shorter running time under the same number of iteration steps.展开更多
Data fitting is an extensively employed modeling tool in geometric design. With the advent of the big data era, the data sets to be fitted are made larger and larger, leading to more and more least-squares fitting sys...Data fitting is an extensively employed modeling tool in geometric design. With the advent of the big data era, the data sets to be fitted are made larger and larger, leading to more and more least-squares fitting systems with singular coefficient matrices. LSPIA (least-squares progressive iterative approximation) is an efficient iterative method for the least-squares fitting. However, the convergence of LSPIA for the singular least-squares fitting systems remains as an open problem. In this paper, the authors showed that LSPIA for the singular least-squares fitting systems is convergent. Moreover, in a special case, LSPIA converges to the Moore-Penrose (M-P) pseudo-inverse solution to the least- squares fitting result of the data set. This property makes LSPIA, an iterative method with clear geometric meanings, robust in geometric modeling applications. In addition, the authors discussed some implementation detail of LSPIA, and presented an example to validate the convergence of LSPIA for the singular least-squares fitting systems.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.61872316,61932018the National Key R&D Plan of China under Grant No.2020YFB1708900.
文摘In this paper,we propose a stochastic geometric iterative method(S-GIM)to approximate the high-resolution 3Dmodels by finite loop subdivision surfaces.Given an input mesh as the fitting target,the initial control mesh is generated using the mesh simplification algorithm.Then,our method adjusts the control mesh iteratively to make its finite loop subdivision surface approximate the input mesh.In each geometric iteration,we randomly select part of points on the subdivision surface to calculate the difference vectors and distribute the vectors to the control points.Finally,the control points are updated by adding the weighted average of these difference vectors.We prove the convergence of S-GIM and verify it by demonstrating error curves in the experiment.In addition,compared with existing geometric iterative methods,S-GIM has a shorter running time under the same number of iteration steps.
基金supported by the Natural Science Foundation of China under Grant No.61379072
文摘Data fitting is an extensively employed modeling tool in geometric design. With the advent of the big data era, the data sets to be fitted are made larger and larger, leading to more and more least-squares fitting systems with singular coefficient matrices. LSPIA (least-squares progressive iterative approximation) is an efficient iterative method for the least-squares fitting. However, the convergence of LSPIA for the singular least-squares fitting systems remains as an open problem. In this paper, the authors showed that LSPIA for the singular least-squares fitting systems is convergent. Moreover, in a special case, LSPIA converges to the Moore-Penrose (M-P) pseudo-inverse solution to the least- squares fitting result of the data set. This property makes LSPIA, an iterative method with clear geometric meanings, robust in geometric modeling applications. In addition, the authors discussed some implementation detail of LSPIA, and presented an example to validate the convergence of LSPIA for the singular least-squares fitting systems.
