In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline th...In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.展开更多
Modifying the knots of a B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical...Modifying the knots of a B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface, the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.展开更多
In present paper, the contour deletion method is developed both to blend surfaces and to fill N-sided holes, which is used for subdividing the NURBS surface. First, according to the non-uniform Catmull-Clark subdivisi...In present paper, the contour deletion method is developed both to blend surfaces and to fill N-sided holes, which is used for subdividing the NURBS surface. First, according to the non-uniform Catmull-Clark subdivision principle, surfaces are blended. The non-uniform Catmull-Clark subdivision method is constructed, which build the surface through interpolating comer vertices and boundary curves. Then the contour deletion method is adapted to remove the controlling mesh boundary contour in the process of segmentation iteration. Last, N sided-hole is filled to generate a integral smooth continuous surface. This method not only guarantee that the blending surface and base surface patches have C2 continuity at the boundary, but also greatly improve the smoothness of the N-side hole filling surface. The results show that, this method simplifies the specific computer-implemented process, broads the scope of application of subdivision surfaces, and solves the incompatible problem between the subdivision surface and classical spline. The resulting surface has both advantages of the subdivision surface and classical spline, and also has better filling effect.展开更多
in the paper, first, using the transinfinite interpolation strategy rectangular free formsurfaces with C0 and C1 cross boundary continuity are respectively generated by three of its fourboundary curves and correspondi...in the paper, first, using the transinfinite interpolation strategy rectangular free formsurfaces with C0 and C1 cross boundary continuity are respectively generated by three of its fourboundary curves and corresponding cross derivatives. Then, their singularity is removed by anapproximation approach. Finally the surfaces are converted to the NURBS surfaces of degrees 5 × 6and 7×10 respectively. At the end of the paper, conclusions and examples are given.展开更多
Based on the development of the non-contact measurement system of free-formsurface, NURBS reconstruction of measurement points of freeform surface is effectively realized bymodifying the objective function and recursi...Based on the development of the non-contact measurement system of free-formsurface, NURBS reconstruction of measurement points of freeform surface is effectively realized bymodifying the objective function and recursive procedure and calculating the optimum number ofcontrol points. The reconstruction precision is evaluated through Ja-cobi's transformation method.The feasibility of the measurement system and effectiveness of the reconstruction algorithm aboveare proved by experiment.展开更多
According to the characteristics of a complex cover panel, its geometry shape is described by the NURBS surface with great description capability. With the reference to the surface classification determined by Gauss c...According to the characteristics of a complex cover panel, its geometry shape is described by the NURBS surface with great description capability. With the reference to the surface classification determined by Gauss curvature, the proportion of the mid-surface area between before and after being developed is derived from the displacement variation of the mid-surface in the normal vector direction of the sheet metal during the sheet metal forming process. Hereby, based on the curve development theory in differential geometry, a novel diagonal point by point surface development method is put forward to estimate a complex cover panel＇s blank contour efficiently. By comparing the sample＇s development result of diagonal point by point surface development method with that of available one-step method, the validity of the proposed surface development method is verified.展开更多
This work presents some numerical aspects of isogeometric boundary element methods(IGABEM).The behavior of hyper-singular and nearly-singular integration is first explored on the distorted NURBS surface.Several numeri...This work presents some numerical aspects of isogeometric boundary element methods(IGABEM).The behavior of hyper-singular and nearly-singular integration is first explored on the distorted NURBS surface.Several numerical treatments are proposed to enhance the quadrature in the framework of isogeometric analysis.Then a numerical implementation of IGABEM on the trimmed NURBS is detailed.Based on this idea,the surface crack problem is modeled incorporation with the phantom element method.The proposed method allows the crack to intersect with the boundary of the body while preserving the original parametrization of the NURBS-based CAD geometry.展开更多
An improved algorithm of Delaunay triangulation is proposed by expanding the scope from a convex polygon to an arbitrary polygon area in which holes can be contained in the subdivision procedure. The data structure of...An improved algorithm of Delaunay triangulation is proposed by expanding the scope from a convex polygon to an arbitrary polygon area in which holes can be contained in the subdivision procedure. The data structure of generated triangles and the exuviationslike method play a key role, and a single connectivity domain (SCD) without holes is constructed as the initial part of the algorithm. Meanwhile, some examples show that the method can be applied to the triangulation of the trimmed NURBS surface. The result of surface tessellation can be used in many applications such as NC machining, finite element analysis, rendering and mechanism interference detection.展开更多
基金Supported by the National Natural Science Foundation of China(61572430,61303144)the Natural Science Foundation of Zhejiang Province(LY15F020002,LY16F020020)the Ningbo Natural Science Foundation(2016A610223)
文摘In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.
