Rida Taji Farouki

Rida Taji Farouki's AcademicInfluence.com Rankings

Rida Taji Farouki

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Electrical Engineering

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Rida Taji Farouki

Computer Science

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Engineering
Computer Science

Rida Taji Farouki's Degrees

PhD Mathematics Stanford University
Bachelors Electrical Engineering California Institute of Technology

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Rida Taji Farouki's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Pythagorean hodographs (1990) (446)
The Bernstein polynomial basis: A centennial retrospective (2012) (423)
Algorithms for polynomials in Bernstein form (1988) (379)
On the numerical condition of polynomials in Bernstein form (1987) (357)
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable (2007) (349)
Triple point of Yukawa systems (1997) (332)
Hermite interpolation by Pythagorean hodograph quintics (1995) (219)
On the optimal stability of the Bernstein basis (1996) (185)
Analytic properties of plane offset curves (1990) (180)
The conformal map z -> z2 of the hodograph plane (1994) (176)
The approximation of non-degenerate offset surfaces (1986) (175)
Exact Taylor series coefficients for variable-feedrate CNC curve interpolators (2001) (166)
Real-time CNC interpolators for Pythagorean-hodograph curves (1996) (151)
Algebraic properties of plane offset curves (1990) (150)
Surface Analysis Methods (1986) (147)
Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves (1998) (141)
Computer simulations of environmental influences on galaxy evolution in dense clusters. II. rapid tidal encounters (1981) (137)
Pythagorean-hodograph space curves (1994) (134)
Thermodynamics of strongly‐coupled Yukawa systems near the one‐component‐plasma limit. II. Molecular dynamics simulations (1994) (129)
Hermite Interpolation by Rotation-Invariant Spatial Pythagorean-Hodograph Curves (2002) (129)
Algorithms for time-optimal control of CNC machines along curved tool paths (2005) (128)
Approximation by interval Bezier curves (1992) (126)
Pythagorean-Hodograph Curves (2002) (123)
Real rational curves are not 'unit speed' (1991) (109)
The elastic bending energy of Pythagorean-hodograph curves (1996) (103)
Thermodynamics of strongly‐coupled Yukawa systems near the one‐component‐plasma limit. I. Derivation of the excess energy (1994) (103)
Exact offset procedures for simple solids (1985) (100)
G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate functions on open-architecture CNC machines (1999) (99)
Phase diagram of Yukawa systems near the one-component-plasma limit revisited (1996) (96)
Performance analysis of CNC interpolators for time-dependent feedrates along PH curves (2001) (95)
Legendre-Bernstein basis transformations (2000) (91)
Construction ofC2 Pythagorean-hodograph interpolating splines by the homotopy method (1996) (90)
Construction and shape analysis of PH quintic Hermite interpolants (2001) (89)
Plasma–particulate interactions in nonuniform plasmas with finite flows (1994) (80)
The characterization of parametric surface sections (1986) (77)
On the stability of transformations between power and Bernstein polynomial forms (1991) (77)
Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I. Theoretical foundations (1999) (75)
Structural invariance of spatial Pythagorean hodographs (2002) (74)
Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures (2008) (73)
Automatic parsing of degenerate quadric-surface intersections (1989) (70)
The bisector of a point and a plane parametric curve (1994) (70)
Characterization and construction of helical polynomial space curves (2004) (67)
Path planning with offset curves for layered fabrication processes (1995) (66)
Computer simulations of environmental influences on galaxy evolution in dense clusters. I. Ram-pressure stripping (1980) (66)
1. Pythagorean - Hodograph Curves in Practical Use (1992) (66)
Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves (2003) (65)
A Hierarchy of Geometric Forms (1985) (64)
Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains (2003) (63)
Optimal tool orientation control for 5-axis CNC milling with ball-end cutters (2013) (61)
Efficient Solution of the Complex Quadratic Tridiagonal System for C2 PH Quintic Splines (2001) (60)
Phase transitions of dense systems of charged ‘‘dust’’ grains in plasmas (1992) (59)
High-speed cornering by CNC machines under prescribed bounds on axis accelerations and toolpath contour error (2012) (59)
Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds (2007) (59)
