scholarly journals C2 rational quartic interpolation spline with local shape preserving property

2015 ◽  
Vol 46 ◽  
pp. 57-63 ◽  
Author(s):  
Yuanpeng Zhu ◽  
Xuli Han
Keyword(s):  
Interpolation Spline ◽  
Shape Preserving ◽  
Local Shape

scholarly journals C1Rational Quadratic Trigonometric Interpolation Spline for Data Visualization

2015 ◽  
Vol 2015 ◽  
pp. 1-20 ◽  
Author(s):  
Shengjun Liu ◽  
Zhili Chen ◽  
Yuanpeng Zhu
Keyword(s):  
Trigonometric Interpolation ◽  
Data Sets ◽  
Order Of Approximation ◽  
Shape Parameters ◽  
Interpolation Spline ◽  
Shape Preserving ◽  
Shape Preserving Interpolation ◽  
Trigonometric Spline ◽  
The Given ◽  
Data Constraints

A newC1piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated asO(h3). Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.

Shape-Preserving Planar Quadratic Bézier Interpolation Spline with Minimal Stretch Energy

2020 ◽  
Vol 48 (3) ◽  
pp. 20190809
Author(s):  
Juncheng Li ◽  
Chengzhi Liu ◽  
Li Zhang
Keyword(s):  
Interpolation Spline ◽  
Shape Preserving

scholarly journals Shape preserving design of geometrically nonlinear structures using topology optimization

2019 ◽  
Vol 59 (4) ◽  
pp. 1033-1051 ◽  
Author(s):  
Yu Li ◽  
Jihong Zhu ◽  
Fengwen Wang ◽  
Weihong Zhang ◽  
Ole Sigmund
Keyword(s):  
Topology Optimization ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Shape Preserving

Ceramic Nanoparticle Assemblies with Tailored Shapes and Tailored Chemistries via Biosculpting and Shape-Preserving Inorganic Conversion

2005 ◽  
Vol 5 (1) ◽  
pp. 63-67 ◽  
Author(s):  
M.B. Dickerson ◽  
R.R. Naik ◽  
P.M. Sarosi ◽  
G. Agarwal ◽  
M.O. Stone ◽  
...  
Keyword(s):  
Shape Preserving ◽  
Nanoparticle Assemblies

The Curvature Theory of Line Trajectories in Spatial Kinematics

1981 ◽  
Vol 103 (4) ◽  
pp. 718-724 ◽  
Author(s):  
J. M. McCarthy ◽  
B. Roth
Keyword(s):  
Planar Motion ◽  
Spatial Motion ◽  
Third Order ◽  
Local Shape ◽  
The Third ◽  
Moving Body ◽  
Physical Representation ◽  
Curvature Theory ◽  
Spatial Kinematics ◽  
Differential Properties

This paper develops the differential properties of ruled surfaces in a form which is applicable to spatial kinematics. Derivations are presented for the three curvature parameters which define the local shape of a ruled surface. Related parameters are also developed which allow a physical representation of this shape as generated by a cylindric-cylindric crank. These curvature parameters are then used to define all the lines in the moving body which instantaneously generate speciality shaped trajectories. Such lines may be used in the synthesis of spatial motions in the same way that the points on the inflection circle and cubic of stationary curvature are used to synthesize planar motion. As an example of this application several special sets of lines are defined: the locus of all lines which for a general spatial motion instantaneously generate helicoids to the second order and the locus of lines generating right hyperboloids to the third order.

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