Rida T. Farouki

According to our database1, Rida T. Farouki authored at least 145 papers between 1983 and 2025.

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Bibliography

2025
Control point modifications that preserve the Pythagorean-hodograph nature of planar quintic curves.
J. Comput. Appl. Math., 2025

Application of a metric for complex polynomials to bounded modification of planar Pythagorean-hodograph curves.
J. Comput. Appl. Math., 2025

2023
Partition of the space of planar quintic Pythagorean-hodograph curves.
Comput. Aided Geom. Des., October, 2023

Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints.
Comput. Aided Geom. Des., June, 2023

2022
Identifying Pythagorean-Hodograph Curves Closest to Prescribed Planar Bézier Curves.
Comput. Aided Des., 2022

On the construction of polynomial minimal surfaces with Pythagorean normals.
Appl. Math. Comput., 2022

2021
Approximation of monotone clothoid segments by degree 7 Pythagorean-hodograph curves.
J. Comput. Appl. Math., 2021

Real-time needle guidance for venipuncture based on optical coherence tomography.
Comput. methods Biomech. Biomed. Eng. Imaging Vis., 2021

Planar projections of spatial Pythagorean-hodograph curves.
Comput. Aided Geom. Des., 2021

Accurate Real-time CNC Curve Interpolators Based Upon Richardson Extrapolation.
Comput. Aided Des., 2021

Spatial C2 closed loops of prescribed arc length defined by Pythagorean-hodograph curves.
Appl. Math. Comput., 2021

2020
Computing the roots of sparse high-degree polynomials that arise from the study of random simplicial complexes.
Numer. Algorithms, 2020

Mapping rational rotation-minimizing frames from polynomial curves on to rational curves.
Comput. Aided Geom. Des., 2020

Construction of periodic adapted orthonormal frames on closed space curves.
Comput. Aided Geom. Des., 2020

Singular cases of planar and spatial <i>C</i><sup>1</sup> Hermite interpolation problems based on quintic Pythagorean-hodograph curves.
Comput. Aided Geom. Des., 2020

Optimized Routine of Machining Distortion Characterization Based on Gaussian Surface Curvature.
Proceedings of the 2nd International Conference of the DFG International Research Training Group 2057, 2020

2019
Existence of Pythagorean-hodograph quintic interpolants to spatial <i>G</i><sup>1</sup> Hermite data with prescribed arc lengths.
J. Symb. Comput., 2019

Rational minimal-twist motions on curves with rotation-minimizing Euler-Rodrigues frames.
J. Comput. Appl. Math., 2019

Construction of rational curves with rational arc lengths by direct integration.
Comput. Aided Geom. Des., 2019

Optimization of Corner Blending Curves.
Comput. Aided Des., 2019

Minkowski products of unit quaternion sets.
Adv. Comput. Math., 2019

2018
<i>C</i><sup>1</sup> and <i>C</i><sup>2</sup> interpolation of orientation data along spatial Pythagorean-hodograph curves using rational adapted spline frames.
Comput. Aided Geom. Des., 2018

Reduced difference polynomials and self-intersection computations.
Appl. Math. Comput., 2018

Rational frames of minimal twist along space curves under specified boundary conditions.
Adv. Comput. Math., 2018

2017
Helical polynomial curves interpolating G<sup>1</sup> data with prescribed axes and pitch angles.
Comput. Aided Geom. Des., 2017

A real-time CNC interpolator algorithm for trimming and filling planar offset curves.
Comput. Aided Des., 2017

A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames.
Adv. Comput. Math., 2017

2016
Solution of a quadratic quaternion equation with mixed coefficients.
J. Symb. Comput., 2016

Geometry of the ringed surfaces in R<sup>4</sup> that generate spatial Pythagorean hodographs.
J. Symb. Comput., 2016

Construction of G<sup>1</sup> planar Hermite interpolants with prescribed arc lengths.
Comput. Aided Geom. Des., 2016

Rational rotation-minimizing frames - Recent advances and open problems.
Appl. Math. Comput., 2016

Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form.
Adv. Comput. Math., 2016

