Edit Profile (opens in new tab) Farouki, Rida T. Co-Author Distance Author ID: farouki.rida-t Published as: Farouki, Rida T.; Farouki, R. T.; Farouki, Rida more...less Documents Indexed: 148 Publications since 1985, including 1 Book and 1 Additional arXiv Preprint 3 Contributions as Editor Co-Authors: 66 Co-Authors with 113 Joint Publications 1,062 Co-Co-Authors all top 5 Co-Authors 32 single-authored 23 Sestini, Alessandra 15 Sakkalis, Takis 14 Giannelli, Carlotta 14 Manni, Carla 12 Han, Chang Yong 7 Sampoli, Maria Lucia 6 Hass, Joel 6 Pelosi, Francesca 5 Neff, C. Andrew 5 Tsai, Yi-Feng 4 Krajnc, Marjeta 4 Ramamurthy, Rajesh 4 Sederberg, Thomas W. 4 Vitrih, Vito 4 Žagar, Emil 3 Biard, Luc 3 Choi, Hyeong In 3 Gentili, Graziano 3 Pottmann, Helmut 3 Rajan, V. T. 3 Song, Xiaowen 3 Stoppato, Caterina 3 Szafran, Nicolas 2 al-Kandari, Mohammad 2 Dospra, Petroula 2 Goodman, Timothy N. T. 2 Jee, Sungchul 2 Johnstone, John K. 2 Li, Shiqiao 2 Manjunathaiah, Jairam 2 Ravani, Bahram 2 Šír, Zbyněk 2 Smith, Tait S. 2 Yuan, Guo-Feng 2 Zheng, Jianmin 1 Albrecht, Gudrun 1 Alghanemi, Azeb 1 Boyadjieff, Casey L. 1 Costantini, Paolo Giuseppe 1 Dalvie, M. 1 Deshmukh, Sharief 1 Dong, Bohan 1 Feldman, Bryan E. 1 Gutierrez, Robert 1 Hormann, Kai 1 Jüttler, Bert 1 Kaul, Anil 1 Kim, Soohyun 1 Kuspa, Bethany K. 1 Kwon, Song-Hwa 1 Li, Hongbo 1 Moon, Hwan Pyo 1 Nicholas, David 1 Nittler, Kevin M. 1 Noakes, Lyle 1 Nudo, Federico 1 O’Connor, Michael A. 1 Perwass, Christian B. U. 1 Rampersad, Joanne 1 Sauer, Tomas 1 Shah, Sagar 1 Strom, Jeffrey A. 1 Timar, Sebastian D. 1 Vaserstein, Leonid N. 1 Wang, Dingkang 1 Wilson, C. S. all top 5 Serials 62 Computer Aided Geometric Design 14 Advances in Computational Mathematics 11 Journal of Symbolic Computation 9 Journal of Computational and Applied Mathematics 4 Mathematics of Computation 4 Applied Mathematics and Computation 4 Numerical Algorithms 3 IMA Journal of Numerical Analysis 2 The Mathematical Intelligencer 2 ACM Transactions on Mathematical Software 2 International Journal of Computational Geometry & Applications 1 Journal of Computational Physics 1 Geometriae Dedicata 1 Information Sciences 1 Applied Numerical Mathematics 1 ACM Transactions on Graphics 1 CAD. Computer-Aided Design 1 Computer Vision, Graphics, and Image Processing 1 Applicable Algebra in Engineering, Communication and Computing 1 Filomat 1 Annals of Numerical Mathematics 1 Reliable Computing 1 Mechanism and Machine Theory 1 Graphical Models 1 Mathematics in Computer Science 1 Geometry and Computing all top 5 Fields 110 Numerical analysis (65-XX) 40 Computer science (68-XX) 36 Differential geometry (53-XX) 17 Approximations and expansions (41-XX) 9 Algebraic geometry (14-XX) 9 Geometry (51-XX) 6 Mechanics of particles and systems (70-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Systems theory; control (93-XX) 3 General and overarching topics; collections (00-XX) 3 Field theory and polynomials (12-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Functions of a complex variable (30-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 138 Publications have been cited 2,469 times in 872 Documents Cited by ▼ Year ▼ Pythagorean-hodograph curves. Algebra and geometry inseparable. Zbl 1144.51004 Farouki, Rida T. 165 2008 The Bernstein polynomial basis: a centennial retrospective. Zbl 1252.65039 Farouki, Rida T. 112 2012 Algorithms for polynomials in Bernstein form. Zbl 0648.65007 Farouki, R. T.; Rajan, V. T. 108 1988 On the numerical condition of polynomials in Bernstein form. Zbl 0636.65012 Farouki, R. T.; Rajan, V. T. 103 1987 Hermite interpolation by Pythagorean hodograph quintics. Zbl 0847.68125 Farouki, R. T.; Neff, C. A. 97 1995 The conformal map \(z\to z^ 2\) of the hodograph plane. Zbl 0806.65005 Farouki, Rida T. 86 1994 On the optimal stability of the Bernstein basis. Zbl 0853.65051 Farouki, R. T.; Goodman, T. N. T. 68 1996 Pythagorean-hodograph space curves. Zbl 0829.65011 Farouki, Rida T.; Sakkalis, Takis 67 1994 Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves. Zbl 1001.41003 Farouki, Rida T.; al-Kandari, Mohammad; Sakkalis, Takis 66 2002 Analytic properties of plane offset curves. Zbl 0718.53003 Farouki, R. T.; Neff, C. A. 57 1990 Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures. Zbl 1172.65307 Farouki, Rida T.; Giannelli, Carlotta; Manni, Carla; Sestini, Alessandra 46 2008 Pythagorean-hodograph curves in practical use. Zbl 0770.41017 Farouki, Rida T. 44 1992 Construction and shape analysis of PH quintic Hermite interpolants. Zbl 0971.68186 Moon, H. P.; Farouki, R. T.; Choi, H. I. 42 2001 Algebraic properties of plane offset curves. Zbl 0724.65008 Farouki, R. T.; Neff, C. A. 39 1990 Construction of \(C^ 2\) Pythagorean-hodograph interpolating splines by the homotopy method. Zbl 0866.65008 Albrecht, Gudrun; Farouki, Rida T. 