@article{MTMT:30324099,
	title = {Adjusting the energies of curves defined by control points},
	url = {https://m2.mtmt.hu/api/publication/30324099},
	author = {Juhász, Imre and Róth, Ágoston-István},
	doi = {10.1016/j.cad.2018.09.003},
	journal-iso = {COMPUT AIDED DESIGN},
	journal = {COMPUTER-AIDED DESIGN},
	volume = {107},
	unique-id = {30324099},
	issn = {0010-4485},
	year = {2019},
	eissn = {1879-2685},
	pages = {77-88},
	orcid-numbers = {Juhász, Imre/0000-0003-3066-0301}
}

@article{MTMT:3096980,
	title = {Control point based exact description of trigonometric/hyperbolic curves, surfaces and volumes},
	url = {https://m2.mtmt.hu/api/publication/3096980},
	author = {Róth, Ágoston-István},
	doi = {10.1016/j.cam.2015.05.003},
	journal-iso = {J COMPUT APPL MATH},
	journal = {JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS},
	volume = {290},
	unique-id = {3096980},
	issn = {0377-0427},
	year = {2015},
	eissn = {1879-1778},
	pages = {74-91}
}

@article{MTMT:3096977,
	title = {Control point based exact description of curves and surfaces, in extended Chebyshev spaces},
	url = {https://m2.mtmt.hu/api/publication/3096977},
	author = {Róth, Ágoston-István},
	doi = {10.1016/j.cagd.2015.09.005},
	journal-iso = {COMPUT AIDED GEOM D},
	journal = {COMPUTER AIDED GEOMETRIC DESIGN},
	volume = {40},
	unique-id = {3096977},
	issn = {0167-8396},
	year = {2015},
	eissn = {1879-2332},
	pages = {40-58}
}

@inproceedings{MTMT:2547772,
	title = {A generalization of the Overhauser spline},
	url = {https://m2.mtmt.hu/api/publication/2547772},
	author = {Juhász, Imre and Róth, Ágoston-István},
	booktitle = {VII. Magyar Számítógépes Grafika és Geometria Konferencia},
	unique-id = {2547772},
	year = {2014},
	pages = {52-59},
	orcid-numbers = {Juhász, Imre/0000-0003-3066-0301}
}

@article{MTMT:2516029,
	title = {A scheme for interpolation with trigonometric spline curves},
	url = {https://m2.mtmt.hu/api/publication/2516029},
	author = {Juhász, Imre and Róth, Ágoston-István},
	doi = {10.1016/j.cam.2013.12.034},
	journal-iso = {J COMPUT APPL MATH},
	journal = {JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS},
	volume = {263},
	unique-id = {2516029},
	issn = {0377-0427},
	abstract = {We present a method for the interpolation of a given sequence of data points with Cn continuous trigonometric spline curves of order n+1 (n≥1) that are produced by blending elliptical arcs. Ready to use explicit formulae for the control points of the interpolating arcs are also provided. Each interpolating arc depends on a global parameter α∈(0,π) that can be used for global shape modification. Associating non-negative weights with data points, rational trigonometric interpolating spline curves can be obtained, where weights can be used for local shape modification. The proposed interpolation scheme is a generalization of the Overhauser spline, and it includes a Cn Bézier spline interpolation method as the limiting case α→0. © 2013 Elsevier B.V. All rights reserved.},
	keywords = {interpolation; Blending; Shape parameters; Trigonometric spline; Overhauser spline; Bézier spline},
	year = {2014},
	eissn = {1879-1778},
	pages = {246-261},
	orcid-numbers = {Juhász, Imre/0000-0003-3066-0301}
}

@article{MTMT:2145302,
	title = {A class of generalized B-spline curves},
	url = {https://m2.mtmt.hu/api/publication/2145302},
	author = {Juhász, Imre and Róth, Ágoston-István},
	doi = {10.1016/j.cagd.2012.06.007},
	journal-iso = {COMPUT AIDED GEOM D},
	journal = {COMPUTER AIDED GEOMETRIC DESIGN},
	volume = {30},
	unique-id = {2145302},
	issn = {0167-8396},
	abstract = {The classical B-spline functions of order k≥2 are recursively defined as a special combination of two consecutive B-spline functions of order k-1. At each step, this recursive definition is based, in general, on different reparametrizations of the strictly increasing identity (linear core) function φ(u)=u. This paper generalizes the concept of the classical normalized B-spline functions by considering monotone increasing continuously differentiable nonlinear core functions instead of the classical linear one. These nonlinear core functions are not only interesting from a theoretical perspective, but they also provide a large variety of shapes. We show that many advantageous properties (like the non-negativity, local support, the partition of unity, the effect of multiple knot values, the special case of Bernstein polynomials and endpoint interpolation conditions) of the classical normalized B-spline functions remain also valid for this generalized case, moreover we also provide characterization theorems for not so obvious (geometrical) properties like the first and higher order continuity of the generalized normalized B-spline functions, C1 continuous envelope contact property of the family of curves obtained by altering a selected knot value between its neighboring knots. Characterization theorems are illustrated by test examples. We also outline new research directions by ending our paper with a list of open problems and conjectures underpinned by numerous successful numerical tests. © 2012 Elsevier B.V.},
	keywords = {ENVELOPE; B-SPLINE CURVES; Corner cutting; B-spline-like functions},
	year = {2013},
	eissn = {1879-2332},
	pages = {85-115},
	orcid-numbers = {Juhász, Imre/0000-0003-3066-0301}
}