Optimal parameterizations (1997) (58)
Simulations of merging disk galaxies (1982) (57)
Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations (1987) (56)
A shock‐tracking algorithm for surface evolution under reactive‐ion etching (1993) (55)
Performance analysis of cross-coupled controllers for CNC machines based upon precise real-time contour error measurement (2012) (54)
Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics (2005) (54)
Voronoi diagram and medial axis algorithm for planar domains with curved boundaries — II: Detailed algorithm description (1999) (53)
A control polygon scheme for design of planar C2 PH quintic spline curves (2007) (52)
Design of rational rotation-minimizing rigid body motions by Hermite interpolation (2011) (52)
Minkowski Geometric Algebra of Complex Sets (2001) (52)
Approximation of rolling-ball blends for free-form parametric surfaces (1996) (51)
Pythagorean-hodograph quintic transition curves of monotone curvature (1997) (51)
Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves (2010) (48)
Computing Minkowski sums of plane curves (1995) (47)
Contour machining of free-form surfaces with real-time PH curve CNC interpolators (1999) (47)
Specified-Precision Computation of Curve/Curve Bisectors (1998) (46)
Solution of inverse dynamics problems for contour error minimization in CNC machines (2010) (46)
Computing Point/Curve and Curve/Curve Bisectors (1992) (45)
Rational rotation-minimizing frames on polynomial space curves of arbitrary degree (2010) (45)
Exact rotation-minimizing frames for spatial Pythagorean-hodograph curves (2002) (42)
Physical constraints on feedrates, feed accelerations along curved tool paths (2000) (41)
Rational Pythagorean-hodograph space curves (2011) (40)
DESIGN OF RATIONAL CAM PROFILES WITH PYTHAGOREAN-HODOGRAPH CURVES (1998) (40)
Construction of G1 planar Hermite interpolants with prescribed arc lengths (2016) (39)
Topological criterion for selection of quintic Pythagorean-hodograph Hermite interpolants (2008) (38)
MASS SEGREGATION RELAXATION, AND THE COULOMB LOGARITHM IN N-BODY SYSTEMS (AGAIN) (1982) (38)
Construction of G2 rounded corners with Pythagorean-hodograph curves (2014) (37)
Spatial C^2 PH quintic splines (2003) (36)
Linear perturbation methods for topologically consistent representations of free-form surface intersections (2004) (36)
Helical polynomial curves and double Pythagorean hodographs I. Quaternion and Hopf map representations (2009) (35)
Analysis of the offset to a parabola (1995) (34)
Computation of optimal composite re-parameterizations (2001) (33)
On the numerical condition of algebraic curves and surfaces 1. Implicit equations (1988) (33)
Algorithm 812: BPOLY: An object-oriented library of numerical algorithms for polynomials in Bernstein form (2001) (33)
A complete classification of quintic space curves with rational rotation-minimizing frames (2012) (32)
Inverse kinematics for optimal tool orientation control in 5-axis CNC machining (2014) (31)
Singular Points of Algebraic Curves (1990) (31)
Rational space curves are not "unit speed" (2007) (31)
Quintic space curves with rational rotation-minimizing frames (2009) (31)
Rational rotation-minimizing frames - Recent advances and open problems (2016) (30)
Flux considerations in the coupling of Monte Carlo plasma sheath simulations with feature evolution models (1992) (29)
BOUNDARY-CONDITION REFINEMENT OF THE CHILD-LANGMUIR LAW FOR COLLISIONLESS DC PLASMA SHEATHS (1990) (29)
Polynomial and Rational Pythagorean-Hodograph Curves Reconciled (1994) (28)
Algorithms for Minkowski products and implicitly‐defined complex sets (2000) (28)
Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme (2007) (28)
Hierarchical merging and the structure of elliptical galaxies (1983) (27)
Efficient high-speed cornering motions based on continuously-variable feedrates. I. Real-time interpolator algorithms (2016) (27)
Existence conditions for Coons patches interpolating geodesic boundary curves (2009) (27)
Exact Minkowski Products of N Complex Disks (2002) (27)
A real-time surface interpolator methodology for precision CNC machining of swept surfaces (2016) (27)
Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves (2009) (27)
Degenerate point/curve and curve/curve bisectors arising in medial axis computations for planar domains with curved boundaries (1998) (27)
C2 interpolation of spatial data subject to arc-length constraints using Pythagorean-hodograph quintic splines (2014) (26)
Shape‐preserving interpolation by G1 and G2 PH quintic splines (2003) (26)
Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants (2013) (25)