38 1996 The elastic bending energy of Pythagorean-hodograph curves. Zbl 0875.68861 Farouki, Rida T. 38 1996 Legendre-Bernstein basis transformations. Zbl 0962.65042 Farouki, Rida T. 37 2000 Characterization and construction of helical polynomial space curves. Zbl 1059.65016 Farouki, Rida T.; Han, Chang Yong; Manni, Carla; Sestini, Alessandra 37 2004 On the stability of transformations between power and Bernstein polynomial forms. Zbl 0725.65018 Farouki, R. T. 32 1991 Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves. Zbl 1049.68723 Farouki, Rida T.; Manjunathaiah, Jairam; Nicholas, David; Yuan, Guo-Feng; Jee, Sungchul 32 1998 The approximation of non-degenerate offset surfaces. Zbl 0621.65003 Farouki, R. T. 31 1986 Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves. Zbl 1069.65551 Farouki, Rida T.; Han, Chang Yong 31 2003 Real-time CNC interpolators for Pythagorean-hodograph curves. Zbl 0875.68875 Farouki, Rida T.; Shah, Sagar 30 1996 Design of rational rotation-minimizing rigid body motions by Hermite interpolation. Zbl 1241.65026 Farouki, Rida T.; Giannelli, Carlotta; Manni, Carla; Sestini, Alessandra 29 2012 Real rational curves are not ‘unit speed’. Zbl 0746.41019 Farouki, Rida T.; Sakkalis, Takis 28 1991 Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics. Zbl 1065.68103 Pelosi, Francesca; Farouki, Rida T.; Manni, Carla; Sestini, Alessandra 27 2005 Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains. Zbl 1069.65517 Farouki, Rida T.; Goodman, T. N. T.; Sauer, Thomas 27 2003 Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves. Zbl 1202.53004 Farouki, Rida T. 27 2010 Construction of \(G^1\) planar Hermite interpolants with prescribed arc lengths. Zbl 1418.65021 Farouki, Rida T. 26 2016 Rational rotation-minimizing frames on polynomial space curves of arbitrary degree. Zbl 1204.53009 Farouki, Rida T.; Sakkalis, Takis 25 2010 Singular points of algebraic curves. Zbl 0699.14035 Sakkalis, Takis; Farouki, Rida 24 1990 Exact rotation-minimizing frames for spatial Pythagorean-hodograph curves. Zbl 1055.68124 Farouki, Rida T. 24 2002 Quintic space curves with rational rotation-minimizing frames. Zbl 1205.65079 Farouki, Rida T.; Giannelli, Carlotta; Manni, Carla; Sestini, Alessandra 22 2009 Helical polynomial curves and double Pythagorean hodographs. I: Quaternion and Hopf map representations. Zbl 1187.53005 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 22 2009 Topological criterion for selection of quintic pythagorean-hodograph Hermite interpolants. Zbl 1172.65322 Choi, Hyeong In; Farouki, Rida T.; Kwon, Song-Hwa; Moon, Hwan Pyo 21 2008 Minkowski geometric algebra of complex sets. Zbl 0987.51012 Farouki, Rida T.; Pyo Moon, Hwan; Ravani, Bahram 20 2001 Efficient solution of the complex quadratic tridiagonal system for \(C^2\) PH quintic splines. Zbl 0987.65016 Farouki, Rida T.; Kuspa, Bethany K.; Manni, Carla; Sestini, Alessandra 20 2001 A complete classification of quintic space curves with rational rotation-minimizing frames. Zbl 1232.53004 Farouki, Rida T.; Sakkalis, Takis 19 2012 Rational Pythagorean-hodograph space curves. Zbl 1210.65037 Farouki, Rida T.; Šír, Zbyněk 19 2011 Spatial \(C^2\) PH quintic splines. Zbl 1044.65010 Farouki, Rida T.; Manni, Carla; Sestini, Alessandra 18 2003 A control polygon scheme for design of planar \(C^2\) PH quintic spline curves. Zbl 1171.65347 Pelosi, Francesca; Sampoli, Maria Lucia; Farouki, Rida T.; Manni, Carla 18 2007 Existence conditions for coons patches interpolating geodesic boundary curves. Zbl 1205.65078 Farouki, R. T.; Szafran, N.; Biard, L. 18 2009 Existence of Pythagorean-hodograph quintic interpolants to spatial \(G^1\) Hermite data with prescribed arc lengths. Zbl 1432.65024 Farouki, Rida T. 17 2019 On the numerical condition of algebraic curves and surfaces. I: Implicit equations. Zbl 0709.65011 Farouki, R. T.; Rajan, V. T. 17 1988 New developments in theory, algorithms, and applications for Pythagorean-hodograph curves. Zbl 07150019 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 17 2019 Performance analysis of CNC interpolators for time-dependent feedrates along PH curves. Zbl 0971.68172 Tsai, Yi-Feng; Farouki, Rida T.; Feldman, Bryan 15 2001 Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants. Zbl 1286.65021 Farouki, Rida T.; Han, Chang Yong; Dospra, Petroula; Sakkalis, Takis 15 2013 Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves. Zbl 1168.53001 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 15 2009 The characterization of parametric surface sections. Zbl 0631.65012 Farouki, R. T. 14 1986 On the numerical condition of Bernstein-Bézier subdivision processes. Zbl 0749.65008 Farouki, R. T.; Neff, C. A. 14 1990 Shape-preserving interpolation by \(G^1\) and \(G^2\) PH quintic splines. Zbl 1022.65008 Farouki, Rida