scholarly journals Application of a Four Quadratic Rational Interpolation Spline Curve

2014 ◽  
Vol 04 (01) ◽  
pp. 14-20
Author(s):  
琳 符
Keyword(s):  
Rational Interpolation ◽  
Interpolation Spline ◽  
Spline Curve

scholarly journals Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xinru Liu ◽  
Yuanpeng Zhu ◽  
Shengjun Liu
Keyword(s):  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Rectangular Domain ◽  
Interpolation Spline ◽  
Spline Surface ◽  
Surface Data ◽  
Shape Preserving Interpolation ◽  
The Given ◽  
Surface Construction ◽  
Special Case

A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.

scholarly journals Nonnegativity Preserving Interpolation byC1Bivariate Rational Spline Surface

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Xingxuan Peng ◽  
Zhihong Li ◽  
Qian Sun
Keyword(s):  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Original Data ◽  
Interpolation Spline ◽  
Numerical Examples ◽  
Rational Spline ◽  
Spline Surface ◽  
Rectangular Grids

This paper is concerned with the nonnegativity preserving interpolation of data on rectangular grids. The function is a kind of bivariate rational interpolation spline with parameters, which isC1in the whole interpolation region. Sufficient conditions are derived on coefficients in the rational spline to ensure that the surfaces are always nonnegative if the original data are nonnegative. The gradients at the data sites are modified if necessary to ensure that the nonnegativity conditions are fulfilled. Some numerical examples are illustrated in the end of this paper.

Method of Corner Smooth Transition Based on Interpolation Spline

2013 ◽  
Vol 655-657 ◽  
pp. 1260-1266
Author(s):  
Jian Huang ◽  
Ai Ping Song ◽  
Jian Ming Tao ◽  
Dan Ping Yi
Keyword(s):  
Machine Tool ◽  
High Speed ◽  
Transition Process ◽  
Smooth Transition ◽  
Curvature Radius ◽  
Adjustment Coefficient ◽  
Interpolation Spline ◽  
Processing Efficiency ◽  
Spline Curve ◽  
The Impact

Adjustable form cubic interpolation spline curve, changing its form adjustment coefficient can adjust the curvature radius and shape. Using this spline curve can realize the high-speed smooth connecting between adjacent processing trajectory during NC movement. To internal outline corner transition, use cambered spline transfer curve; To external outline corner transition, can use cambered or toroidal spline transfer curve. During the corner transition process, keep the speed constant, adjust the curvature the curvature radius to control the value of acceleration. Corner smooth transition based on the interpolation spline, can effectively reduce the mutation of acceleration, improve processing efficiency, and weaken the impact to the machine tool.

scholarly journals Rational Cubics and Conics Representation: A Practical Approach

1970 ◽  
Vol 1 (2) ◽  
Author(s):  
M. Sarfraz ◽  
Z. Habib
Keyword(s):  
Computer Graphics ◽  
Cubic Spline ◽  
Practical Approach ◽  
Shape Parameters ◽  
Conic Sections ◽  
Interpolation Spline ◽  
Cubic Curves ◽  
Spline Curve ◽  
Special Cases

A rational cubic spline, with one family of shape parameters, has been discussed with the view to its application in Computer Graphics. It incorporates both conic sections and parametric cubic curves as special cases. The parameters (weights), in the description of the spline curve can be used to modify the shape of the curve, locally and globally, at the knot intervals. The rational cubic spline attains parametric   smoothness whereas the stitching of the conic segments preserves visually reasonable smoothness at the neighboring knots. The curve scheme is interpolatory and can plot parabolic, hyperbolic, elliptic, and circular splines independently as well as bits and pieces of a rational cubic spline.Key Words: Computer Graphics, Interpolation, Spline, Conic, Rational Cubic

C˜2 Continuous Cubic Hermite Interpolation Splines with Second-Order Elliptic Variation

2021 ◽  
Vol 7 (6) ◽  
pp. 6317-6331
Author(s):  
Jie Li ◽  
Yaoyao Tu ◽  
Shilong Fei
Keyword(s):  
Shape Control ◽  
Spline Function ◽  
Hermite Interpolation ◽  
Second Order ◽  
Basis Functions ◽  
Interpolation Spline ◽  
Selection Scheme ◽  
Spline Curve ◽  
Spline Curves ◽  
Two Parameters

In order to solve the deficiency of Hermite interpolation spline with second-order elliptic variation in shape control and continuity, c-2 continuous cubic Hermite interpolation spline with second-order elliptic variation was designed. A set of cubic Hermite basis functions with two parameters was constructed. According to this set of basis functions, the three-order Hermite interpolation spline curves were defined in segments 02, and the parameter selection scheme was discussed. The corresponding cubic Hermite interpolation spline function was studied, and the method to determine the residual term and the best interpolation function was given. The results of an example show that when the interpolation conditions remain unchanged, the cubic Hermite interpolation spline curves not only reach 02 continuity, but also can use the parameters to control the shape of the curves locally or globally. By determining the best values of the parameters, the cubic Hermite interpolation spline function can get a better interpolation effect, and the smoothness of the interpolation spline curve is the best.

C 2-(C 3-) continuous interpolation spline curve and surface

1998 ◽  
Vol 13 (3) ◽  
pp. 238-245
Author(s):  
Fang Kui ◽  
Tan Jianrong ◽  
Zhu Guoqing
Keyword(s):  
Interpolation Spline ◽  
Spline Curve ◽  
Continuous Interpolation

Description and Smoothing of NC Motion Path Based on the Cubic Trigonometric Interpolation Spline

2013 ◽  
Vol 365-366 ◽  
pp. 515-521 ◽  
Author(s):  
Jian Ming Tao ◽  
Ai Ping Song ◽  
Dan Ping Yi
Keyword(s):  
Smooth Transition ◽  
Motion Path ◽  
Trigonometric Interpolation ◽  
Feed Speed ◽  
Control Points ◽  
Interpolation Spline ◽  
Spline Curve ◽  
Nc Machine ◽  
The Stability ◽  
The Impact

In order to better describe the complex motion path of NC machining and realize the smooth transition between path segments, a kind of cubic trigonometric interpolation spline curve was put forward based on a set of special basis function. The spline curve which with adjustable shape satisfies the C1 continuity and it can accurately describe some common engineering curves such as straight line, circular arc and free curve. According to the given information of control points, different shapes of interpolation spline curve can be gotten by changing the adjustment coefficients. Through selecting proper control points and shape adjustment coefficients near the corner, insert the spline curve can realize the smooth transition at the corner of adjacent NC motion path segments, which can ensure the stability of motion path and the continuous of feed speed. Meanwhile, it also can reduce the impact to NC machine.

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