The appriximation properties of generalized conic curves are studied in this paper. A generalized conic curve is defined as one of the following curves or their affine and translation e-quivalent curves:(i) conic curv...The appriximation properties of generalized conic curves are studied in this paper. A generalized conic curve is defined as one of the following curves or their affine and translation e-quivalent curves:(i) conic curves i including parabolas, hyperbolas and ellipses;(ii) generalized monomial curves, including curves of the form x=yr,.r R.r=0,1, in the x-y Cartesian coordinate system;(iii) exponential spiral curves of the form p=Apolar coordinate system.This type of curves has many important properties such as convexity , approximation property, effective numerical computation property and the subdivision property etc. Applications of these curves in both interpolation and approximations using piecewise generalized conic segment are also developed. It is shown that these generalized conic splines are very similar to the cubic polynomial splines and the best error of approximation is or at least in general provided appropriate procedures are used. Finally some numerical examples of interpolation and approximations with generalized conic splines are given.展开更多
Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference...Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference analysis, a systematic method to construct Cn (n≥ 0) interpolatorycurves by subdivision from given data is described and the mask (filter) of the algorithm is presentedexplicitly. This algorithm generates a Cn smooth curve which interpolates the initial control points.Control parameters are also provided so that the shape of the final curve can be adjusted according torequirements. An immediate generalisation of the method is the construction of smooth interpolatorysubdivision algorithms over uniform triangular networks (tensor product type data) in Rm. The mainresults of this algorithm for smooth interpolatory surface subdivision algorrthm are also included.AMS(MOS) : 65D05 , 65D15 , 65D17.展开更多
An application of techniques is presented to construct G￣1 smooth surfaces by using acombination of the rectangular and triangular Bezier patches of degree as low as possible. TheG￣1 smooth surfaces have the local p...An application of techniques is presented to construct G￣1 smooth surfaces by using acombination of the rectangular and triangular Bezier patches of degree as low as possible. TheG￣1 smooth surfaces have the local property and interpolate the given data and inherit thetopology imposed by the given space convex quadrilateral partition and triangulation. The papergeneralizes current approaches for assembling of rectangular and triangular patches.展开更多
A smooth interpolatory subdivision algorithm for the generation of surfaces over arbi-trary triangulations is introduced and its convergence properties over nonuniform triangulationsstudied. For uniform data, this met...A smooth interpolatory subdivision algorithm for the generation of surfaces over arbi-trary triangulations is introduced and its convergence properties over nonuniform triangulationsstudied. For uniform data, this method is a generalization of the analysis for univariatesubdivision algorithms and for nonuniform data, an extraordinary point analysis is introducedand the local subdivision matrix anaiysis presented. It is proved that the algorithm producessmooth surfaces over arbitrary triangular networks provided the shape parameters are kept with-in an appropriate range. Finally, two graphical examples of surface interpolation overnonuniform data are given to show the smoothing process of the algorithm.AMS (MOS): 65D05, 65D15,65D17.展开更多
The undirected graph to express engineering drawings is discussed .The principle to re-solve and reason the undirected graph is presented, and the algorithm finally transforms theundirected graph into the resolvable d...The undirected graph to express engineering drawings is discussed .The principle to re-solve and reason the undirected graph is presented, and the algorithm finally transforms theundirected graph into the resolvable directed graph. Therefore,a rapid and simple way is suppliedfor variational design. A prototype of this algorithm has been implemented, and some examplesare given.展开更多
This paper deals with the technology of computer graphics and its application in ana-lyzing complex nonlinear proceas. We have investigated metal crystallization, which is a complexnonlinear process and is difficult t...This paper deals with the technology of computer graphics and its application in ana-lyzing complex nonlinear proceas. We have investigated metal crystallization, which is a complexnonlinear process and is difficult to analyze by using the conventional numerical rnethod to estab-lish a complete and accurate mathematical modcl. Based on the principles of metal crystallizationand Cellular Automata algorithm, the author separated, in time and space, the process ofccystailization into periodically growing airays, so that the simulation of metal crystallization isrealized.展开更多
n the SUN work station network environment, based on Client/ Server model, wedesigned and implemented the dEDBMS system a distributed Engineering DataBase Manage-ment System. This paper presents its system architectu...n the SUN work station network environment, based on Client/ Server model, wedesigned and implemented the dEDBMS system a distributed Engineering DataBase Manage-ment System. This paper presents its system architecture first, then discusses its three parts:theclient software EDBMS / 2, the server software EDB server, the interfaee software EDBclient, and introduces some implementation details.展开更多