T.; Manni, Carla; Sestini, Alessandra 14 2003 Voronoi diagram and medial axis algorithm for planar domains with curved boundaries. I: Theoretical foundations. Zbl 0939.65018 Ramamurthy, Rajesh; Farouki, Rida T. 13 1999 Exact Minkowski products of \(N\) complex disks. Zbl 1028.65048 Farouki, Rida T.; Pottmann, Helmut 13 2002 Rational rotation-minimizing frames – recent advances and open problems. Zbl 1410.53001 Farouki, Rida T. 13 2016 The bisector of a point and a plane parametric curve. Zbl 0796.65013 Farouki, Rida T.; Johnstone, John K. 13 1994 Optimal parameterizations. Zbl 0906.68156 Farouki, Rida T. 13 1997 Algorithms for Minkowski products and implicitly-defined complex sets. Zbl 0948.65016 Farouki, Rida T.; Moon, Hwan Pyo; Ravani, Bahram 12 2000 Identification and “reverse engineering” of Pythagorean-hodograph curves. Zbl 1375.65022 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 12 2015 Exact offset procedures for simple solids. Zbl 0583.65095 Farouki, R. T. 12 1985 Algorithm 812: BPOLY: An object-oriented library of numerical algorithms for polynomials in Bernstein form. Zbl 1070.65515 Tsai, Yi-Feng; Farouki, Rida T. 12 2001 Automatic parsing of degenerate quadric-surface intersections. Zbl 0746.68093 Farouki, R. T.; Neff, C. A.; O’Connor, M. A. 12 1989 Design of rational cam profiles with Pythagorean-hodograph curves. Zbl 1049.70536 Farouki, R. T.; Manjunathaiah, J.; Jee, S. 11 1998 Computing Minkowski sums of plane curves. Zbl 0854.68102 Kaul, Anil; Farouki, Rida T. 11 1995 Linear perturbation methods for topologically consistent representations of free-form surface intersections. Zbl 1069.65567 Song, Xiaowen; Sederberg, Thomas W.; Zheng, Jianmin; Farouki, Rida T.; Hass, Joel 11 2004 Polynomial and rational Pythagorean-hodograph curves reconciled. Zbl 0878.68120 Farouki, Rida T.; Pottmann, Helmut 11 1996 Convergent inversion approximations for polynomials in Bernstein form. Zbl 0939.68126 Farouki, R. T. 10 1999 Specified-precision computation of curve/curve bisectors. Zbl 1026.65010 Farouki, Rida T.; Ramamurthy, Rajesh 10 1998 Computation of optimal composite re-parameterizations. Zbl 0984.68161 Costantini, Paolo; Farouki, Rida T.; Manni, Carla; Sestini, Alessandra 10 2001 Rational space curves are not “unit speed”. Zbl 1171.65331 Farouki, Rida T.; Sakkalis, Takis 10 2007 Construction of \(G^2\) rounded corners with Pythagorean-hodograph curves. Zbl 1293.65027 Farouki, Rida T. 9 2014 Smooth curve design with double-Tschirnhausen cubics. Zbl 0855.65005 Farouki, Rida T.; Peters, Jörg 9 1996 Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3. Zbl 1244.14023 Sakkalis, Takis; Farouki, Rida T. 9 2012 Rotation-minimizing osculating frames. Zbl 1284.65031 Farouki, Rida T.; Giannelli, Carlotta; Sampoli, Maria Lucia; Sestini, Alessandra 8 2014 Optimal tool orientation control for 5-axis CNC milling with ball-end cutters. Zbl 1261.65018 Farouki, Rida T.; Li, Shiqiao 8 2013 Contour machining of free-form surfaces with real-time PH curve CNC interpolators. Zbl 0908.68175 Farouki, Rida T.; Tsai, Yi-Feng; Yuan, Guo-Feng 7 1999 Shape-preserving interpolation of spatial data by Pythagorean-hodograph quintic spline curves. Zbl 1312.65013 Farouki, Rida T.; Manni, Carla; Sampoli, Maria Lucia; Sestini, Alessandra 7 2015 Rational frames of minimal twist along space curves under specified boundary conditions. Zbl 1419.14046 Farouki, Rida T.; Moon, Hwan Pyo 7 2018 Computing point/curve and curve/curve bisectors. Zbl 0813.65021 Farouki, R. T.; Johnstone, J. K. 7 1994 Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form. Zbl 1334.65034 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 7 2016 Evaluating the boundary and covering degree of planar Minkowski sums and other geometrical convolutions. Zbl 1140.65020 Farouki, Rida T.; Hass, Joel 7 2007 Voronoi diagram and medial axis algorithm for planar domains with curved boundaries. II: Detailed algorithm description. Zbl 0962.65017 Ramamurthy, Rajesh; Farouki, Rida T. 6 1999 Least-squares tool path approximation with Pythagorean-hodograph curves for high-speed CNC machining. Zbl 0959.65027 Farouki, R. T.; Saitou, K.; Tsai, Y.