@article{MTMT:1766889,
	title = {Constrained surface interpolation by means of a genetic algorithm},
	url = {https://m2.mtmt.hu/api/publication/1766889},
	author = {Róth, Ágoston-István and Juhász, Imre},
	doi = {10.1016/j.cad.2011.05.002},
	journal-iso = {COMPUT AIDED DESIGN},
	journal = {COMPUTER-AIDED DESIGN},
	volume = {43},
	unique-id = {1766889},
	issn = {0010-4485},
	abstract = {We propose an evolutionary technique (a genetic algorithm) to solve heavily constrained optimization problems defined on interpolating tensor product surfaces by adjusting the parameter values associated with the data points to be interpolated. Throughout our study we assume that the functional, which operates on these types of interpolating surfaces, is described by a surface integral and fulfills the following conditions: it is not necessarily a smooth functional (i.e., it may have vanishing gradient vectors), it is bounded (i.e., the optimization algorithm can converge in a finite number of steps), it is invariant under parametrization, rigid body transformation and uniform scaling (i.e., different surface parametrization at different scales should generate the same optimized shape). We have successfully tested the proposed algorithm for functionals that involve: minimal surface area, minimal Willmore, umbilic deviation and total curvature energies, minimal third-order scale invariant weighted Mehlum-Tarrou energies, and isoperimetric like problems. In general, our algorithm can be used in the case of any kind of not necessarily smooth surface fairing functionals. The run-time and memory complexities of the suggested algorithm are reasonable. Moreover, the algorithm is independent of the type of tensor product surface. (C) 2011 Elsevier Ltd. All rights reserved.},
	keywords = {PARAMETRIZATION; GENETIC ALGORITHM; Constrained optimization problems; Surface fairing functionals and energies; Interpolating tensor product surfaces},
	year = {2011},
	eissn = {1879-2685},
	pages = {1194-1210},
	orcid-numbers = {Juhász, Imre/0000-0003-3066-0301}
}

@article{MTMT:1771591,
	title = {Control point based exact description of a class of closed curves and surfaces},
	url = {https://m2.mtmt.hu/api/publication/1771591},
	author = {Róth, Ágoston-István and Juhász, Imre},
	doi = {10.1016/j.cagd.2009.11.005},
	journal-iso = {COMPUT AIDED GEOM D},
	journal = {COMPUTER AIDED GEOMETRIC DESIGN},
	volume = {27},
	unique-id = {1771591},
	issn = {0167-8396},
	abstract = {Based oil cyclic curves/surfaces introduced in Roth et a]. (2009), we specify control point configurations that result an exact description of those closed curves and surfaces the coordinate functions of which are (separable) trigonometric polynomials of finite degree. This class of curves/surfaces comprises several famous closed curves like ellipses, epi- and hypocycloids, Lissajous curves, torus knots, foliums: and surfaces such as sphere. torus and other surfaces of revolution, and even special surfaces like the non-orientable Roman surface of Steiner. Moreover, we show that higher order (mixed partial) derivatives of cyclic curves/surfaces are also cyclic curves/surfaces, and we describe the connection between the cyclic and Fourier bases of the vector space of trigonometric polynomials of finite degree. (C) 2009 Elsevier B.V. All rights reserved.},
	keywords = {C-CURVES; B-SPLINE CURVES; Basis transformation; Closed surfaces; Closed curves; Cyclic surfaces; Cyclic curves},
	year = {2010},
	eissn = {1879-2332},
	pages = {179-201},
	orcid-numbers = {Juhász, Imre/0000-0003-3066-0301}
}

@article{MTMT:1368892,
	title = {Closed rational trigonometric curves and surfaces},
	url = {https://m2.mtmt.hu/api/publication/1368892},
	author = {Juhász, Imre and Róth, Ágoston-István},
	doi = {10.1016/j.cam.2010.03.009},
	journal-iso = {J COMPUT APPL MATH},
	journal = {JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS},
	volume = {234},
	unique-id = {1368892},
	issn = {0377-0427},
	year = {2010},
	eissn = {1879-1778},
	pages = {2390-2404},
	orcid-numbers = {Juhász, Imre/0000-0003-3066-0301}
}

@inproceedings{MTMT:1300490,
	title = {Interpolation with cyclic curves and surfaces},
	url = {https://m2.mtmt.hu/api/publication/1300490},
	author = {Róth, Ágoston-István and Juhász, Imre},
	booktitle = {V. Magyar Számítógépes Grafika és Geometria Konferencia},
	unique-id = {1300490},
	year = {2010},
	pages = {58-64},
	orcid-numbers = {Juhász, Imre/0000-0003-3066-0301}
}