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Fields of interest:
- Numerical analysis
- CAGD
- Curves and surface approximation
- Geometric interpolation
- Splines
- PH curves, PN surfaces
- Multivariate polynomial interpolation
- Subdivision schemes
Due to marriage in August 2017 my surname Krajnc changed to Knez.
Publications:
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M. Knez, F. Pelosi, M. L. Sampoli:
Construction of G2 spatial interpolants with prescribed arc lengths
, submitted.
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R.T. Farouki, M. Knez, V. Vitrih, E. Žagar: On the construction of polynomial minimal surfaces with Pythagorean normals,
Applied mathematics and computation, 2022, art. 127439 (12 str.)
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M. Kuralt, A. Cmok Kučič, R. Gašperšič, J. Grošelj, M. Knez, A. Fidler:
Gingival shape analysis using surface curvature estimation of the intraoral scans
BMC oral health, 2022, vol. 22, str. 1-11
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J. Grošelj, M. Knez: Generalized C1 Clough-Tocher splines for CAGD and FEM,
Computer methods in applied mechanics and engineering, May 2022, vol. 395, art. 114983 (22 str.)
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M. Knez, F. Pelosi, M. L. Sampoli:
Construction of G2 planar Hermite interpolants with prescribed arc lengths,
Applied Mathematics and Computation, Avg. 2022, vol. 426, art. 127092.
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R.T. Farouki, M. Knez, V. Vitrih, E. Žagar: Spatial C2 closed loops of prescribed arc length defined by Pythagorean-hodograph curves,
Applied mathematics and computation,
vol. 391, 2021, art. 125653 (15 pages)
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R.T. Farouki, M. Knez, V. Vitrih, E. Žagar: Planar projections of spatial Pythagorean-hodograph curves,
Computer Aided Geometric Design, vol. 91, 2021, art.
102049 (15 pages)
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J. Grošelj, M. Knez: A construction of edge B-spline functions for a C1 polynomial spline on two triangles and its application to Argyris type splines,
Computers and Mathematics with Applications, vol. 99, str. 329-344, 2021.
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K. Ferjančič, M. Krajnc, V. Vitrih: On C2 rational motions of degree six, Journal of computational and applied mathematics. vol. 388, str. 1-17, 2021
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M. Knez, M. L. Sampoli:
Geometric interpolation of ER frames with G^2 Pythagorean-hodograph curves of degree 7,
Computer Aided Geometric Design, 88, 2021, art. 102001 (19 pages).
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M. Knez, M. L. Sampoli:
Geometric interpolation of ER frames with G^2 Pythagorean-hodograph curves of degree 7,
The Mathematica notebook with examples
(nb )
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J. Grošelj, M. Kapl, M. Knez, T. Takacs, V. Vitrih:
A super-smooth C^1 spline space over mixed triangle and quadrilateral meshes,
Computers and Mathematics with Applications, 80 (12), 2623-2643, 2020.
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M. Knez, F. Pelosi, M. L. Sampoli:
Spline surfaces with C^1 quintic PH isoparametric curves,
Computer Aided Geometric Design, 79, 2020.
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J. Grošelj, M. Knez:
On stable representations of Bell elements,
Computers and Mathematics with Applications, 79 (10), 2020, 2924-2941.
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J. Grošelj, M. Knez:
Interpolation with C^2 quartic macro-elements based on 10-splits,
Journal of Computational and Applied Mathematics 362, 2019, 143-160.
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M. Knez:
G^1 motion interpolation using cubic PH biarcs with prescribed length,
Comput. Aided Geom. Design 67, 2018, 21-33.
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M. Knez, E. Žagar:
Interpolation of circular arcs by parametric polynomials of maximal geometric smoothness,
Comput. Aided Geom. Design 63, 2018, 66-77.
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J. Grošelj, M. Knez:
A B-spline basis for C^1 quadratic splines on triangulations with a 10-split,
Journal of Computational and Applied Mathematics 343, 2018, 413-427.