-F. 6 1998 A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames. Zbl 1390.53005 Farouki, Rida T.; Gentili, Graziano; Giannelli, Carlotta; Sestini, Alessandra; Stoppato, Caterina 6 2017 Design of \(C ^{2}\) spatial Pythagorean-hodograph quintic spline curves by control polygons. Zbl 1354.65029 Farouki, Rida T.; Manni, Carla; Pelosi, Francesca; Sampoli, Maria Lucia 6 2012 Computing with barycentric polynomials. Zbl 0746.65011 Farouki, Rida T. 6 1991 Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme. Zbl 1118.65011 Hass, Joel; Farouki, Rida T.; Han, Chang Yong; Song, Xiaowen; Sederberg, Thomas W. 6 2007 Root neighborhoods, generalized lemniscates, and robust stability of dynamic systems. Zbl 1192.65018 Farouki, Rida T.; Han, Chang Yong 6 2007 Approximation of monotone clothoid segments by degree 7 Pythagorean-hodograph curves. Zbl 1484.65035 Farouki, Rida T.; Pelosi, Francesca; Sampoli, Maria Lucia 6 2021 Graphical methods for surface differential geometry. Zbl 0667.65008 Farouki, R. T. 5 1987 Cycles upon cycles: An anecdotal history of higher curves in science and engineering. Zbl 0904.65017 Farouki, Rida T.; Rampersad, Joanne 5 1998 Minkowski geometric algebra and the stability of characteristic polynomials. Zbl 1175.93182 Farouki, Rida T.; Moon, Hwan Pyo 5 2003 A geometric product formulation for spatial pythagorean hodograph curves with applications to Hermite interpolation. Zbl 1171.65348 Perwass, Christian B. U.; Farouki, Rida T.; Noakes, Lyle 5 2007 Geometric design using space curves with rational rotation-minimizing frames. Zbl 1274.65037 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 5 2010 Construction and smoothing of triangular Coons patches with geodesic boundary curves. Zbl 1209.65021 Farouki, R. T.; Szafran, N.; Biard, L. 5 2010 Construction of rational surface patches bounded by lines of curvature. Zbl 1210.65034 Biard, Luc; Farouki, Rida T.; Szafran, Nicolas 5 2010 Singular cases of planar and spatial \(C^1\) Hermite interpolation problems based on quintic Pythagorean-hodograph curves. Zbl 1450.65006 Farouki, Rida T.; Hormann, Kai; Nudo, Federico 5 2020 Algorithm 952: PHquintic: a library of basic functions for the construction and analysis of planar quintic Pythagorean-hodograph curves. Zbl 1347.65045 Dong, Bohan; Farouki, Rida T. 4 2015 Bipolar and multipolar coordinates. Zbl 0967.65026 Farouki, Rida T.; Moon, Hwan Pyo 4 2000 Inverse kinematics for optimal tool orientation control in 5-axis CNC machining. Zbl 1302.65048 Farouki, Rida T.; Han, Chang Yong; Li, Shiqiao 4 2014 Algebraically rectifiable parametric curves. Zbl 0808.65010 Sakkalis, Takis; Farouki, Rida T. 4 1993 Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints. Zbl 1528.65015 Farouki, Rida T.; Pelosi, Francesca; Sampoli, Maria Lucia 1 2023 The Cartesian ovals. Zbl 1519.14030 Farouki, Rida T. 1 2022 Approximation of monotone clothoid segments by degree 7 Pythagorean-hodograph curves. Zbl 1484.65035 Farouki, Rida T.; Pelosi, Francesca; Sampoli, Maria Lucia 6 2021 Spatial \(C^2\) closed-loops of prescribed arc length defined by Pythagorean-hodograph curves. Zbl 1462.51016 Farouki, Rida T.; Knez, Marjeta; Vitrih, Vito; Žagar, Emil 2 2021 Planar projections of spatial Pythagorean-hodograph curves. Zbl 1480.65044 Farouki, Rida T.; Knez, Marjeta; Vitrih, Vito; Žagar, Emil 2 2021 Singular cases of planar and spatial \(C^1\) Hermite interpolation problems based on quintic Pythagorean-hodograph curves. Zbl 1450.65006 Farouki, Rida T.; Hormann, Kai; Nudo, Federico 5 2020 Mapping rational rotation-minimizing frames from polynomial curves on to rational curves. Zbl 1505.65056 Farouki, Rida T.; Šír, Zbyněk 3 2020 Construction of periodic adapted orthonormal frames on closed space curves. Zbl 1453.65036 Farouki, Rida T.; Kim, Soo Hyun; Moon, Hwan Pyo 2 2020 Existence of Pythagorean-hodograph quintic interpolants to spatial \(G^1\) Hermite data with prescribed arc lengths. Zbl 1432.65024 Farouki, Rida T. 17 2019 New developments in theory, algorithms, and applications for Pythagorean-hodograph curves. Zbl 07150019 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 17 2019 Rational minimal-twist motions on curves with rotation-minimizing Euler-Rodrigues frames. Zbl 1410.53002 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 3 2019 Construction of rational curves with rational arc lengths by direct integration. Zbl 1505.65055 Farouki, Rida T.; Sakkalis, Takis 3 2019 Space curves defined by curvature-torsion relations and associated helices. Zbl 1499.53036 Deshmukh, Sharief; Alghanemi, Azeb; Farouki, Rida T. 3 2019 Rational frames of minimal twist along space curves under specified boundary conditions. Zbl 1419.14046 Farouki, Rida T.; Moon, Hwan Pyo 7 2018 \(C^{1}\) and \(C^{2}\) interpolation of orientation data along spatial Pythagorean-hodograph curves using rational adapted spline frames. Zbl 1505.65083 Moon, Hwan Pyo; Farouki, Rida T. 3 2018 A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames. Zbl 1390.53005 Farouki, Rida T.; Gentili, Graziano; Giannelli, Carlotta; Sestini, Alessandra; Stoppato, Caterina 6 2017 Construction of \(G^1\) planar Hermite interpolants with prescribed arc lengths. Zbl 1418.65021 Farouki, Rida T. 26 2016 Rational rotation-minimizing frames – recent advances and open problems. Zbl 1410.53001 Farouki, Rida T. 13 2016 Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form. Zbl 1334.65034 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 7 2016 Tensor-product surface patches with Pythagorean-hodograph