Pythagorean hodographs

1990 ◽  
Vol 34 (5) ◽  
pp. 736-752 ◽  
Author(s):  
R. T. Farouki ◽  
T. Sakkalis
Keyword(s):  
Pythagorean Hodographs

scholarly journals Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves

2009 ◽  
Vol 44 (4) ◽  
pp. 307-332 ◽  
Author(s):  
Rida T. Farouki ◽  
Carlotta Giannelli ◽  
Alessandra Sestini
Keyword(s):  
Polynomial Curves ◽  
Low Degree ◽  
Pythagorean Hodographs

Minkowski Pythagorean hodographs

1999 ◽  
Vol 16 (8) ◽  
pp. 739-753 ◽  
Author(s):  
Hwan Pyo Moon
Keyword(s):  
Pythagorean Hodographs

scholarly journals Helical polynomial curves and double Pythagorean hodographs I. Quaternion and Hopf map representations

2009 ◽  
Vol 44 (2) ◽  
pp. 161-179 ◽  
Author(s):  
Rida T. Farouki ◽  
Carlotta Giannelli ◽  
Alessandra Sestini
Keyword(s):  
Polynomial Curves ◽  
Hopf Map ◽  
Pythagorean Hodographs

A New Variable Feedrate CNC Interpolator for Abrasive Waterjet System

2009 ◽  
Vol 626-627 ◽  
pp. 339-344
Author(s):  
Wei Xiao Tang ◽  
X.D. Zhang ◽  
L. Wang
Keyword(s):  
Experimental Data ◽  
Traverse Speed ◽  
Abrasive Waterjet ◽  
Free Form ◽  
Jet Lag ◽  
Taper Angle ◽  
Kerf Taper ◽  
Pythagorean Hodographs ◽  
Ph Curve ◽  
Cut Surface

It is becoming general that the contour of part is defined with free-form curves for abrasive waterjet cutting. In this paper, the effect of the traverse speed on cut surface quality is discussed. After that, the free-form Pythagorean Hodographs (PH) curve is defined and its main characteristics are discussed. A new CNC interpolator capable of driving the nozzle along the PH curves at the feedrate adaptable of the curvature of the contour is presented. The taper shape or jet lag can be minimized with it through the variation of the traverse speed. Experimental data indicate that a decrease of about 58 per cent in kerf taper angle can be obtained under a given condition.

Structural invariance of spatial Pythagorean hodographs

2002 ◽  
Vol 19 (6) ◽  
pp. 395-407 ◽  
Author(s):  
Rida T. Farouki ◽  
Mohammad al-Kandari ◽  
Takis Sakkalis
Keyword(s):  
Structural Invariance ◽  
Pythagorean Hodographs
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