The papcr gives an approach to construct shape preserving piece wise cubic, where twocubic picces are allowed by inscrting at most a new knot in each data subinterval, and these cubicpieees is C2 continuous at each ne...The papcr gives an approach to construct shape preserving piece wise cubic, where twocubic picces are allowed by inscrting at most a new knot in each data subinterval, and these cubicpieees is C2 continuous at each new knot. Two numerical examples show that the method is effec.tive and visually pleasing.展开更多
This paper presents a new method of Boolean operation First, a linesegment-polygonclassification theorem is proposed. Then, according to this theorem and basic idea for Booleanoperation, we give the discussion and app...This paper presents a new method of Boolean operation First, a linesegment-polygonclassification theorem is proposed. Then, according to this theorem and basic idea for Booleanoperation, we give the discussion and apposition of the new method. At last, a typical applicationis given.展开更多
文摘The appriximation properties of generalized conic curves are studied in this paper. A generalized conic curve is defined as one of the following curves or their affine and translation e-quivalent curves:(i) conic curves i including parabolas, hyperbolas and ellipses;(ii) generalized monomial curves, including curves of the form x=yr,.r R.r=0,1, in the x-y Cartesian coordinate system;(iii) exponential spiral curves of the form p=Apolar coordinate system.This type of curves has many important properties such as convexity , approximation property, effective numerical computation property and the subdivision property etc. Applications of these curves in both interpolation and approximations using piecewise generalized conic segment are also developed. It is shown that these generalized conic splines are very similar to the cubic polynomial splines and the best error of approximation is or at least in general provided appropriate procedures are used. Finally some numerical examples of interpolation and approximations with generalized conic splines are given.
文摘Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference analysis, a systematic method to construct Cn (n≥ 0) interpolatorycurves by subdivision from given data is described and the mask (filter) of the algorithm is presentedexplicitly. This algorithm generates a Cn smooth curve which interpolates the initial control points.Control parameters are also provided so that the shape of the final curve can be adjusted according torequirements. An immediate generalisation of the method is the construction of smooth interpolatorysubdivision algorithms over uniform triangular networks (tensor product type data) in Rm. The mainresults of this algorithm for smooth interpolatory surface subdivision algorrthm are also included.AMS(MOS) : 65D05 , 65D15 , 65D17.
文摘An application of techniques is presented to construct G￣1 smooth surfaces by using acombination of the rectangular and triangular Bezier patches of degree as low as possible. TheG￣1 smooth surfaces have the local property and interpolate the given data and inherit thetopology imposed by the given space convex quadrilateral partition and triangulation. The papergeneralizes current approaches for assembling of rectangular and triangular patches.
文摘A smooth interpolatory subdivision algorithm for the generation of surfaces over arbi-trary triangulations is introduced and its convergence properties over nonuniform triangulationsstudied. For uniform data, this method is a generalization of the analysis for univariatesubdivision algorithms and for nonuniform data, an extraordinary point analysis is introducedand the local subdivision matrix anaiysis presented. It is proved that the algorithm producessmooth surfaces over arbitrary triangular networks provided the shape parameters are kept with-in an appropriate range. Finally, two graphical examples of surface interpolation overnonuniform data are given to show the smoothing process of the algorithm.AMS (MOS): 65D05, 65D15,65D17.
文摘The undirected graph to express engineering drawings is discussed .The principle to re-solve and reason the undirected graph is presented, and the algorithm finally transforms theundirected graph into the resolvable directed graph. Therefore,a rapid and simple way is suppliedfor variational design. A prototype of this algorithm has been implemented, and some examplesare given.
文摘This paper deals with the technology of computer graphics and its application in ana-lyzing complex nonlinear proceas. We have investigated metal crystallization, which is a complexnonlinear process and is difficult to analyze by using the conventional numerical rnethod to estab-lish a complete and accurate mathematical modcl. Based on the principles of metal crystallizationand Cellular Automata algorithm, the author separated, in time and space, the process ofccystailization into periodically growing airays, so that the simulation of metal crystallization isrealized.
文摘n the SUN work station network environment, based on Client/ Server model, wedesigned and implemented the dEDBMS system a distributed Engineering DataBase Manage-ment System. This paper presents its system architecture first, then discusses its three parts:theclient software EDBMS / 2, the server software EDB server, the interfaee software EDBclient, and introduces some implementation details.
文摘The papcr gives an approach to construct shape preserving piece wise cubic, where twocubic picces are allowed by inscrting at most a new knot in each data subinterval, and these cubicpieees is C2 continuous at each new knot. Two numerical examples show that the method is effec.tive and visually pleasing.
文摘This paper presents a new method of Boolean operation First, a linesegment-polygonclassification theorem is proposed. Then, according to this theorem and basic idea for Booleanoperation, we give the discussion and apposition of the new method. At last, a typical applicationis given.