isoparametric curves. Zbl 1433.65021 Farouki, Rida T.; Pelosi, Francesca; Sampoli, Maria Lucia; Sestini, Alessandra 4 2016 Solution of a quadratic quaternion equation with mixed coefficients. Zbl 1329.15039 Farouki, Rida T.; Gentili, Graziano; Giannelli, Carlotta; Sestini, Alessandra; Stoppato, Caterina 2 2016 Geometry of the ringed surfaces in \(\mathbb{R}^4\) that generate spatial Pythagorean hodographs. Zbl 1326.53013 Farouki, Rida T.; Gutierrez, Robert 1 2016 Identification and “reverse engineering” of Pythagorean-hodograph curves. Zbl 1375.65022 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 12 2015 Shape-preserving interpolation of spatial data by Pythagorean-hodograph quintic spline curves. Zbl 1312.65013 Farouki, Rida T.; Manni, Carla; Sampoli, Maria Lucia; Sestini, Alessandra 7 2015 Algorithm 952: PHquintic: a library of basic functions for the construction and analysis of planar quintic Pythagorean-hodograph curves. Zbl 1347.65045 Dong, Bohan; Farouki, Rida T. 4 2015 Rational swept surface constructions based on differential and integral sweep curve properties. Zbl 1375.65023 Farouki, Rida T.; Nittler, Kevin M. 1 2015 Arc lengths of rational Pythagorean-hodograph curves. Zbl 1375.65021 Farouki, Rida T. 1 2015 Construction of \(G^2\) rounded corners with Pythagorean-hodograph curves. Zbl 1293.65027 Farouki, Rida T. 9 2014 Rotation-minimizing osculating frames. Zbl 1284.65031 Farouki, Rida T.; Giannelli, Carlotta; Sampoli, Maria Lucia; Sestini, Alessandra 8 2014 Inverse kinematics for optimal tool orientation control in 5-axis CNC machining. Zbl 1302.65048 Farouki, Rida T.; Han, Chang Yong; Li, Shiqiao 4 2014 Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants. Zbl 1286.65021 Farouki, Rida T.; Han, Chang Yong; Dospra, Petroula; Sakkalis, Takis 15 2013 Optimal tool orientation control for 5-axis CNC milling with ball-end cutters. Zbl 1261.65018 Farouki, Rida T.; Li, Shiqiao 8 2013 Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves. Zbl 1284.65062 Farouki, Rida T.; Dospra, Petroula; Sakkalis, Takis 4 2013 An interpolation scheme for designing rational rotation-minimizing camera motions. Zbl 1315.65011 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 3 2013 Corrigendum to “Rational rotation-minimizing frames on polynomial space curves of arbitrary degree”. Zbl 1283.53010 Farouki, Rida T.; Sakkalis, Takis 2 2013 The Bernstein polynomial basis: a centennial retrospective. Zbl 1252.65039 Farouki, Rida T. 112 2012 Design of rational rotation-minimizing rigid body motions by Hermite interpolation. Zbl 1241.65026 Farouki, Rida T.; Giannelli, Carlotta; Manni, Carla; Sestini, Alessandra 29 2012 A complete classification of quintic space curves with rational rotation-minimizing frames. Zbl 1232.53004 Farouki, Rida T.; Sakkalis, Takis 19 2012 Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3. Zbl 1244.14023 Sakkalis, Takis; Farouki, Rida T. 9 2012 Design of \(C ^{2}\) spatial Pythagorean-hodograph quintic spline curves by control polygons. Zbl 1354.65029 Farouki, Rida T.; Manni, Carla; Pelosi, Francesca; Sampoli, Maria Lucia 6 2012 Rational Pythagorean-hodograph space curves. Zbl 1210.65037 Farouki, Rida T.; Šír, Zbyněk 19 2011 Equivalence of distinct characterizations for rational rotation-minimizing frames on quintic space curves. Zbl 1252.65040 Farouki, Rida T.; Sakkalis, Takis 3 2011 Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves. Zbl 1202.53004 Farouki, Rida T. 27 2010 Rational rotation-minimizing frames on polynomial space curves of arbitrary degree. Zbl 1204.53009 Farouki, Rida T.; Sakkalis, Takis 25 2010 Geometric design using space curves with rational rotation-minimizing frames. Zbl 1274.65037 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 5 2010 Construction and smoothing of triangular Coons patches with geodesic boundary curves. Zbl 1209.65021 Farouki, R. T.; Szafran, N.; Biard, L. 5 2010 Construction of rational surface patches bounded by lines of curvature. Zbl 1210.65034 Biard, Luc; Farouki, Rida T.; Szafran, Nicolas 5 2010 Quintic space curves with rational rotation-minimizing frames. Zbl 1205.65079 Farouki, Rida T.; Giannelli, Carlotta; Manni, Carla; Sestini, Alessandra 22 2009 Helical polynomial curves and double Pythagorean hodographs. I: Quaternion and Hopf map representations. Zbl 1187.53005 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 22 2009 Existence conditions for coons patches interpolating geodesic boundary curves. Zbl 1205.65078 Farouki, R. T.; Szafran, N.; Biard, L. 18 2009 Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves. Zbl 1168.53001 Farouki, Rida T.; Giannelli, Carlotta; Sestini, Alessandra 15 2009 Non-existence of rational arc length parameterizations for curves in \(\mathbb R^n\). Zbl 1166.53002 Sakkalis, Takis; Farouki, Rida T.; Vaserstein, Leonid 