2015
Algorithm 952: PHquintic: A Library of Basic Functions for the Construction and Analysis of Planar Quintic Pythagorean-Hodograph Curves.
ACM Trans. Math. Softw., 2015

Rational swept surface constructions based on differential and integral sweep curve properties.
Comput. Aided Geom. Des., 2015

Identification and "reverse engineering" of Pythagorean-hodograph curves.
Comput. Aided Geom. Des., 2015

Arc lengths of rational Pythagorean-hodograph curves.
Comput. Aided Geom. Des., 2015

2014
C<sup>2</sup> interpolation of spatial data subject to arc-length constraints using Pythagorean-hodograph quintic splines.
Graph. Model., 2014

Inverse kinematics for optimal tool orientation control in 5-axis CNC machining.
Comput. Aided Geom. Des., 2014

Rotation-minimizing osculating frames.
Comput. Aided Geom. Des., 2014

Construction of G<sup>2</sup> rounded corners with Pythagorean-hodograph curves.
Comput. Aided Geom. Des., 2014

2013
Corrigendum to "Rational rotation-minimizing frames on polynomial space curves of arbitrary degree" [J. Symbolic Comput. 45(8) (2010) 844-856].
J. Symb. Comput., 2013

Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves.
J. Symb. Comput., 2013

Optimal tool orientation control for 5-axis CNC milling with ball-end cutters.
Comput. Aided Geom. Des., 2013

Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants.
Comput. Aided Geom. Des., 2013

An interpolation scheme for designing rational rotation-minimizing camera motions.
Adv. Comput. Math., 2013

2012
Design of rational rotation-minimizing rigid body motions by Hermite interpolation.
Math. Comput., 2012

Foreword to the Special Focus on Mathematics and Algorithms for CAM and CNC.
Math. Comput. Sci., 2012

A complete classification of quintic space curves with rational rotation-minimizing frames.
J. Symb. Comput., 2012

Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3.
J. Comput. Appl. Math., 2012

The Bernstein polynomial basis: A centennial retrospective.
Comput. Aided Geom. Des., 2012

2011
Equivalence of distinct characterizations for rational rotation-minimizing frames on quintic space curves.
Comput. Aided Geom. Des., 2011

Rational Pythagorean-hodograph space curves.
Comput. Aided Geom. Des., 2011

2010
Rational rotation-minimizing frames on polynomial space curves of arbitrary degree.
J. Symb. Comput., 2010

Construction and smoothing of triangular Coons patches with geodesic boundary curves.
Comput. Aided Geom. Des., 2010

Construction of rational surface patches bounded by lines of curvature.
Comput. Aided Geom. Des., 2010

Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves.
Adv. Comput. Math., 2010

Design of C 2 Spatial Pythagorean-Hodograph Quintic Spline Curves by Control Polygons.
Proceedings of the Curves and Surfaces, 2010

2009
Spatial camera orientation control by rotation-minimizing directed frames.
Comput. Animat. Virtual Worlds, 2009

Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves.
J. Symb. Comput., 2009

Helical polynomial curves and double Pythagorean hodographs I. Quaternion and Hopf map representations.
J. Symb. Comput., 2009

Existence conditions for Coons patches interpolating geodesic boundary curves.
Comput. Aided Geom. Des., 2009

Quintic space curves with rational rotation-minimizing frames.
Comput. Aided Geom. Des., 2009

Construction of Bézier surface patches with Bézier curves as geodesic boundaries.
Comput. Aided Des., 2009

2008
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Geometry and Computing 1, Springer, ISBN: 978-3-540-73398-0, 2008

Pythagorean-hodograph curves and related topics.
Comput. Aided Geom. Des., 2008

Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures.
Comput. Aided Geom. Des., 2008

Topological criterion for selection of quintic Pythagorean-hodograph Hermite interpolants.
Comput. Aided Geom. Des., 2008

Geometric Design Using Space Curves with Rational Rotation-Minimizing Frames.
Proceedings of the Mathematical Methods for Curves and Surfaces, 2008