Optimal slicing of free-form surfaces (2002) (25)
Rotation-minimizing osculating frames (2014) (25)
On the numerical condition of Bernstein-Bézier subdivision processes (1990) (23)
Construction of Bézier surface patches with Bézier curves as geodesic boundaries (2009) (23)
Conic Approximation of Conic Offsets (1997) (21)
New Developments in Theory, Algorithms, and Applications for Pythagorean–Hodograph Curves (2019) (21)
Convergent inversion approximations for polynomials in Bernstein form (2000) (20)
Existence of Pythagorean-hodograph quintic interpolants to spatial G1 Hermite data with prescribed arc lengths (2019) (20)
Efficient high-speed cornering motions based on continuously-variable feedrates. II. Implementation and performance analysis (2017) (20)
Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3 (2012) (20)
Gauss map computation for free-form surfaces (2001) (19)
A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames (2016) (18)
Computing with barycentric polynomials (1991) (18)
Graphical methods for surface differential geometry (1987) (18)
Identification and "reverse engineering" of Pythagorean-hodograph curves (2015) (18)
Real-time CNC interpolators for Bézier conics (2001) (18)
Curves and surfaces in geometrical optics (1992) (18)
Construction of rational surface patches bounded by lines of curvature (2010) (17)
Shape-preserving interpolation of spatial data by Pythagorean-hodograph quintic spline curves (2015) (16)
Spline Approximation of Effective Potentials under Periodic Boundary Conditions (1994) (16)
Topologically consistent trimmed surface approximations based on triangular patches (2004) (16)
A real-time CNC interpolator algorithm for trimming and filling planar offset curves (2017) (15)
Design of C 2 Spatial Pythagorean-Hodograph Quintic Spline Curves by Control Polygons (2010) (15)
Spatial camera orientation control by rotation‐minimizing directed frames (2009) (15)
Simulations of galaxy mergers : cannibalism and dynamical friction. (1983) (14)
Construction and smoothing of triangular Coons patches with geodesic boundary curves (2010) (14)
Path planning with Pythagorean-hodograph curves for unmanned or autonomous vehicles (2018) (13)
Evaluating the boundary and covering degree of planar Minkowski sums and other geometrical convolutions (2007) (13)
Non-existence of rational arc length parameterizations for curves in Rn (2009) (13)
Minkowski roots of complex sets (2000) (13)
Computational methods for rapid prototyping of analytic solid models (1996) (13)
Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form (2016) (13)
Numerical Stability in Geometric Algorithms and Representations (1988) (12)
Experimental study of contouring accuracy for CNC machines executing curved paths with constant and curvature-dependent feedrates (2013) (12)
Least squares tool path approximation with Pythagorean hodograph curves for high speed CNC machining (2002) (12)
Experimental performance analysis of an inverse dynamics CNC compensation scheme for high-speed execution of curved toolpaths (2014) (12)
The collapse and violent relaxation of N-body systems - Mass segregation and the secondary maximum (1983) (12)
Cycles upon cycles: an anecdotal history of higher curves in science and engineering (1998) (11)
Exact equations of simple wavefronts (1992) (11)
Pythagorean-hodograph curves and related topics (2008) (11)
Spatial camera orientation control by rotation-minimizing directed frames (2009) (10)
Bipolar and Multipolar Coordinates (2000) (10)
Algebraically rectifiable parametric curves (1993) (10)
Curves from Motion, Motion from Curves (2000) (9)
Noninvasive high resolution mechanical strain maps of the spine intervertebral disc using nonrigid registration of magnetic resonance images. (2012) (9)
A geometric product formulation for spatial Pythagorean hodograph curves with applications to Hermite interpolation (2007) (9)
Geometric Design Using Space Curves with Rational Rotation-Minimizing Frames (2008) (9)
Algorithm 952 (2015) (8)
Rational frames of minimal twist along space curves under specified boundary conditions (2018) (8)
An interpolation scheme for designing rational rotation-minimizing camera motions (2013) (8)
Approximation of monotone clothoid segments by degree 7 Pythagorean-hodograph curves (2021) (8)
Root neighborhoods, generalized lemniscates, and robust stability of dynamic systems (2007) (8)
Computational issues in solid boundary evaluation (1988) (8)
Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves (2013) (7)
Rational swept surface constructions based on differential and integral sweep curve properties (2015) (7)