4 2009 Pythagorean-hodograph curves. Algebra and geometry inseparable. Zbl 1144.51004 Farouki, Rida T. 165 2008 Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures. Zbl 1172.65307 Farouki, Rida T.; Giannelli, Carlotta; Manni, Carla; Sestini, Alessandra 46 2008 Topological criterion for selection of quintic pythagorean-hodograph Hermite interpolants. Zbl 1172.65322 Choi, Hyeong In; Farouki, Rida T.; Kwon, Song-Hwa; Moon, Hwan Pyo 21 2008 Preface: Pythagorean-hodograph curves and related topics. Zbl 1172.65300 3 2008 Computing the Minkowski value of the exponential function over a complex disk. Zbl 1166.65323 Choi, Hyeong In; Farouki, Rida T.; Han, Chang Yong; Moon, Hwan Pyo 2 2008 A control polygon scheme for design of planar \(C^2\) PH quintic spline curves. Zbl 1171.65347 Pelosi, Francesca; Sampoli, Maria Lucia; Farouki, Rida T.; Manni, Carla 18 2007 Rational space curves are not “unit speed”. Zbl 1171.65331 Farouki, Rida T.; Sakkalis, Takis 10 2007 Evaluating the boundary and covering degree of planar Minkowski sums and other geometrical convolutions. Zbl 1140.65020 Farouki, Rida T.; Hass, Joel 7 2007 Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme. Zbl 1118.65011 Hass, Joel; Farouki, Rida T.; Han, Chang Yong; Song, Xiaowen; Sederberg, Thomas W. 6 2007 Root neighborhoods, generalized lemniscates, and robust stability of dynamic systems. Zbl 1192.65018 Farouki, Rida T.; Han, Chang Yong 6 2007 A geometric product formulation for spatial pythagorean hodograph curves with applications to Hermite interpolation. Zbl 1171.65348 Perwass, Christian B. U.; Farouki, Rida T.; Noakes, Lyle 5 2007 Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics. Zbl 1065.68103 Pelosi, Francesca; Farouki, Rida T.; Manni, Carla; Sestini, Alessandra 27 2005 Solution of elementary equations in the Minkowski geometric algebra of complex sets. Zbl 1065.51002 Farouki, Rida T.; Han, Chang Yong 4 2005 Boundary evaluation algorithms for Minkowski combinations of complex sets using topological analysis of implicit curves. Zbl 1087.65011 Farouki, Rida T.; Han, Chang Yong; Hass, Joel 3 2005 Smoothing of time-optimal feedrates for Cartesian CNC machines. Zbl 1141.68626 Boyadjieff, Casey L.; Farouki, Rida T.; Timar, Sebastian D. 1 2005 Characterization and construction of helical polynomial space curves. Zbl 1059.65016 Farouki, Rida T.; Han, Chang Yong; Manni, Carla; Sestini, Alessandra 37 2004 Linear perturbation methods for topologically consistent representations of free-form surface intersections. Zbl 1069.65567 Song, Xiaowen; Sederberg, Thomas W.; Zheng, Jianmin; Farouki, Rida T.; Hass, Joel 11 2004 Computation of Minkowski values of polynomials over complex sets. Zbl 1073.12006 Farouki, Rida T.; Han, Chang Yong 4 2004 Topologically consistent trimmed surface approximations based on triangular patches. Zbl 1069.65552 Farouki, Rida T.; Han, Chang Yong; Hass, Joel; Sederberg, Thomas W. 3 2004 Robust plotting of generalized lemniscates. Zbl 1059.65020 Farouki, Rida T.; Han, Chang Yong 2 2004 Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves. Zbl 1069.65551 Farouki, Rida T.; Han, Chang Yong 31 2003 Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains. Zbl 1069.65517 Farouki, Rida T.; Goodman, T. N. T.; Sauer, Thomas 27 2003 Spatial \(C^2\) PH quintic splines. Zbl 1044.65010 Farouki, Rida T.; Manni, Carla; Sestini, Alessandra 18 2003 Shape-preserving interpolation by \(G^1\) and \(G^2\) PH quintic splines. Zbl 1022.65008 Farouki, Rida T.; Manni, Carla; Sestini, Alessandra 14 2003 Minkowski geometric algebra and the stability of characteristic polynomials. Zbl 1175.93182 Farouki, Rida T.; Moon, Hwan Pyo 5 2003 Minkowski combinations of complex sets: Geometry, algorithms, and applications. Zbl 1047.65029 Farouki, Rida T. 2 2003 Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves. Zbl 1001.41003 Farouki, Rida T.; al-Kandari, Mohammad; Sakkalis, Takis 66 2002 Exact rotation-minimizing frames for spatial Pythagorean-hodograph curves. Zbl 1055.68124 Farouki, Rida T. 24 2002 Exact Minkowski products of \(N\) complex disks. Zbl 1028.65048 Farouki, Rida T.; Pottmann, Helmut 13 2002 Special issue: Advances in geometrical algorithms and representations. Zbl 0989.00012 3 2002 Construction and shape analysis of PH quintic Hermite interpolants. Zbl 0971.68186 Moon, H. P.; Farouki, R. T.; Choi, H. I. 42 2001 Minkowski geometric algebra of complex sets. Zbl 0987.51012 Farouki, Rida T.; Pyo Moon, Hwan; Ravani, Bahram 20 2001 Efficient solution of the complex quadratic tridiagonal system for \(C^2\) PH quintic splines. Zbl 0987.65016 Farouki, Rida T.; Kuspa, Bethany K.; Manni, Carla; Sestini, Alessandra 20 2001 Performance analysis of CNC interpolators for time-dependent feedrates along PH curves. Zbl 0971.68172 Tsai, Yi-Feng; Farouki, Rida T.; Feldman, Bryan 