2007
Time-Optimal feedrates along Curved Paths for Cartesian CNC Machines with prescribed Bounds on Axis velocities and Accelerations.
Int. J. Robotics Autom., 2007

A geometric product formulation for spatial Pythagorean hodograph curves with applications to Hermite interpolation.
Comput. Aided Geom. Des., 2007

A control polygon scheme for design of planar C<sup>2</sup> PH quintic spline curves.
Comput. Aided Geom. Des., 2007

Rational space curves are not "unit speed".
Comput. Aided Geom. Des., 2007

Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme.
Adv. Comput. Math., 2007

Root neighborhoods, generalized lemniscates, and robust stability of dynamic systems.
Appl. Algebra Eng. Commun. Comput., 2007

Computing the Minkowski Value of the Exponential Function over a Complex Disk.
Proceedings of the Computer Mathematics, 8th Asian Symposium, 2007

2005
Boundary evaluation algorithms for Minkowski combinations of complex sets using topological analysis of implicit curves.
Numer. Algorithms, 2005

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics.
Adv. Comput. Math., 2005

Solution of elementary equations in the Minkowski geometric algebra of complex sets.
Adv. Comput. Math., 2005

Smoothing of Time-Optimal Feedrates for Cartesian CNC Machines.
Proceedings of the Mathematics of Surfaces XI, 2005

2004
Computation of Minkowski Values of Polynomials over Complex Sets.
Numer. Algorithms, 2004

Corrigendum to: 'Linear perturbation methods for topologically consistent representations of free-form surface intersections': Computer Aided Geometric Design 21 (2004) 303-319.
Comput. Aided Geom. Des., 2004

Linear perturbation methods for topologically consistent representations of free-form surface intersections.
Comput. Aided Geom. Des., 2004

Topologically consistent trimmed surface approximations based on triangular patches.
Comput. Aided Geom. Des., 2004

2003
Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves.
Comput. Aided Geom. Des., 2003

Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains.
Comput. Aided Geom. Des., 2003

2002
Exact Minkowski Products of N Complex Disks.
Reliab. Comput., 2002

Exact rotation-minimizing frames for spatial Pythagorean-hodograph curves.
Graph. Model., 2002

Optimal slicing of free-form surfaces.
Comput. Aided Geom. Des., 2002

Structural invariance of spatial Pythagorean hodographs.
Comput. Aided Geom. Des., 2002

Hermite Interpolation by Rotation-Invariant Spatial Pythagorean-Hodograph Curves.
Adv. Comput. Math., 2002

Minkowski Geometric Algebra and the Stability of Characteristic Polynomials.
Proceedings of the Third International Workshop "Visualization and Mathematics", 2002

Pythagorean-Hodograph Curves.
Proceedings of the Handbook of Computer Aided Geometric Design, 2002

2001
Algorithm 812: BPOLY: An object-oriented library of numerical algorithms for polynomials in Bernstein form.
ACM Trans. Math. Softw., 2001

Efficient Solution of the Complex Quadratic Tridiagonal System for C2 PH Quintic Splines.
Numer. Algorithms, 2001

Performance analysis of CNC interpolators for time-dependent feedrates along PH curves.
Comput. Aided Geom. Des., 2001

Gauss map computation for free-form surfaces.
Comput. Aided Geom. Des., 2001

Construction and shape analysis of PH quintic Hermite interpolants.
Comput. Aided Geom. Des., 2001

Real-time CNC interpolators for Bézier conics.
Comput. Aided Geom. Des., 2001

Computation of optimal composite re-parameterizations.
Comput. Aided Geom. Des., 2001

Exact Taylor series coefficients for variable-feedrate CNC curve interpolators.
Comput. Aided Des., 2001

2000
Physical constraints on feedrates, feed accelerations along curved tool paths.
Comput. Aided Geom. Des., 2000

Algorithms for Minkowski products and implicitly-defined complex sets.
Adv. Comput. Math., 2000

Bipolar and Multipolar Coordinates.
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces, 2000

Minkowski Roots of Complex Sets.
Proceedings of the Geometric Modeling and Processing 2000, 2000

