A complete system of addition laws on an elliptic curve E is a collection of addition laws with the property that for any pair of points P1, P2 on E at least one of the addition laws in the collection can be used to c...A complete system of addition laws on an elliptic curve E is a collection of addition laws with the property that for any pair of points P1, P2 on E at least one of the addition laws in the collection can be used to compute P1＋P2. This paper proposes a complete set of the addition laws for arbitrary twisted Jacobi intersection curve.展开更多
In this papaert an INTEGRAL CURVE ALGORITHM is preselited, which turns the intersection curve of surfaces into the form of integral one and then uses 'PREDICTORCORRECTOR' technique to evaluate the intersection...In this papaert an INTEGRAL CURVE ALGORITHM is preselited, which turns the intersection curve of surfaces into the form of integral one and then uses 'PREDICTORCORRECTOR' technique to evaluate the intersection of surfaces.No matter how the surfaces are defined, the method always deaIs with the intersection curves in the same wny. To find a point on the curve one need only to calculate the JACOBI determinants of 'PREDICTOR point' and 'CORRECToR point' while the second order precision is guatanteed. Thus, not only is the problem of finding the intersection of surfaces resolved, but also the algorithms for generating both plane curve and space curve are unified.展开更多
This study presents a novel approach to computing all intersections between two Bézier curves using cubic hybridclipping. Each intersection is represented by two strip intervals that contain an intersection. In e...This study presents a novel approach to computing all intersections between two Bézier curves using cubic hybridclipping. Each intersection is represented by two strip intervals that contain an intersection. In each step, one curve isbounded by two fat lines, and the other is bounded by two cubic Bézier curves, clipping away the domain that doesnot contain the intersections. By selecting the moving control points of the cubic hybrid curves, better cubic polynomial bounds are obtained to make the proposed method more efficient. It was proved that the two strip intervalshave second- and fourth-order convergence rates for transversal intersections. Experimental results show that thenew algorithm is the most efficient among all existing curve/curve intersection approaches.展开更多
Based on the viewpoint of duality, this paper studies the interaction between a curved surface body and an inside particle. By convex/concave bodies with geometric duality, interaction potentials of particles located ...Based on the viewpoint of duality, this paper studies the interaction between a curved surface body and an inside particle. By convex/concave bodies with geometric duality, interaction potentials of particles located outside and inside the curved surface bodies are shown to have duality. With duality, the curvature-based potential between a curved surface body and an inside particle is derived. Furthermore, the normal and tangential driving forces exerted on the particle are studied and expressed as a function of curvatures and curvature gradients. Numerical experiments are designed to test accuracy of the curvature-based potential.展开更多
Traditional 3D printing is based on stereolithography or standard tessellation language models,which contain many redundant data and have low precision.This paper proposes a slicing and support structure generation al...Traditional 3D printing is based on stereolithography or standard tessellation language models,which contain many redundant data and have low precision.This paper proposes a slicing and support structure generation algorithm for 3D printing directly on boundary representation(B-rep)models.First,surface slicing is performed by efficiently computing the intersection curves between the faces of the B-rep models and each slicing plane.Then,the normals of the B-rep models are used to detect where the support structures should be located and the support structures are generated.Experimental results show the efficiency and stability of our algorithm.展开更多
基金Supported by the National Natural Science Foundation of China (10990011)the Science Research Startup Foundation of North China University of Technology
文摘A complete system of addition laws on an elliptic curve E is a collection of addition laws with the property that for any pair of points P1, P2 on E at least one of the addition laws in the collection can be used to compute P1＋P2. This paper proposes a complete set of the addition laws for arbitrary twisted Jacobi intersection curve.
文摘In this papaert an INTEGRAL CURVE ALGORITHM is preselited, which turns the intersection curve of surfaces into the form of integral one and then uses 'PREDICTORCORRECTOR' technique to evaluate the intersection of surfaces.No matter how the surfaces are defined, the method always deaIs with the intersection curves in the same wny. To find a point on the curve one need only to calculate the JACOBI determinants of 'PREDICTOR point' and 'CORRECToR point' while the second order precision is guatanteed. Thus, not only is the problem of finding the intersection of surfaces resolved, but also the algorithms for generating both plane curve and space curve are unified.
基金This work was supported by the National Key R&D Program of China,No.2020YFB1708900Natural Science Foundation of China,No.61872328.
文摘This study presents a novel approach to computing all intersections between two Bézier curves using cubic hybridclipping. Each intersection is represented by two strip intervals that contain an intersection. In each step, one curve isbounded by two fat lines, and the other is bounded by two cubic Bézier curves, clipping away the domain that doesnot contain the intersections. By selecting the moving control points of the cubic hybrid curves, better cubic polynomial bounds are obtained to make the proposed method more efficient. It was proved that the two strip intervalshave second- and fourth-order convergence rates for transversal intersections. Experimental results show that thenew algorithm is the most efficient among all existing curve/curve intersection approaches.
基金Project supported by the National Natural Science Foundation of China(Nos.11672150 and11272175)the Natural Science Foundation of Jiangsu Province(No.BK20130910)the specialized Research Found for Doctoral Program of Higher Education(No.2013000211004)
文摘Based on the viewpoint of duality, this paper studies the interaction between a curved surface body and an inside particle. By convex/concave bodies with geometric duality, interaction potentials of particles located outside and inside the curved surface bodies are shown to have duality. With duality, the curvature-based potential between a curved surface body and an inside particle is derived. Furthermore, the normal and tangential driving forces exerted on the particle are studied and expressed as a function of curvatures and curvature gradients. Numerical experiments are designed to test accuracy of the curvature-based potential.
基金This work is was funded by National Natural Science Foundation of China under Grant No.61672307.
文摘Traditional 3D printing is based on stereolithography or standard tessellation language models,which contain many redundant data and have low precision.This paper proposes a slicing and support structure generation algorithm for 3D printing directly on boundary representation(B-rep)models.First,surface slicing is performed by efficiently computing the intersection curves between the faces of the B-rep models and each slicing plane.Then,the normals of the B-rep models are used to detect where the support structures should be located and the support structures are generated.Experimental results show the efficiency and stability of our algorithm.