15 2001 Algorithm 812: BPOLY: An object-oriented library of numerical algorithms for polynomials in Bernstein form. Zbl 1070.65515 Tsai, Yi-Feng; Farouki, Rida T. 12 2001 Computation of optimal composite re-parameterizations. Zbl 0984.68161 Costantini, Paolo; Farouki, Rida T.; Manni, Carla; Sestini, Alessandra 10 2001 Gauss map computation for free-form surfaces. Zbl 0984.68162 Smith, Tait S.; Farouki, Rida T. 2 2001 Real-time CNC interpolators for Bézier conics. Zbl 0983.68218 Farouki, R. T.; Manni, C.; Sestini, A. 2 2001 Legendre-Bernstein basis transformations. Zbl 0962.65042 Farouki, Rida T. 37 2000 Algorithms for Minkowski products and implicitly-defined complex sets. Zbl 0948.65016 Farouki, Rida T.; Moon, Hwan Pyo; Ravani, Bahram 12 2000 Bipolar and multipolar coordinates. Zbl 0967.65026 Farouki, Rida T.; Moon, Hwan Pyo 4 2000 Physical constraints on feedrates and feed accelerations along curved tool paths. Zbl 0938.68126 Farouki, R. T.; Tsai, Y.-F.; Wilson, C. S. 3 2000 Voronoi diagram and medial axis algorithm for planar domains with curved boundaries. I: Theoretical foundations. Zbl 0939.65018 Ramamurthy, Rajesh; Farouki, Rida T. 13 1999 Convergent inversion approximations for polynomials in Bernstein form. Zbl 0939.68126 Farouki, R. T. 10 1999 Contour machining of free-form surfaces with real-time PH curve CNC interpolators. Zbl 0908.68175 Farouki, Rida T.; Tsai, Yi-Feng; Yuan, Guo-Feng 7 1999 Voronoi diagram and medial axis algorithm for planar domains with curved boundaries. II: Detailed algorithm description. Zbl 0962.65017 Ramamurthy, Rajesh; Farouki, Rida T. 6 1999 Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves. Zbl 1049.68723 Farouki, Rida T.; Manjunathaiah, Jairam; Nicholas, David; Yuan, Guo-Feng; Jee, Sungchul 32 1998 Design of rational cam profiles with Pythagorean-hodograph curves. Zbl 1049.70536 Farouki, R. T.; Manjunathaiah, J.; Jee, S. 11 1998 ...and 38 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,014 Authors 105 Farouki, Rida T. 23 Lávička, Miroslav 23 Sestini, Alessandra 20 Han, Chang Yong 20 Šír, Zbyněk 19 Jüttler, Bert 18 Krajnc, Marjeta 18 Peña, Juan Manuel 18 Sakkalis, Takis 16 Giannelli, Carlotta 15 Sánchez-Reyes, Javier 15 Winkler, Joab R. 14 Sampoli, Maria Lucia 13 Alcazar, Juan Gerardo 13 Kwon, Song-Hwa 13 Sendra, Juan Rafael 12 Kim, Gwang Il 12 Manni, Carla 12 Žagar, Emil 11 Bizzarri, Michal 10 Pérez-Díaz, Sonia 10 Vitrih, Vito 10 Vršek, Jan 10 Wang, Guozhao 9 Ahn, Young Joon 9 Choi, Hyeong In 9 Rababah, Abedallah 8 Albrecht, Gudrun 8 Bastl, Bohumír 8 Corless, Robert Malcolm 8 Delgado, Jorge F. M. 8 Kim, Soohyun 8 Meek, Dereck S. 8 Pelosi, Francesca 8 Pottmann, Helmut 8 Pyo Moon, Hwan 8 Romani, Lucia 8 Walton, Desmond J. 7 Hoffmann, Christoph M. 7 Korpinar, Talat 7 Monterde, Juan 7 Sendra, Juana 7 Wang, Wenping 6 Goldman, Ronald N. 6 Kosinka, Jiří 6 Lu, Lizheng 6 Marco García, Ana 6 Martínez, José-Javier 6 Peternell, Martin 6 Scott, Michael A. 5 Ait-Haddou, Rachid 5 AlQudah, Mohammad A. 5 Biard, Luc 5 Bourne, Martin 5 Caravantes, Jorge 5 Díaz-Toca, Gema María 5 Fang, Lincong 5 Gonzalez-Vega, Laureano 5 Hass, Joel 5 Kong, Jae-Hoon 5 Kozak, Jernej 5 Lee, Sunhong 5 Lu, Wei 5 Luo, Zhongxuan 5 Noldeke, Georg 5 Peña, Jorge 5 Schröcker, Hans-Peter 5 Sederberg, Thomas W. 5 Shen, Liyong 4 Beccari, Carolina Vittoria 4 Cattiaux-Huillard, Isabelle 4 Dospra, Petroula 4 Elber, Gershon 4 Garloff, Jürgen 4 Hothorn, Torsten 4 Hu, Wenyu 4 Khan, Asif 4 Kirby, Robert C. 4 Lee, Hyun Chol 4 Neff, C. Andrew 4 Paluszny, Marco 4 Patrikalakis, Nicholas M. 4 Ramamurthy, Rajesh 4 Saini, Laura 4 Simsek, Yilmaz 4 Su, Yi 4 Thomas, Derek C. 4 Titi, Jihad 4 Viaña, Raquel 4 Woźny, Paweł 4 Zhu, Chungang 4 Zidna, Ahmed 3 Ainsworth, Mark 3 Aldaz, Jésus Munárriz 3 Allen, Larry 3 AlMheidat, Maalee N. 3 Bajaj, Chandrajit L. 3 Băleanu, Dumitru I. 3 Barrio, Roberto 3 Baş, Selçuk ...and 914 more Authors all top 5 Cited in 184 Serials 244 Computer Aided Geometric Design 85 Journal of Computational and Applied Mathematics 35 Applied Mathematics and Computation 33 Journal of Symbolic Computation 28 Advances in Computational Mathematics 15 Computer Methods in Applied Mechanics and Engineering 15 Numerical Algorithms 12 Mathematics of Computation 10 Mathematics and Computers in Simulation 9 Linear Algebra and its Applications 8 Theoretical Computer Science 8 Applied Mathematical Modelling 7 Applied Numerical Mathematics 7 International Journal of Computational Geometry & Applications 7 Computational Geometry 7 Computational and Applied Mathematics 6 Boletim da Sociedade Paranaense de Matemática. Terceira Série 6 Advances in Difference Equations 5 Mathematical Methods in the Applied Sciences 5 Journal of Approximation Theory 5 Journal of Pure and Applied Algebra 5 Numerische Mathematik 5 International Journal of Production Research 5 SIAM