C^n-CONTINUOUS B-TYPE SPLINE CURVES WITH ITSLOCALIZATION INTERPOLATION AND APPROXIMATION

This paper presents a class of Cn- continuous B- type spline curves with some paramet- ric factors.The length of their local support is equal to4.Taking the different values of the parametric factors,the curves can become free- type curves or interpolate a set of given points even mix the both cases.When the parametric factors satisfy the certain conditions,the degrees of the curves can be decreased as low as possible.Besides,when all the parametric factors tend to zero,the curves globally approximate to the control polygon.

A Finite Element Cable Model and Its Applications Based on the Cubic Spline Curve

For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.

A fast direct point-by-point generating algorithm for B Spline curves and surfaces

Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix trans- formation from B Spline representation to Bézier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.

C2 Continuous Quartic Hermite Spline Curves with Shape Parameters

In order to relieve the deficiency of the usual cubic Hermite spline curves,the quartic Hermite spline curves with shape parameters is further studied in this work. The interpolation error and estimator of the quartic Hermite spline curves are given. And the characteristics of the quartic Hermite spline curves are discussed.The quartic Hermite spline curves not only have the same interpolation and continuity properties of the usual cubic Hermite spline curves, but also can achieve local or global shape adjustment and C;continuity by the shape parameters when the interpolation conditions are fixed.

A Class of Spline Curves with Four Local Shape Parameters

A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape parameters. Comput. Aided Geom. Design, 28：151-163 （2011）], is proposed. Without solving a linear system, the spline curves can be used to interpolate sets of points with C2 continuity partly or entirely. The shape parameters have a predictable adjusting role on the sp[ine curves.

C^2-(C^3-) Continuous Interpolation Spline Curve and Surface

Free-formed or sculptured surfaces in engineering products are frequently constructed from a set of measured 3D data points. C2- (C3-) continuity approach is important in this field. This paper presents a method of rectangular interpolation of given 3D data array which is regularly arranged. The interpolation surface which is constructed by tensor product has desirable properties (second-order or third-order continuity locality) and is implemented and adjusted easily. Higher order continuity methods are also briefly discussed.

Many-Knot Spline Interpolating Curves and Their Applications in Font Design

Many-knot spline interpolating is a class of curves and surfaces fitting method presentedin 1974. Many-knot spline interpolating curves are suitable to computer aided geometric design anddata points interpolation. In this paped, the properties of many-knot spline interpolating curves arediscussed and their applications in font design are considered. The differences between many-knotspline interpolating curves and the curves genoaed by exceeding-lacking adjuStment algorithm aregiven.

Paths of algebraic hyperbolic curves

Cubic algebraic hyperbolic （AH） Bezier curves and AH spline curves are defined with a positive parameter a in the space spanned by {1, t, sinht, cosht}. Modifying the value of a yields a family ofAH Bezier or spline curves with the family parameter α. For a fixed point on the original curve, it will move on a defined curve called ＂path of AH curve＂ （AH Bezier and AH spline curves） when a changes. We describe the geometric effects of the paths and give a method to specify a curve passing through a given point.

Research into Freedom Surface Modeling System of Double Beta Spline in Space

In this paper, we present the double Beta spline curved surface which is controlled by double parameters including the algorithm principles, the treatment of boundary conditions, the alternation of projection, the algorithms of elimination hiddle line, the process to display and the primiples to produce the shaded curved surface. Based on all the above, a freedom surface modeling system (FSMS) is designed and some examples developed on FSMS are verified and analyzed.

Optimization Design of Hydraulic Valve Block and Its Internal Flow Channel Based on Additive Manufacturing

Hydraulic valve block is an important part of the hydraulic system.The traditional hydraulic valve block is made by turning and milling,drilling and boring,which leads to many right-angle bending and closed cavity structure of process holes in its internal flow channel,seriously affecting the flow performance of oil.Based on the new design space provided by additive manufacturing technology,the internal hydraulic flow channel of valve block is optimized by using B-spline curve.Computational fluid dynamics analysis is carried out on the hydraulic flow channel to determine the optimal flow channel structure with the smallest pressure drop.The weight reduction of hydraulic valve block is carried out through topology optimization.According to the results of topology optimization,using the method of selective laser melting(SLM),the printing of the hydraulic valve block is completed.The optimized hydraulic channel reduces the pressure loss by 31.4%compared with the traditional hydraulic channel.Compared with the traditional valve block,the hydraulic valve block manufactured by SLM with topology optimization reduces the weight by 33.9%.Therefore,the proposed flow channel optimization and valve block lightweight method provide a new reference for the performance improvement of the internal flow channel of hydraulic valve block and the overall lightweight design of valve block.

CORNER-CUTTING SUBDIVISION SURFACES OF GENERAL DEGREES WITH PARAMETERS

As a corner-cutting subdivision scheme,Lane-Riesefeld algorithm possesses the concise and unified form for generating uniform B-spline curves:vertex splitting plus repeated midpoint averaging.In this paper,we modify the second midpoint averaging step of the Lane-Riesefeld algorithm by introducing a parameter which controls the size of corner cutting,and generalize the strategy to arbitrary topological surfaces of general degree.By adjusting the free parameter,the proposed method can generate subdivision surfaces with flexible shapes.Experimental results demonstrate that our algorithm can produce subdivision surfaces with comparable or even better quality than the other state-of-the-art approaches by carefully choosing the free parameters.