基金Project supported by the National Natural Science Foundation of China (No. 60473130) and the National Basic Research Program (973) of China (No. G2004CB318000)
文摘Modifying the knots of a B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface, the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.
基金Supported by NUAA Fundamental Research Funds(NZ2013201)
文摘In present paper, the contour deletion method is developed both to blend surfaces and to fill N-sided holes, which is used for subdividing the NURBS surface. First, according to the non-uniform Catmull-Clark subdivision principle, surfaces are blended. The non-uniform Catmull-Clark subdivision method is constructed, which build the surface through interpolating comer vertices and boundary curves. Then the contour deletion method is adapted to remove the controlling mesh boundary contour in the process of segmentation iteration. Last, N sided-hole is filled to generate a integral smooth continuous surface. This method not only guarantee that the blending surface and base surface patches have C2 continuity at the boundary, but also greatly improve the smoothness of the N-side hole filling surface. The results show that, this method simplifies the specific computer-implemented process, broads the scope of application of subdivision surfaces, and solves the incompatible problem between the subdivision surface and classical spline. The resulting surface has both advantages of the subdivision surface and classical spline, and also has better filling effect.
文摘in the paper, first, using the transinfinite interpolation strategy rectangular free formsurfaces with C0 and C1 cross boundary continuity are respectively generated by three of its fourboundary curves and corresponding cross derivatives. Then, their singularity is removed by anapproximation approach. Finally the surfaces are converted to the NURBS surfaces of degrees 5 × 6and 7×10 respectively. At the end of the paper, conclusions and examples are given.
基金This project is supported by Provincial Natural Science Foundation of Zhejiang of China (No.599026).
文摘Based on the development of the non-contact measurement system of free-formsurface, NURBS reconstruction of measurement points of freeform surface is effectively realized bymodifying the objective function and recursive procedure and calculating the optimum number ofcontrol points. The reconstruction precision is evaluated through Ja-cobi's transformation method.The feasibility of the measurement system and effectiveness of the reconstruction algorithm aboveare proved by experiment.
文摘According to the characteristics of a complex cover panel, its geometry shape is described by the NURBS surface with great description capability. With the reference to the surface classification determined by Gauss curvature, the proportion of the mid-surface area between before and after being developed is derived from the displacement variation of the mid-surface in the normal vector direction of the sheet metal during the sheet metal forming process. Hereby, based on the curve development theory in differential geometry, a novel diagonal point by point surface development method is put forward to estimate a complex cover panel＇s blank contour efficiently. By comparing the sample＇s development result of diagonal point by point surface development method with that of available one-step method, the validity of the proposed surface development method is verified.
基金National Natural Science Foundation of China(NSFC)under Grant(No.51904202).
文摘This work presents some numerical aspects of isogeometric boundary element methods(IGABEM).The behavior of hyper-singular and nearly-singular integration is first explored on the distorted NURBS surface.Several numerical treatments are proposed to enhance the quadrature in the framework of isogeometric analysis.Then a numerical implementation of IGABEM on the trimmed NURBS is detailed.Based on this idea,the surface crack problem is modeled incorporation with the phantom element method.The proposed method allows the crack to intersect with the boundary of the body while preserving the original parametrization of the NURBS-based CAD geometry.
文摘An improved algorithm of Delaunay triangulation is proposed by expanding the scope from a convex polygon to an arbitrary polygon area in which holes can be contained in the subdivision procedure. The data structure of generated triangles and the exuviationslike method play a key role, and a single connectivity domain (SCD) without holes is constructed as the initial part of the algorithm. Meanwhile, some examples show that the method can be applied to the triangulation of the trimmed NURBS surface. The result of surface tessellation can be used in many applications such as NC machining, finite element analysis, rendering and mechanism interference detection.