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M. Krajnc:
Interpolation with spatial rational Pythagorean-hodograph curves of class 4,
The Mathematica notebook with examples
(nb )
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M. Krajnc:
Interpolation with spatial rational Pythagorean-hodograph curves of class 4,
Comput. Aided Geom. Design 56, 2017, 16-34.
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J. Grošelj, M. Krajnc:
Quartic splines on Powell-Sabin triangulations,
The Mathematica notebook with examples
(nb )
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J. Grošelj, M. Krajnc:
Quartic splines on Powell-Sabin triangulations,
Comput. Aided Geom. Des. 49, 2016, 1-16.
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J. Kozak, M. Krajnc, V. Vitrih:
G^1 interpolation by rational cubic PH curves in R^3,
Comput. Aided Geom. Des. 42, 2016, 7–22.
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K. Ferjančič, M. Krajnc, V. Vitrih:
Construction of G^3 rational motion of degree eight,
Applied Mathematics and Computation, 272 (1), 2016, 127–138.
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J. Grošelj, M. Krajnc:
C1 cubic splines on Powell–Sabin triangulations,
Applied Mathematics and Computation, 272 (1), 2016, 114–126.
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J. Kozak, M. Krajnc, M. Rogina, V. Vitrih: Pythagorean-hodograph Cycloidal curves,
Journal of Numerical Mathematics, 23 (5), 2015, 345–360.
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J. Kozak, M. Krajnc, V. Vitrih:
Parametric curves with Pythagorean binormal,
Advances in Computational Mathematics, 41 (4), 2015, 813–832.
- M. Krajnc, M. L. Sampoli, A. Sestini, E. Žagar:
C^1 interpolation by rational biarcs with rational
rotation minimizing directed frames,
Comput. Aided Geom. Des. 31 (7–8), 2014, 427–440.
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B. Bastl, M. Bizzarri, B. Kovač, M. Krajnc, M. Lavicka, K. Michalkova, Z. Sir, V. Vitrih, E. Žagar:
C^2 Hermite interpolation by Pythagorean-hodograph quintic triarcs,
Comput. Aided Geom. Des. 31 (7–8), 2014, 412–426.
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G. Jaklic, J. Kozak, M. Krajnc, V. Vitrih, E. Žagar: Interpolation by G^2 quintic Pythagorean-hodograph curves,
Numer. Math. Theor. Meth. Appl. 7, 2014, 374-398.
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J. Kozak, M. Krajnc, V. Vitrih: Dual representation of spatial rational Pythagorean-hodograph curves,
Comput. Aided Geom. Des. 31 (1), 2014, str. 43–56.
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M. Krajnc, K. Pockaj, V. Vitrih: Construction of low degree rational Lagrange motions,
Journal of Computational and Applied Mathematics 256, 2014, 92–103.
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B. Bastl, M. Bizzarri, M. Krajnc, M. Lavicka, K. Slaba, Z. Sir, V. Vitrih, E. Zagar: C^1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs,
Journal of Computational and Applied Mathematics 257, 2014, str. 65–78.
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G. Jaklic, J. Kozak, M. Krajnc, V. Vitrih, E. Žagar: High order parametric polynomial approximation of conic sections,
Constructive Approximation, 38, 2013, 1-18.
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G. Jaklic, B. Juettler, M. Krajnc, V. Vitrih, E. Žagar: Hermite interpolation by rational G^k motions of low degree,
Journal of Computational and Applied Mathematics 240, 2013, 20–30.
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G. Jaklic, J. Kozak, M. Krajnc, V. Vitrih, E. Žagar: Hermite geometric interpolation by rational Bézier spatial curves,
J. Numer. Anal., 50 (5), 2012, 2695–2715
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M. Krajnc, V. Vitrih: Motion design with Euler-Rodrigues frames of quintic
Pythagorean-hodograph curves,
Mathematics and Computers in simulation, 82 (9), 2012, 1696–1711.
