A control polygon scheme for design of planar PH quintic spline curves

2007 ◽  
Vol 24 (1) ◽  
pp. 28-52 ◽  
Author(s):  
Francesca Pelosi ◽  
Maria Lucia Sampoli ◽  
Rida T. Farouki ◽  
Carla Manni
Keyword(s):  
Quintic Spline ◽  
Control Polygon ◽  
Spline Curves

Design of C 2 Spatial Pythagorean-Hodograph Quintic Spline Curves by Control Polygons

2012 ◽  
pp. 253-269 ◽  
Author(s):  
Rida T. Farouki ◽  
Carla Manni ◽  
Francesca Pelosi ◽  
Maria Lucia Sampoli
Keyword(s):  
Quintic Spline ◽  
Spline Curves ◽  
Pythagorean Hodograph

scholarly journals High speed contouring enhanced with C2 PH quintic spline curves

2012 ◽  
Vol 19 (2) ◽  
pp. 311-319 ◽  
Author(s):  
J. Jahanpour
Keyword(s):  
High Speed ◽  
Quintic Spline ◽  
Spline Curves

scholarly journals Shape-preserving interpolation of spatial data by Pythagorean-hodograph quintic spline curves

2014 ◽  
Vol 35 (1) ◽  
pp. 478-498 ◽  
Author(s):  
R. T. Farouki ◽  
C. Manni ◽  
M. L. Sampoli ◽  
A. Sestini
Keyword(s):  
Spatial Data ◽  
Shape Preserving ◽  
Quintic Spline ◽  
Spline Curves ◽  
Pythagorean Hodograph ◽  
Shape Preserving Interpolation

scholarly journals Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form

2015 ◽  
Vol 42 (1) ◽  
pp. 199-225 ◽  
Author(s):  
Rida T. Farouki ◽  
Carlotta Giannelli ◽  
Alessandra Sestini
Keyword(s):  
Quintic Spline ◽  
B Spline ◽  
Spline Curves ◽  
Pythagorean Hodograph ◽  
Local Modification

Cubic TP B-Spline Curves with a Shape Parameter

2013 ◽  
Vol 11 ◽  
pp. 59-72 ◽  
Author(s):  
Mridula Dube ◽  
Reenu Sharma
Keyword(s):  
Tensor Product ◽  
Shape Parameter ◽  
Control Points ◽  
Shape Parameters ◽  
Special Shape ◽  
B Spline ◽  
Control Polygon ◽  
Spline Curves ◽  
Trigonometric Spline ◽  
The Given

In this paper a new kind of splines, called cubic trigonometric polynomial B-spline (cubic TP B-spline) curves with a shape parameter, are constructed over the space spanned by As each piece of the curve is generated by three consecutive control points, they posses many properties of the quadratic B-spline curves. These trigonometric curves with a non-uniform knot vector are C1 and G2 continuous. They are C2 continuous when choosing special shape parameter for non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves when choosing special shape parameters. With the increase of the shape parameter, the trigonometric spline curves approximate to the control polygon. The given curves posses many properties of the quadratic B-spline curves. The generation of tensor product surfaces by these new splines is straightforward.

PIECEWISE QUARTIC TRIGONOMETRIC POLYNOMIAL B-SPLINE CURVES WITH TWO SHAPE PARAMETERS

2012 ◽  
Vol 12 (04) ◽  
pp. 1250028
Author(s):  
MRIDULA DUBE ◽  
REENU SHARMA
Keyword(s):  
Trigonometric Polynomial ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curve ◽  
Control Polygon ◽  
Spline Curves ◽  
Spline Surfaces ◽  
Polynomial Curve ◽  
Trigonometric Spline ◽  
The Given

Analogous to the quartic B-splines curve, a piecewise quartic trigonometric polynomial B-spline curve with two shape parameters is presented in this paper. Each curve segment is generated by three consecutive control points. The given curve posses many properties of the B-spline curve. These curves are closer to the control polygon than the different other curves considered in this paper, for different values of shape parameters for each curve. With the increase of the value of shape parameters, the curve approach to the control polygon. For nonuniform and uniform knot vector the given curves have C0, G3; C1, G3; C1, G7; and C3 continuity for different choice of shape parameters. A quartic trigonometric Bézier curves are also introduced as a special case of the given trigonometric spline curves. A comparison of quartic trigonometric polynomial curve is made with different other curves. In the last, quartic trigonometric spline surfaces with two shape parameters are constructed. They have most properties of the corresponding curves.

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