Equilibrium configuration of a bounded inextensible membrane subject to solar radiation pressure (2017) (7)
Solution of elementary equations in the Minkowski geometric algebra of complex sets (2005) (7)
Optimization of Corner Blending Curves (2019) (7)
Hierarchical segmentations of algebraic curves and some applications (1989) (7)
Smoothing of Time-Optimal Feedrates for Cartesian CNC Machines (2005) (7)
Tensor-product surface patches with Pythagorean-hodograph isoparametric curves (2016) (6)
Equivalence of distinct characterizations for rational rotation-minimizing frames on quintic space curves (2011) (6)
Numerical simulation of the plasma and gravitational dynamics of a galactic magnetic monopole halo (1984) (6)
Algorithm 952: PHquintic: A Library of Basic Functions for the Construction and Analysis of Planar Quintic Pythagorean-Hodograph Curves (2015) (6)
Singular cases of planar and spatial C1 Hermite interpolation problems based on quintic Pythagorean-hodograph curves (2020) (6)
Minkowski Geometric Algebra and the Stability of Characteristic Polynomials (2002) (6)
Solution of a quadratic quaternion equation with mixed coefficients (2015) (6)
Inverse dynamics toolpath compensation for CNC machines based on model predictive control (2020) (6)
Algorithms for spatial Pythagoreanhodograph curves (2006) (5)
A general framework for solving inverse dynamics problems in multi-axis motion control. (2019) (5)
Boundary evaluation algorithms for Minkowski combinations of complex sets using topological analysis of implicit curves (2005) (5)
Arc lengths of rational Pythagorean-hodograph curves (2015) (5)
Corrigendum to "Rational rotation-minimizing frames on polynomial space curves of arbitrary degree" [J. Symbolic Comput. 45(8) (2010) 844-856] (2013) (5)
Ion energetics in collisionless sheaths of rf process plasmas (1992) (5)
Computation of Minkowski Values of Polynomials over Complex Sets (2004) (5)
C1 and C2 interpolation of orientation data along spatial Pythagorean-hodograph curves using rational adapted spline frames (2018) (5)
On integrating lines of curvature (1998) (5)
High-speed cornering by CNC machines under prescribed bounds on axis accelerations and toolpath contour error (2011) (4)
Mapping rational rotation-minimizing frames from polynomial curves on to rational curves (2020) (4)
The Mathematical Evolution of Wavefronts (1992) (4)
Time-Optimal feedrates along Curved Paths for Cartesian CNC Machines with prescribed Bounds on Axis velocities and Accelerations (2007) (4)
Construction of rational curves with rational arc lengths by direct integration (2019) (4)
ALGORITHMS FOR SPATIAL PYTHAGOREAN-HODOGRAPH CURVES (4)
Pythagorean Hodographs in ℝ3 (2008) (3)
Planar projections of spatial Pythagorean-hodograph curves (2021) (3)
Efficient high-speed cornering motions based on continuously-variable feedrates. I. Real-time interpolator algorithms (2016) (3)
Feedrate modulation for accurate traversal of trimmed planar offset paths (2018) (3)
Rational minimal-twist motions on curves with rotation-minimizing Euler-Rodrigues frames (2019) (3)
Simulations of galaxy mergers. (1983) (2)
Geometry of the ringed surfaces in R4 that generate spatial Pythagorean hodographs (2016) (2)
Hydrodynamic analysis of electron motion in the cathode fall using a Monte Carlo simulation (1992) (2)
Construction of periodic adapted orthonormal frames on closed space curves (2020) (2)
Arc—length Parameterization (2008) (2)
Minkowski products of unit quaternion sets (2019) (2)
Robust plotting of generalized lemniscates (2004) (2)
Minkowski Pythagorean Hodographs (2008) (2)
Helical polynomial curves interpolating G1 data with prescribed axes and pitch angles (2017) (2)
Erratum to “Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds”: [Robot. Comput. Integr. Manuf. 24(1) (2008) 16–31] (2009) (2)
Approximation by Interval (1992) (2)
Real—time CNC Interpolators (2008) (2)
Corrigendum to: 'Linear perturbation methods for topologically consistent representations of free-form surface intersections': Computer Aided Geometric Design 21 (2004) 303-319 (2004) (2)
Reduced difference polynomials and self-intersection computations (2018) (2)
The Bernstein Basis (2008) (2)
A real-time surface interpolator methodology for precision CNC machining of swept surfaces (2015) (1)
Shigley Hauler— A competitive project illustrating basic machine design principles (2016) (1)
Rational Pythagorean-hodograph Curves (2008) (1)
Real-time compensation of backlash positional errors in CNC machines by localized feedrate modulation (2022) (1)
Identifying Pythagorean-Hodograph Curves Closest to Prescribed Planar Bézier Curves (2022) (1)
