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2020 – today
- 2024
[i1]Rida T. Farouki, Marjeta Knez, Vito Vitrih, Emil Zagar:
Application of a metric for complex polynomials to bounded modification of planar Pythagorean-hodograph curves. CoRR abs/2402.09850 (2024)- 2023
- [j129]Rida T. Farouki, Francesca Pelosi, Maria Lucia Sampoli:
Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints. Comput. Aided Geom. Des. 103: 102192 (2023) - [j128]Rida T. Farouki:
Partition of the space of planar quintic Pythagorean-hodograph curves. Comput. Aided Geom. Des. 106: 102242 (2023) - 2022
- [j127]Rida T. Farouki, Marjeta Knez
, Vito Vitrih, Emil Zagar:
On the construction of polynomial minimal surfaces with Pythagorean normals. Appl. Math. Comput. 435: 127439 (2022) - [j126]Rida T. Farouki:
Identifying Pythagorean-Hodograph Curves Closest to Prescribed Planar Bézier Curves. Comput. Aided Des. 149: 103266 (2022) - 2021
- [j125]Rida T. Farouki, Marjeta Knez, Vito Vitrih, Emil Zagar:
Spatial C2 closed loops of prescribed arc length defined by Pythagorean-hodograph curves. Appl. Math. Comput. 391: 125653 (2021) - [j124]Rida T. Farouki:
Accurate Real-time CNC Curve Interpolators Based Upon Richardson Extrapolation. Comput. Aided Des. 135: 103005 (2021) - [j123]Rida T. Farouki, Marjeta Knez, Vito Vitrih, Emil Zagar:
Planar projections of spatial Pythagorean-hodograph curves. Comput. Aided Geom. Des. 91: 102049 (2021) - [j122]Rida T. Farouki, Jack R. Swett, Rachel Ward Rohlen, David B. Smith:
Real-time needle guidance for venipuncture based on optical coherence tomography. Comput. methods Biomech. Biomed. Eng. Imaging Vis. 9(6): 643-650 (2021) - [j121]Rida T. Farouki, Francesca Pelosi, Maria Lucia Sampoli:
Approximation of monotone clothoid segments by degree 7 Pythagorean-hodograph curves. J. Comput. Appl. Math. 382: 113110 (2021) - 2020
- [j120]Rida T. Farouki, Soo Hyun Kim, Hwan Pyo Moon:
Construction of periodic adapted orthonormal frames on closed space curves. Comput. Aided Geom. Des. 76: 101802 (2020) - [j119]Rida T. Farouki, Zbynek Sír:
Mapping rational rotation-minimizing frames from polynomial curves on to rational curves. Comput. Aided Geom. Des. 78: 101833 (2020) - [j118]Rida T. Farouki, Kai Hormann, Federico Nudo:
Singular cases of planar and spatial C1 Hermite interpolation problems based on quintic Pythagorean-hodograph curves. Comput. Aided Geom. Des. 82: 101930 (2020) - [j117]Rida T. Farouki, Jeffrey A. Strom:
Computing the roots of sparse high-degree polynomials that arise from the study of random simplicial complexes. Numer. Algorithms 83(4): 1653-1670 (2020) - [c11]Destiny R. Garcia, Barbara Linke, Rida T. Farouki:
Optimized Routine of Machining Distortion Characterization Based on Gaussian Surface Curvature. iPMVM 2020: 5:1-5:17
2010 – 2019
- 2019
- [j116]Rida T. Farouki, Graziano Gentili, Hwan Pyo Moon, Caterina Stoppato:
Minkowski products of unit quaternion sets. Adv. Comput. Math. 45(3): 1607-1629 (2019) - [j115]Rida T. Farouki, Francesca Pelosi, Maria Lucia Sampoli:
Optimization of Corner Blending Curves. Comput. Aided Des. 117 (2019) - [j114]Rida T. Farouki, Takis Sakkalis:
Construction of rational curves with rational arc lengths by direct integration. Comput. Aided Geom. Des. 74 (2019) - [j113]Rida T. Farouki, Carlotta Giannelli, Alessandra Sestini:
Rational minimal-twist motions on curves with rotation-minimizing Euler-Rodrigues frames. J. Comput. Appl. Math. 352: 240-254 (2019) - [j112]Rida T. Farouki:
Existence of Pythagorean-hodograph quintic interpolants to spatial G1 Hermite data with prescribed arc lengths. J. Symb. Comput. 95: 202-216 (2019) - 2018
- [j111]Rida T. Farouki, Hwan Pyo Moon:
Rational frames of minimal twist along space curves under specified boundary conditions. Adv. Comput. Math. 44(5): 1627-1650 (2018) - [j110]Rida T. Farouki:
Reduced difference polynomials and self-intersection computations. Appl. Math. Comput. 324: 174-190 (2018) - [j109]Hwan Pyo Moon, Rida T. Farouki:
C1 and C2 interpolation of orientation data along spatial Pythagorean-hodograph curves using rational adapted spline frames. Comput. Aided Geom. Des. 66: 1-15 (2018) - 2017
- [j108]Rida T. Farouki, Graziano Gentili, Carlotta Giannelli, Alessandra Sestini, Caterina Stoppato:
A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames. Adv. Comput. Math. 43(1): 1-24 (2017) - [j107]Rida T. Farouki, Jyothirmai Srinathu:
A real-time CNC interpolator algorithm for trimming and filling planar offset curves. Comput. Aided Des. 86: 1-11 (2017) - [j106]Rida T. Farouki:
Helical polynomial curves interpolating G1 data with prescribed axes and pitch angles. Comput. Aided Geom. Des. 56: 4-15 (2017) - 2016
- [j105]Rida T. Farouki, Carlotta Giannelli, Alessandra Sestini:
Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form. Adv. Comput. Math. 42(1): 199-225 (2016) - [j104]Rida T. Farouki:
Rational rotation-minimizing frames - Recent advances and open problems. Appl. Math. Comput. 272: 80-91 (2016) - [j103]Rida T. Farouki:
Construction of G1 planar Hermite interpolants with prescribed arc lengths. Comput. Aided Geom. Des. 46: 64-75 (2016) - [j102]Rida T. Farouki, Robert Gutierrez:
Geometry of the ringed surfaces in R4 that generate spatial Pythagorean hodographs. J. Symb. Comput. 73: 87-103 (2016) - [j101]Rida T. Farouki, Graziano Gentili, Carlotta Giannelli, Alessandra Sestini, Caterina Stoppato:
Solution of a quadratic quaternion equation with mixed coefficients. J. Symb. Comput. 74: 140-151 (2016) - 2015
- [j100]Rida T. Farouki, Kevin M. Nittler:
Rational swept surface constructions based on differential and integral sweep curve properties. Comput. Aided Geom. Des. 33: 1-16 (2015) - [j99]Rida T. Farouki:
Arc lengths of rational Pythagorean-hodograph curves. Comput. Aided Geom. Des. 34: 1-4 (2015) - [j98]Rida T. Farouki, Carlotta Giannelli, Alessandra Sestini:
Identification and "reverse engineering" of Pythagorean-hodograph curves. Comput. Aided Geom. Des. 34: 21-36 (2015) - [j97]Bohan Dong, Rida T. Farouki:
Algorithm 952: PHquintic: A Library of Basic Functions for the Construction and Analysis of Planar Quintic Pythagorean-Hodograph Curves. ACM Trans. Math. Softw. 41(4): 28:1-28:20 (2015) - 2014
- [j96]Rida T. Farouki, Chang Yong Han, Shiqiao Li:
Inverse kinematics for optimal tool orientation control in 5-axis CNC machining. Comput. Aided Geom. Des. 31(1): 13-26 (2014) - [j95]Rida T. Farouki, Carlotta Giannelli, Maria Lucia Sampoli, Alessandra Sestini:
Rotation-minimizing osculating frames. Comput. Aided Geom. Des. 31(1): 27-42 (2014) - [j94]Rida T. Farouki:
Construction of G2 rounded corners with Pythagorean-hodograph curves. Comput. Aided Geom. Des. 31(2): 127-139 (2014) - [j93]Mathieu Huard, Rida T. Farouki, Nathalie Sprynski, Luc Biard:
C2 interpolation of spatial data subject to arc-length constraints using Pythagorean-hodograph quintic splines. Graph. Model. 76(1): 30-42 (2014) - 2013
- [j92]Rida T. Farouki, Carlotta Giannelli, Alessandra Sestini:
An interpolation scheme for designing rational rotation-minimizing camera motions. Adv. Comput. Math. 38(1): 63-82 (2013) - [j91]Rida T. Farouki, Shiqiao Li:
Optimal tool orientation control for 5-axis CNC milling with ball-end cutters. Comput. Aided Geom. Des. 30(2): 226-239 (2013) - [j90]Rida T. Farouki, Chang Yong Han, Petroula Dospra, Takis Sakkalis:
Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants. Comput. Aided Geom. Des. 30(7): 653-671 (2013) - [j89]Rida T. Farouki, Petroula Dospra, Takis Sakkalis:
Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves. J. Symb. Comput. 58: 1-17 (2013) - [j88]Rida T. Farouki, Takis Sakkalis:
Corrigendum to "Rational rotation-minimizing frames on polynomial space curves of arbitrary degree" [J. Symbolic Comput. 45(8) (2010) 844-856]. J. Symb. Comput. 58: 99-102 (2013) - 2012
- [j87]Rida T. Farouki:
The Bernstein polynomial basis: A centennial retrospective. Comput. Aided Geom. Des. 29(6): 379-419 (2012) - [j86]Takis Sakkalis, Rida T. Farouki:
Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3. J. Comput. Appl. Math. 236(17): 4375-4382 (2012) - [j85]Rida T. Farouki, Takis Sakkalis:
A complete classification of quintic space curves with rational rotation-minimizing frames. J. Symb. Comput. 47(2): 214-226 (2012) - [j84]Hongbo Li, Rida T. Farouki, Dingkang Wang:
Foreword to the Special Focus on Mathematics and Algorithms for CAM and CNC. Math. Comput. Sci. 6(3): 267-268 (2012) - [j83]Rida T. Farouki, Carlotta Giannelli, Carla Manni, Alessandra Sestini:
Design of rational rotation-minimizing rigid body motions by Hermite interpolation. Math. Comput. 81(278): 879-903 (2012) - 2011
- [j82]Rida T. Farouki, Zbynek Sír:
Rational Pythagorean-hodograph space curves. Comput. Aided Geom. Des. 28(2): 75-88 (2011) - [j81]Rida T. Farouki, Takis Sakkalis:
Equivalence of distinct characterizations for rational rotation-minimizing frames on quintic space curves. Comput. Aided Geom. Des. 28(7): 436-445 (2011) - 2010
- [j80]Rida T. Farouki:
Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves. Adv. Comput. Math. 33(3): 331-348 (2010) - [j79]Rida T. Farouki, Nicolas Szafran, Luc Biard:
Construction and smoothing of triangular Coons patches with geodesic boundary curves. Comput. Aided Geom. Des. 27(4): 301-312 (2010) - [j78]Luc Biard, Rida T. Farouki, Nicolas Szafran:
Construction of rational surface patches bounded by lines of curvature. Comput. Aided Geom. Des. 27(5): 359-371 (2010) - [j77]Rida T. Farouki, Takis Sakkalis:
Rational rotation-minimizing frames on polynomial space curves of arbitrary degree. J. Symb. Comput. 45(8): 844-856 (2010) - [c10]Rida T. Farouki, Carla Manni, Francesca Pelosi, Maria Lucia Sampoli:
Design of C 2 Spatial Pythagorean-Hodograph Quintic Spline Curves by Control Polygons. Curves and Surfaces 2010: 253-269
2000 – 2009
- 2009
- [j76]Rida T. Farouki, Nicolas Szafran, Luc Biard:
Construction of Bézier surface patches with Bézier curves as geodesic boundaries. Comput. Aided Des. 41(11): 772-781 (2009) - [j75]Rida T. Farouki, Carlotta Giannelli, Carla Manni, Alessandra Sestini:
Quintic space curves with rational rotation-minimizing frames. Comput. Aided Geom. Des. 26(5): 580-592 (2009) - [j74]Rida T. Farouki, Nicolas Szafran, Luc Biard:
Existence conditions for Coons patches interpolating geodesic boundary curves. Comput. Aided Geom. Des. 26(5): 599-614 (2009) - [j73]Rida T. Farouki, Carlotta Giannelli, Alessandra Sestini:
Helical polynomial curves and double Pythagorean hodographs I. Quaternion and Hopf map representations. J. Symb. Comput. 44(2): 161-179 (2009) - [j72]Rida T. Farouki, Carlotta Giannelli, Alessandra Sestini:
Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves. J. Symb. Comput. 44(4): 307-332 (2009) - [j71]Rida T. Farouki, Carlotta Giannelli:
Spatial camera orientation control by rotation-minimizing directed frames. Comput. Animat. Virtual Worlds 20(4): 457-472 (2009) - 2008
- [b1]Rida T. Farouki:
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable. Geometry and Computing 1, Springer 2008, ISBN 978-3-540-73397-3, pp. 1-729 - [j70]Rida T. Farouki, Bert Jüttler, Carla Manni:
Pythagorean-hodograph curves and related topics. Comput. Aided Geom. Des. 25(4-5): 203-204 (2008) - [j69]Rida T. Farouki, Carlotta Giannelli, Carla Manni, Alessandra Sestini:
Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures. Comput. Aided Geom. Des. 25(4-5): 274-297 (2008) - [j68]Hyeong In Choi, Rida T. Farouki, Song-Hwa Kwon, Hwan Pyo Moon:
Topological criterion for selection of quintic Pythagorean-hodograph Hermite interpolants. Comput. Aided Geom. Des. 25(6): 411-433 (2008) - [c9]Rida T. Farouki, Carlotta Giannelli, Alessandra Sestini:
Geometric Design Using Space Curves with Rational Rotation-Minimizing Frames. MMCS 2008: 194-208 - 2007
- [j67]Rida T. Farouki, Chang Yong Han:
Root neighborhoods, generalized lemniscates, and robust stability of dynamic systems. Appl. Algebra Eng. Commun. Comput. 18(1-2): 169-189 (2007) - [j66]Joel Hass, Rida T. Farouki, Chang Yong Han, Xiaowen Song, Thomas W. Sederberg:
Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme. Adv. Comput. Math. 27(1): 1-26 (2007) - [j65]Francesca Pelosi, Maria Lucia Sampoli, Rida T. Farouki, Carla Manni:
A control polygon scheme for design of planar C2 PH quintic spline curves. Comput. Aided Geom. Des. 24(1): 28-52 (2007) - [j64]Christian Perwass, Rida T. Farouki, Lyle Noakes:
A geometric product formulation for spatial Pythagorean hodograph curves with applications to Hermite interpolation. Comput. Aided Geom. Des. 24(4): 220-237 (2007) - [j63]Rida T. Farouki, Takis Sakkalis:
Rational space curves are not "unit speed". Comput. Aided Geom. Des. 24(4): 238-240 (2007) - [j62]Sebastian D. Timar, Rida T. Farouki, Casey L. Boyadjieff:
Time-Optimal feedrates along Curved Paths for Cartesian CNC Machines with prescribed Bounds on Axis velocities and Accelerations. Int. J. Robotics Autom. 22(2) (2007) - [c8]Hyeong In Choi, Rida T. Farouki, Chang Yong Han, Hwan Pyo Moon:
Computing the Minkowski Value of the Exponential Function over a Complex Disk. ASCM 2007: 1-21 - 2005
- [j61]Rida T. Farouki, Chang Yong Han:
Solution of elementary equations in the Minkowski geometric algebra of complex sets. Adv. Comput. Math. 22(4): 301-323 (2005) - [j60]Francesca Pelosi, Rida T. Farouki, Carla Manni, Alessandra Sestini:
Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics. Adv. Comput. Math. 22(4): 325-352 (2005) - [j59]Rida T. Farouki, Chang Yong Han, Joel Hass:
Boundary evaluation algorithms for Minkowski combinations of complex sets using topological analysis of implicit curves. Numer. Algorithms 40(3): 251-283 (2005) - [c7]Casey L. Boyadjieff, Rida T. Farouki, Sebastian D. Timar:
Smoothing of Time-Optimal Feedrates for Cartesian CNC Machines. IMA Conference on the Mathematics of Surfaces 2005: 84-101 - 2004
- [j58]Xiaowen Song, Thomas W. Sederberg, Jianmin Zheng, Rida T. Farouki, Joel Hass:
Linear perturbation methods for topologically consistent representations of free-form surface intersections. Comput. Aided Geom. Des. 21: 303-319 (2004) - [j57]Xiaowen Song, Thomas W. Sederberg, Jianmin Zheng, Rida T. Farouki, Joel Hass:
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. 21: 321 (2004) - [j56]Rida T. Farouki, Chang Yong Han, Joel Hass, Thomas W. Sederberg:
Topologically consistent trimmed surface approximations based on triangular patches. Comput. Aided Geom. Des. 21: 459-478 (2004) - [j55]Rida T. Farouki, Chang Yong Han:
Computation of Minkowski Values of Polynomials over Complex Sets. Numer. Algorithms 36(1): 13-29 (2004) - 2003
- [j54]Rida T. Farouki, Tim N. T. Goodman, Tomas Sauer:
Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains. Comput. Aided Geom. Des. 20(4): 209-230 (2003) - [j53]Rida T. Farouki, Chang Yong Han:
Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves. Comput. Aided Geom. Des. 20(7): 435-454 (2003) - 2002
- [j52]Rida T. Farouki, Mohammad al-Kandari, Takis Sakkalis:
Hermite Interpolation by Rotation-Invariant Spatial Pythagorean-Hodograph Curves. Adv. Comput. Math. 17(4): 369-383 (2002) - [j51]Tait S. Smith, Rida T. Farouki, Mohammad al-Kandari, Helmut Pottmann:
Optimal slicing of free-form surfaces. Comput. Aided Geom. Des. 19(1): 43-64 (2002) - [j50]Rida T. Farouki, Mohammad al-Kandari, Takis Sakkalis:
Structural invariance of spatial Pythagorean hodographs. Comput. Aided Geom. Des. 19(6): 395-407 (2002) - [j49]Rida T. Farouki:
Exact rotation-minimizing frames for spatial Pythagorean-hodograph curves. Graph. Model. 64(6): 382-395 (2002) - [j48]Rida T. Farouki, Helmut Pottmann:
Exact Minkowski Products of N Complex Disks. Reliab. Comput. 8(1): 43-66 (2002) - [c6]Rida T. Farouki, Hwan Pyo Moon:
Minkowski Geometric Algebra and the Stability of Characteristic Polynomials. VisMath 2002: 163-188 - [p2]Rida T. Farouki:
Pythagorean-Hodograph Curves. Handbook of Computer Aided Geometric Design 2002: 405-427 - 2001
- [j47]Rida T. Farouki, Yi-Feng Tsai:
Exact Taylor series coefficients for variable-feedrate CNC curve interpolators. Comput. Aided Des. 33(2): 155-165 (2001) - [j46]Hwan Pyo Moon, Rida T. Farouki, Hyeong In Choi:
Construction and shape analysis of PH quintic Hermite interpolants. Comput. Aided Geom. Des. 18(2): 93-115 (2001) - [j45]Yi-Feng Tsai, Rida T. Farouki, Bryan Feldman:
Performance analysis of CNC interpolators for time-dependent feedrates along PH curves. Comput. Aided Geom. Des. 18(3): 245-265 (2001) - [j44]Rida T. Farouki, Carla Manni, Alessandra Sestini:
Real-time CNC interpolators for Bézier conics. Comput. Aided Geom. Des. 18(7): 639-655 (2001) - [j43]Tait S. Smith, Rida T. Farouki:
Gauss map computation for free-form surfaces. Comput. Aided Geom. Des. 18(9): 831-850 (2001) - [j42]Paolo Costantini, Rida T. Farouki, Carla Manni, Alessandra Sestini:
Computation of optimal composite re-parameterizations. Comput. Aided Geom. Des. 18(9): 875-897 (2001) - [j41]Rida T. Farouki, Bethany K. Kuspa, Carla Manni, Alessandra Sestini:
Efficient Solution of the Complex Quadratic Tridiagonal System for C2 PH Quintic Splines. Numer. Algorithms 27(1): 35-60 (2001) - [j40]Yi-Feng Tsai, Rida T. Farouki:
Algorithm 812: BPOLY: An object-oriented library of numerical algorithms for polynomials in Bernstein form. ACM Trans. Math. Softw. 27(2): 267-296 (2001) - 2000
- [j39]Rida T. Farouki, Hwan Pyo Moon, Bahram Ravani:
Algorithms for Minkowski products and implicitly-defined complex sets. Adv. Comput. Math. 13(3): 199-229 (2000) - [j38]Rida T. Farouki, Yi-Feng Tsai, Curtis S. Wilson:
Physical constraints on feedrates, feed accelerations along curved tool paths. Comput. Aided Geom. Des. 17(4): 337-359 (2000) - [c5]Rida T. Farouki, Weiqing Gu, Hwan Pyo Moon:
Minkowski Roots of Complex Sets. GMP 2000: 287-300 - [c4]Rida T. Farouki, Hwan Pyo Moon:
Bipolar and Multipolar Coordinates. IMA Conference on the Mathematics of Surfaces 2000: 348-371
1990 – 1999
- 1999
- [j37]Rida T. Farouki, Yi-Feng Tsai, Guo-Feng Yuan:
Contour machining of free-form surfaces with real-time PH curve CNC interpolators. Comput. Aided Geom. Des. 16(1): 61-76 (1999) - [j36]Rida T. Farouki:
Convergent inversion approximations for polynomials in Bernstein form. Comput. Aided Geom. Des. 17(2): 179-196 (1999) - 1998
- [j35]Rida T. Farouki, Jairam Manjunathaiah, David Nicholas, Guo-Feng Yuan, Sungchul Jee:
Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves. Comput. Aided Des. 30(8): 631-640 (1998) - [j34]Rida T. Farouki:
On integrating lines of curvature. Comput. Aided Geom. Des. 15(2): 187-192 (1998) - [j33]Rida T. Farouki, Rajesh Ramamurthy:
Degenerate point/curve and curve/curve bisectors arising in medial axis computations for planar domains with curved boundaries. Comput. Aided Geom. Des. 15(6): 615-635 (1998) - [j32]Rida T. Farouki, Rajesh Ramamurthy:
Specified-Precision Computation of Curve/Curve Bisectors. Int. J. Comput. Geom. Appl. 8(5/6): 599-619 (1998) - 1997
- [j31]Rida T. Farouki:
Pythagorean-hodograph quintic transition curves of monotone curvature. Comput. Aided Des. 29(9): 601-606 (1997) - [j30]Rida T. Farouki:
Optimal parameterizations. Comput. Aided Geom. Des. 14(2): 153-168 (1997) - [j29]Rida T. Farouki:
Conic Approximation of Conic Offsets. J. Symb. Comput. 23(2/3): 301-313 (1997) - 1996
- [j28]Gudrun Albrecht, Rida T. Farouki:
Construction ofC2 Pythagorean-hodograph interpolating splines by the homotopy method. Adv. Comput. Math. 5(1): 417-442 (1996) - [j27]Rida T. Farouki, Ragnar Sverrisson:
Approximation of rolling-ball blends for free-form parametric surfaces. Comput. Aided Des. 28(11): 871-878 (1996) - [j26]Rida T. Farouki:
The elastic bending energy of Pythagorean-hodograph curves. Comput. Aided Geom. Des. 13(3): 227-241 (1996) - [j25]