Shape Preserving Rational Trigonometric Spline Curves

2014 ◽  
Author(s):  
Muhammad Sarfraz ◽  
Farsia Hussain ◽  
Malik Zawwar Hussain
Keyword(s):  
Shape Preserving ◽  
Spline Curves ◽  
Trigonometric Spline

Shape-Preserving Positive Trigonometric Spline Curves

2016 ◽  
Vol 42 (2) ◽  
pp. 763-775
Author(s):  
Malik Zawwar Hussain ◽  
Farsia Hussain ◽  
Muhammad Sarfraz
Keyword(s):  
Shape Preserving ◽  
Spline Curves ◽  
Trigonometric Spline

A subdivision algorithm for trigonometric spline curves

2002 ◽  
Vol 19 (1) ◽  
pp. 71-88 ◽  
Author(s):  
M.K. Jena ◽  
P. Shunmugaraj ◽  
P.C. Das
Keyword(s):  
Spline Curves ◽  
Trigonometric Spline ◽  
Subdivision Algorithm

scholarly journals Data Visualization Using Rational Trigonometric Spline

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Uzma Bashir ◽  
Jamaludin Md. Ali
Keyword(s):  
Data Visualization ◽  
The Other ◽  
Shape Features ◽  
Shape Parameters ◽  
Shape Preserving ◽  
Numerical Examples ◽  
Data Points ◽  
Trigonometric Spline ◽  
The Given

This paper describes the use of trigonometric spline to visualize the given planar data. The goal of this work is to determine the smoothest possible curve that passes through its data points while simultaneously satisfying the shape preserving features of the data. Positive, monotone, and constrained curve interpolating schemes, by using aC1piecewise rational cubic trigonometric spline with four shape parameters, are developed. Two of these shape parameters are constrained and the other two are set free to preserve the inherited shape features of the data as well as to control the shape of the curve. Numerical examples are given to illustrate the worth of the work.

Mitered Offsets and Skeletons for Circular Arc Polygons

2020 ◽  
Vol 30 (03n04) ◽  
pp. 235-256
Author(s):  
Bastian Weiß ◽  
Bert Jüttler ◽  
Franz Aurenhammer
Keyword(s):  
Monotonicity Property ◽  
Free Form ◽  
Shape Preserving ◽  
Circular Arc ◽  
Spline Curves ◽  
Circular Arcs ◽  
Event Driven ◽  
Planar Shapes ◽  
Practical Performance

The offsetting process that defines straight skeletons of polygons is generalized to arc polygons, i.e., to planar shapes with piecewise circular boundaries. The offsets are obtained by shrinking or expanding the circular arcs on the boundary in a co-circular manner, and tracing the paths of their endpoints. These paths define the associated shape-preserving skeleton, which decomposes the input object into patches. While the skeleton forms a forest of trees, the patches of the decomposition have a radial monotonicity property. Analyzing the events that occur during the offsetting process is non-trivial; the boundary of the offsetting object may get into self-contact and may even splice. This leads us to an event-driven algorithm for offset and skeleton computation. Several examples (both manually created ones and approximations of planar free-form shapes by arc spline curves) are analyzed to study the practical performance of our algorithm.

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.

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