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G. Jaklic, J. Kozak, M. Krajnc, V. Vitrih, E. Žagar: An approach to geometric interpolation by Pythagorean-hodograph curves,
Adv. Comput. Math., 37, 2012, 123-150
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B. Juettler, M. Krajnc, E. Žagar: Geometric interpolation by quartic rational spline motions,
Advances in Robot Kinematics: Motion in Man and Machine, Springer, New York, 2010, 377-384.
(pdf )
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G. Jaklic, J. Kozak, M. Krajnc, V. Vitrih, E. Žagar: High order parametric polynomial approximation of quadrics in R^d,
Journal of Mathematical Analysis and Applications 388, 2012, 318-332.
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M. Krajnc: Interpolation scheme for planar cubic G^2 spline curves,
Acta Appl. Math., 113 (2011), 129–143.
(pdf )
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G. Jaklič, J. Kozak, M. Krajnc, V. Vitrih, E. Žagar: On Interpolation by Planar Cubic
G^2 Pythagorean-hodograph Spline Curves, Math. Comput., 79 (2010), 305-326.
(pdf )
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G. Jaklič, J. Kozak, M. Krajnc, V. Vitrih, E. Žagar: Lattices on simplicial partitions,
J. Comput. Appl. Math., 233 (2010), 1704-1715.
(pdf )
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G. Jaklič, J. Kozak, M. Krajnc, V. Vitrih, E. Žagar: Geometric Lagrange Interpolation by Planar Cubic
Pythagorean-hodograph Curves,
Comput. Aided Geom. Design 25 (9), 2008, 720-728.
(pdf )
- M. Krajnc:
Hermite geometric interpolation by cubic G^1 splines,
Nonlinear Analysis: Theory, Methods and Applications 70, 2009, 2614-2626
(pdf )
- G. Jaklič, J. Kozak, M. Krajnc, V. Vitrih, E. Žagar:
Barycentric coordinates for Lagrange interpolation over lattices on a simplex,
Numer. Algor. 48 (1--3), 2008, 93-104.
(pdf )
- G. Jaklič, J. Kozak, M. Krajnc, V. Vitrih, E. Žagar:
On geometric Lagrange interpolation by quadratic parametric patches,
Comput. Aided Geom. Design 25 (6), 2008, 373-384.
(pdf )
- G. Jaklič, J. Kozak, M. Krajnc, E. Žagar:
Approximation of circular arcs by parametric polynomial curves,
Annali dellUniversita di Ferrara, 53 (2007), 271-279.
(pdf )
- G. Jaklič, J. Kozak, M. Krajnc, V. Vitrih, E. Žagar:
Three-pencil lattices on triangulations,
Numer. Algor., 45 (2007), 49-60.
(pdf )
- J. Kozak, M. Krajnc:
Geometric interpolation by planar cubic G1 splines,
BIT Numerical Mathematics, 47 (2007), 547-563.
(pdf )
- G. Jaklič, J. Kozak, M. Krajnc, E. Žagar:
On geometric interpolation by planar parametric polynomial curves,
Math. Comput., 76 (2007), 1981-1993.
(pdf )
- G. Jaklič, J. Kozak, M. Krajnc, E. Žagar:
On geometric interpolation of circle-like curves,
Comput. Aided Geom. Des., 24 (2007), 241-251.
(pdf )
- J. Kozak, M. Krajnc:
Geometric interpolation by planar cubic polynomial curves,
Comput. Aided Geom. Des., 24 (2007), 67-78.
(pdf )
- G. Jaklič, J. Kozak, M. Krajnc, E. Žagar:
Aproksimacija krožnih lokov s parametricnimi polinomskimi krivuljami,
Obz. mat. fiz., 53 (1), 2006, 1-10.
Doctoral thesis:
Geometric interpolation by planar parametric polynomial curves
(pdf )