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 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.

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

scholarly journals Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Yuanpeng Zhu ◽  
Xuli Han ◽  
Shengjun Liu
Keyword(s):  
Error Estimate ◽  
Hermite Interpolation ◽  
Sufficient Conditions ◽  
Basis Functions ◽  
Shape Parameters ◽  
Interpolation Spline ◽  
Triangular Domain ◽  
Type Algorithm ◽  
Special Case ◽  
Monotonicity Preserving

Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class ofC1continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing aC1positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, theG1continuous conditions are deduced for the joining of two patches.

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.

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