The similarity property of conformal parameterization makes it able to locally preserve the shapes between a surface and its parameter domain, as opposed to common parameterization methods. A parametric tool path plan...The similarity property of conformal parameterization makes it able to locally preserve the shapes between a surface and its parameter domain, as opposed to common parameterization methods. A parametric tool path planning method is proposed in this paper through such parameterization of triangular meshes which is furthermore based on the geodesic on meshes. The parameterization has the properties of local similarity and free boundary which are exploited to simplify the formulas for computing path parameters, which play a fundamentally important role in tool path planning, and keep the path boundary-conformed and smooth. Experimental results are given to illustrate the effectiveness of the proposed methods, as well as the error analysis.展开更多
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
Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduct...Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduction is undoubtedly necessary for line drawings.However,most existing methods for artifact drawing rely on the principles of orthographic projection that always cannot avoid angle occlusion and data overlapping while the surface of cultural relics is complex.Therefore,conformal mapping was introduced as a dimensionality reduction way to compensate for the limitation of orthographic projection.Based on the given criteria for assessing surface complexity,this paper proposed a three-dimensional feature guideline extraction method for complex cultural relic surfaces.A 2D and 3D combined factor that measured the importance of points on describing surface features,vertex weight,was designed.Then the selection threshold for feature guideline extraction was determined based on the differences between vertex weight and shape index distributions.The feasibility and stability were verified through experiments conducted on real cultural relic surface data.Results demonstrated the ability of the method to address the challenges associated with the automatic generation of line drawings for complex surfaces.The extraction method and the obtained results will be useful for line graphic drawing,displaying and propaganda of cultural relics.展开更多
A peptides migration model based on the principle of mechanics is presented in capillary zone electrophoresis (CZE). It is shown that the migration that the (tr) is a function of electric (Q), relative molecular mass ...A peptides migration model based on the principle of mechanics is presented in capillary zone electrophoresis (CZE). It is shown that the migration that the (tr) is a function of electric (Q), relative molecular mass (Mr), conformation parameter (Rc) of peptides and electrophoretic condition parameter(A). The conformation parameter is introduced to characterize multifarious shapes owing to the complex conlormation and the various kinds of macromolecules, where Rc≥1/3. The parameters A and Rc can be obtained from experimental data. The times of migration of the nine standard peptides were measured in pH 2.5buffer on different electrophoretic conditions in CZE. The experimental results agreed well with the theoretical prediction.展开更多
基金supported by the National Program on Key Basic Research Project of China (No. 2011CB302400)the National Natural Science Foundation of China (No. 51175495)
文摘The similarity property of conformal parameterization makes it able to locally preserve the shapes between a surface and its parameter domain, as opposed to common parameterization methods. A parametric tool path planning method is proposed in this paper through such parameterization of triangular meshes which is furthermore based on the geodesic on meshes. The parameterization has the properties of local similarity and free boundary which are exploited to simplify the formulas for computing path parameters, which play a fundamentally important role in tool path planning, and keep the path boundary-conformed and smooth. Experimental results are given to illustrate the effectiveness of the proposed methods, as well as the error analysis.
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.
基金National Natural Science Foundation of China(Nos.42071444,42101444)。
文摘Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduction is undoubtedly necessary for line drawings.However,most existing methods for artifact drawing rely on the principles of orthographic projection that always cannot avoid angle occlusion and data overlapping while the surface of cultural relics is complex.Therefore,conformal mapping was introduced as a dimensionality reduction way to compensate for the limitation of orthographic projection.Based on the given criteria for assessing surface complexity,this paper proposed a three-dimensional feature guideline extraction method for complex cultural relic surfaces.A 2D and 3D combined factor that measured the importance of points on describing surface features,vertex weight,was designed.Then the selection threshold for feature guideline extraction was determined based on the differences between vertex weight and shape index distributions.The feasibility and stability were verified through experiments conducted on real cultural relic surface data.Results demonstrated the ability of the method to address the challenges associated with the automatic generation of line drawings for complex surfaces.The extraction method and the obtained results will be useful for line graphic drawing,displaying and propaganda of cultural relics.
文摘A peptides migration model based on the principle of mechanics is presented in capillary zone electrophoresis (CZE). It is shown that the migration that the (tr) is a function of electric (Q), relative molecular mass (Mr), conformation parameter (Rc) of peptides and electrophoretic condition parameter(A). The conformation parameter is introduced to characterize multifarious shapes owing to the complex conlormation and the various kinds of macromolecules, where Rc≥1/3. The parameters A and Rc can be obtained from experimental data. The times of migration of the nine standard peptides were measured in pH 2.5buffer on different electrophoretic conditions in CZE. The experimental results agreed well with the theoretical prediction.