Spatial C2 closed loops of prescribed arc length defined by Pythagorean-hodograph curves (2021) (1)
Tschirnhausen's Cubic (2008) (1)
Rotation – minimizing conformal frames (2013) (1)
The Cartesian Ovals (2022) (1)
Optimized Routine of Machining Distortion Characterization Based on Gaussian Surface Curvature (2020) (1)
Computing the Minkowski Value of the Exponential Function over a Complex Disk (2008) (1)
Foreword to the Special Focus on Mathematics and Algorithms for CAM and CNC (2012) (1)
Accurate Real-time CNC Curve Interpolators Based Upon Richardson Extrapolation (2021) (1)
Computing the roots of sparse high–degree polynomials that arise from the study of random simplicial complexes (2019) (0)
Non—Euclidean Geometry (2008) (0)
Title Identification and " reverse engineering " of Pythagorean-hodograph curves Permalink (2015) (0)
Bézier Curves and Surfaces (2008) (0)
Experimental performance analysis of an inverse dynamics CNC compensation scheme for high-speed execution of curved toolpaths (2014) (0)
Optimal contour orientations for machining of free{form surfaces (2001) (0)
Spatial Hermite Interpolants (2008) (0)
CAGD special issue on ``PH Curves and Related Topics'' (2008) (0)
The Ion Distribution Function in Weakly Collisional Sheaths (1991) (0)
Wave-front propagation from exact algebraic equations (1990) (0)
Flux Integration In 2D vs. 3D in Feature Evolution Models of Plasma Processing (1991) (0)
Dynamics of charged particulates in plasmas (1994) (0)
Manufacture of part (1994) (0)
Topological Approach to the Hermite Interpolation Problem for Quintic Pythagorean Hodograph Curves ∗ † (2006) (0)
C2 Cubic Spline Curves (2008) (0)
UC Davis UC Davis Previously Published Works Title Geometry of the ringed surfaces in R 4 that generate spatial Pythagorean hodographs (2016) (0)
Rational frames of minimal twist along space curves under specified boundary conditions (2018) (0)
Defense Technical Information Center Compilation Part Notice ADP 012017 TITLE : Curves from Motion , Motion from Curves DISTRIBUTION : Approved for public release , distribution unlimited (0)
Rotation—minimizing Frames (2008) (0)
Dynamics Of Charged Partictrlates In Plasmas (1994) (0)
A homotopy method for the determination of intersection curve topology (2003) (0)
The Boltzmann-Poisson System in Weakly Collisional Sheaths (1994) (0)
Equilibrium conﬁguration of a bounded inextensible membrane subject to solar radiation pressure (2017) (0)
Descartes ovals as wavefronts (1991) (0)
Elastic Bending Energy (2008) (0)
Spline Basis Functions (2008) (0)
Minkowski products of unit quaternion sets (2019) (0)
Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints (2023) (0)
UC Davis UC Davis Previously Published Works Title Helical polynomial curves interpolating G 1 data with prescribed axes and pitch angles (2017) (0)
Foreword to the Special Focus on Mathematics and Algorithms for CAM and CNC (2012) (0)
Efficient high-speed cornering motions based on continuously-variable feedrates. II. Implementation and performance analysis (2016) (0)
Title Inverse kinematics for optimal tool orientation control in 5-axis CNC machining Permalink (2013) (0)
Suppression of chip load variations by real-time spindle speed modulation (2018) (0)
Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form (2015) (0)
Computing the roots of sparse high–degree polynomials that arise from the study of random simplicial complexes (2019) (0)
Suppression of chip load variations by real-time spindle speed modulation (2018) (0)
Sliding Mode Control Of Two Arms Manipulating a Flexible Beam (2007) (0)
An interpolation scheme for designing rational rotation-minimizing camera motions (2011) (0)
On the construction of polynomial minimal surfaces with Pythagorean normals (2022) (0)
Planar C2 PH Quintic Splines (2008) (0)
Numerical Simulation of Phase Transitions in Dense Dusty Plasmas (1997) (0)
Planar Hermite Interpolants (2008) (0)
Feedrate modulation for accurate traversal of trimmed planar offset paths (2018) (0)
Computational Astrophysics on the Array Processor (1983) (0)
Real-time needle guidance for venipuncture based on optical coherence tomography (2021) (0)
Helical Polynomial Curves (2008) (0)
A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames (2016) (0)
Rational rotation-minimizing frames on polynomial space curves: recent advances and open problems (2016) (0)

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Rida Taji Farouki's Published Works

Published Works

What Schools Are Affiliated With Rida Taji Farouki?

Rida Taji Farouki's AcademicInfluence.com Rankings