1999
Contour machining of free-form surfaces with real-time PH curve CNC interpolators.
Comput. Aided Geom. Des., 1999

Convergent inversion approximations for polynomials in Bernstein form.
Comput. Aided Geom. Des., 1999

1998
Specified-Precision Computation of Curve/Curve Bisectors.
Int. J. Comput. Geom. Appl., 1998

Degenerate point/curve and curve/curve bisectors arising in medial axis computations for planar domains with curved boundaries.
Comput. Aided Geom. Des., 1998

On integrating lines of curvature.
Comput. Aided Geom. Des., 1998

Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves.
Comput. Aided Des., 1998

1997
Conic Approximation of Conic Offsets.
J. Symb. Comput., 1997

Optimal parameterizations.
Comput. Aided Geom. Des., 1997

Pythagorean-hodograph quintic transition curves of monotone curvature.
Comput. Aided Des., 1997

1996
On the optimal stability of the Bernstein basis.
Math. Comput., 1996

Real-time CNC interpolators for Pythagorean-hodograph curves.
Comput. Aided Geom. Des., 1996

The elastic bending energy of Pythagorean-hodograph curves.
Comput. Aided Geom. Des., 1996

Approximation of rolling-ball blends for free-form parametric surfaces.
Comput. Aided Des., 1996

Construction of<i>C</i><sup>2</sup> Pythagorean-hodograph interpolating splines by the homotopy method.
Adv. Comput. Math., 1996

1995
Computing Minkowski sums of plane curves.
Int. J. Comput. Geom. Appl., 1995

Analysis of the offset to a parabola.
Comput. Aided Geom. Des., 1995

1994
The bisector of a point and a plane parametric curve.
Comput. Aided Geom. Des., 1994

The conformal map z -> z<sub>2</sub> of the hodograph plane.
Comput. Aided Geom. Des., 1994

Pythagorean-hodograph space curves.
Adv. Comput. Math., 1994

Polynomial and Rational Pythagorean-Hodograph Curves Reconciled.
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces, 1994

1993
Algebraically rectifiable parametric curves.
Comput. Aided Geom. Des., 1993

1992
Approximation by interval Bezier curves.
IEEE Computer Graphics and Applications, 1992

Computing Point/Curve and Curve/Curve Bisectors.
Proceedings of the 5th IMA Conference on the Mathematics of Surfaces, 1992

1. Pythagorean - Hodograph Curves in Practical Use.
Proceedings of the Geometry Processing for Design and Manufacturing, 1992

1991
Real rational curves are not 'unit speed'.
Comput. Aided Geom. Des., 1991

On the stability of transformations between power and Bernstein polynomial forms.
Comput. Aided Geom. Des., 1991

1990
Singular Points of Algebraic Curves.
J. Symb. Comput., 1990

Algebraic properties of plane offset curves.
Comput. Aided Geom. Des., 1990

Analytic properties of plane offset curves.
Comput. Aided Geom. Des., 1990

1989
Automatic parsing of degenerate quadric-surface intersections.
ACM Trans. Graph., 1989

1988
Computational issues in solid boundary evaluation.
Inf. Sci., 1988

On the numerical condition of algebraic curves and surfaces 1. Implicit equations.
Comput. Aided Geom. Des., 1988

Algorithms for polynomials in Bernstein form.
Comput. Aided Geom. Des., 1988

Numerical Stability in Geometric Algorithms and Representations.
Proceedings of the 3rd IMA Conference on the Mathematics of Surfaces, 1988

1987
On the numerical condition of polynomials in Bernstein form.
Comput. Aided Geom. Des., 1987

1986
The characterization of parametric surface sections.
Comput. Vis. Graph. Image Process., 1986

Surface Analysis Methods.
IEEE Computer Graphics and Applications, 1986

The approximation of non-degenerate offset surfaces.
Comput. Aided Geom. Des., 1986

1985
A Hierarchy of Geometric Forms.
IEEE Computer Graphics and Applications, 1985

Exact offset procedures for simple solids.
Comput. Aided Geom. Des., 1985

1983
Computational Astrophysics on the Array Processor.
Computer, 1983


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