Journal on Scientific Computing 5 Applied Mathematics. Series B (English Edition) 5 Journal of Inequalities and Applications 5 Journal of Applied Mathematics 5 Mediterranean Journal of Mathematics 5 Mathematics in Computer Science 5 Journal of Theoretical Biology 4 Computers & Mathematics with Applications 4 Journal of Computational Physics 4 Journal of Mathematical Analysis and Applications 4 Journal of Mathematical Physics 4 Applied Mathematics Letters 4 SIAM Journal on Matrix Analysis and Applications 4 International Journal of Computer Mathematics 4 Turkish Journal of Mathematics 4 Journal of Systems Science and Complexity 4 International Journal of Geometric Methods in Modern Physics 3 International Journal for Numerical Methods in Engineering 3 Journal of Geometry 3 Journal of the Korean Mathematical Society 3 International Journal of Algebra and Computation 3 Journal of Global Optimization 3 Annals of Mathematics and Artificial Intelligence 3 International Journal of Shape Modeling 3 Abstract and Applied Analysis 3 Boundary Value Problems 3 Journal of Zhejiang University. Science A 3 Communications in Mathematics and Statistics 3 AIMS Mathematics 2 Discrete Applied Mathematics 2 International Journal of Systems Science 2 Scandinavian Journal of Statistics 2 Journal of Geometry and Physics 2 The Mathematical Intelligencer 2 ACM Transactions on Mathematical Software 2 BIT 2 Computing 2 Numerical Functional Analysis and Optimization 2 Results in Mathematics 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 ACM Transactions on Graphics 2 Constructive Approximation 2 Facta Universitatis. Series Mathematics and Informatics 2 Mathematical and Computer Modelling 2 Journal of Scientific Computing 2 International Journal of Mathematics 2 Computational Statistics and Data Analysis 2 Applicable Algebra in Engineering, Communication and Computing 2 Formal Methods in System Design 2 Advances in Applied Clifford Algebras 2 Engineering Analysis with Boundary Elements 2 Reliable Computing 2 ELA. The Electronic Journal of Linear Algebra 2 Mathematical Problems in Engineering 2 Differential Equations and Dynamical Systems 2 La Gaceta de la Real Sociedad Matemática Española 2 Journal of Applied Mathematics and Computing 2 Annales Universitatis Mariae Curie-Skłodowska. Sectio A1. Informatica 2 International Electronic Journal of Geometry 2 Asian-European Journal of Mathematics 2 Symmetry 2 Journal of Mathematical Research with Applications 2 International Journal of Applied and Computational Mathematics 1 Acta Mechanica 1 Bulletin of the Australian Mathematical Society 1 International Journal of Mathematical Education in Science and Technology 1 Information Processing Letters 1 Journal of the Franklin Institute 1 Linear and Multilinear Algebra 1 Periodica Mathematica Hungarica 1 Physica A 1 Ukrainian Mathematical Journal 1 Automatica 1 Demonstratio Mathematica 1 Fuzzy Sets and Systems 1 Geometriae Dedicata 1 Hokkaido Mathematical Journal ...and 84 more Serials all top 5 Cited in 49 Fields 596 Numerical analysis (65-XX) 182 Computer science (68-XX) 123 Approximations and expansions (41-XX) 113 Differential geometry (53-XX) 84 Algebraic geometry (14-XX) 30 Linear and multilinear algebra; matrix theory (15-XX) 28 Special functions (33-XX) 28 Geometry (51-XX) 28 Operations research, mathematical programming (90-XX) 25 Real functions (26-XX) 22 Partial differential equations (35-XX) 21 Field theory and polynomials (12-XX) 17 Number theory (11-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 16 Statistics (62-XX) 15 Commutative algebra (13-XX) 15 Mechanics of deformable solids (74-XX) 14 Ordinary differential equations (34-XX) 13 Systems theory; control (93-XX) 11 Mechanics of particles and systems (70-XX) 10 Combinatorics (05-XX) 10 Functions of a complex variable (30-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 Biology and other natural sciences (92-XX) 8 Convex and discrete geometry (52-XX) 8 Fluid mechanics (76-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Integral equations (45-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Operator theory (47-XX) 5 Information and communication theory, circuits (94-XX) 4 General and overarching topics; collections (00-XX) 4 Integral transforms, operational calculus (44-XX) 4 Functional analysis (46-XX) 4 Optics, electromagnetic theory (78-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Associative rings and algebras (16-XX) 3 Topological groups, Lie groups (22-XX) 3 Probability theory and stochastic processes (60-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 2 Quantum theory (81-XX) 1 General algebraic systems (08-XX) 1 Category theory; homological algebra (18-XX) 1 Difference and functional equations (39-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX) Citations by Year