TY - JOUR AU - Hoffmann, Miklós AU - Juhász, Imre AU - Troll, Ede Mátyás TI - Caustics of developable surfaces JF - FRONTIERS OF INFORMATION TECHNOLOGY & ELECTRONIC ENGINEERING J2 - FRONT INFORM TECH EL VL - 23 PY - 2022 IS - 3 SP - 479 EP - 487 PG - 9 SN - 2095-9184 DO - 10.1631/FITEE.2000613 UR - https://m2.mtmt.hu/api/publication/31989219 ID - 31989219 N1 - Cited By :1 Export Date: 24 March 2023 Correspondence Address: Hoffmann, M.; Institute of Mathematics and Computer Science, Hungary; email: hoffmann.miklos@uni-eszterhazy.hu Funding details: European Commission, EC Funding details: European Social Fund, ESF, EFOP-3.6.3-VEKOP-16-2017-00002 Funding text 1: Project supported by the European Union and the European Social Fund (No. EFOP-3.6.3-VEKOP-16-2017-00002). Open Access funding provided by European Union and the European Social Fund AB - While considering a mirror and light rays coming either from a point source or from infinity, the reflected light rays may have an envelope, called a caustic curve. In this paper, we study developable surfaces as mirrors. These caustic surfaces, described in a closed form, are also developable surfaces of the same type as the original mirror surface. We provide efficient, algorithmic computation to find the caustic surface of each of the three types of developable surfaces (cone, cylinder, and tangent surface of a spatial curve). We also provide a potential application of the results in contemporary free-form architecture design. LA - English DB - MTMT ER - TY - JOUR AU - Juhász, Imre TI - A NURBS transition between a Bézier curve and its control polygon JF - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS J2 - J COMPUT APPL MATH VL - 396 PY - 2021 PG - 15 SN - 0377-0427 DO - 10.1016/j.cam.2021.113626 UR - https://m2.mtmt.hu/api/publication/31992746 ID - 31992746 LA - English DB - MTMT ER - TY - JOUR AU - Juhász, Imre TI - On the caustics of Bézier curves JF - ANNALES MATHEMATICAE ET INFORMATICAE J2 - ANN MATH INFORM VL - 50 PY - 2019 SP - 93 EP - 100 PG - 8 SN - 1787-5021 DO - 10.33039/ami.2019.11.001 UR - https://m2.mtmt.hu/api/publication/31023261 ID - 31023261 LA - English DB - MTMT ER - TY - JOUR AU - Juhász, Imre AU - Róth, Ágoston-István TI - Adjusting the energies of curves defined by control points JF - COMPUTER-AIDED DESIGN J2 - COMPUT AIDED DESIGN VL - 107 PY - 2019 SP - 77 EP - 88 PG - 12 SN - 0010-4485 DO - 10.1016/j.cad.2018.09.003 UR - https://m2.mtmt.hu/api/publication/30324099 ID - 30324099 LA - English DB - MTMT ER - TY - CHAP AU - Juhász, Imre ED - Szirmay-Kalos, László ED - Renner, Gábor TI - A G^1 closed elliptic spline curve T2 - IX. magyar számítógépes grafika és geometria konferencia, GRAFGEO 2018 PB - Neumann János Számítógép-tudományi Társaság CY - Budapest SN - 9789633132821 PY - 2018 SP - 27 EP - 30 PG - 4 UR - https://m2.mtmt.hu/api/publication/30352834 ID - 30352834 LA - English DB - MTMT ER - TY - CHAP AU - Juhász, Imre ED - Joao, Moura Pires ED - Giuliana, Vitiello ED - Nuno, Datia ED - Ana, Figueiras TI - A Bézier-Like Curve with Two Shape Parameters T2 - 2018 22nd International Conference on Information Visualisation PB - IEEE Computer Society CY - Washington DC SN - 9781538672020 PY - 2018 SP - 604 EP - 609 PG - 6 DO - 10.1109/iV.2018.00108 UR - https://m2.mtmt.hu/api/publication/30350166 ID - 30350166 LA - English DB - MTMT ER - TY - JOUR AU - Juhász, Imre TI - Gardener’s spline curve JF - ANNALES MATHEMATICAE ET INFORMATICAE J2 - ANN MATH INFORM VL - 47 PY - 2017 SP - 109 EP - 118 PG - 10 SN - 1787-5021 UR - https://m2.mtmt.hu/api/publication/3315253 ID - 3315253 LA - English DB - MTMT ER - TY - JOUR AU - Juhász, Imre TI - On geometric Hermite arcs JF - ANNALES MATHEMATICAE ET INFORMATICAE J2 - ANN MATH INFORM VL - 45 PY - 2015 SP - 61 EP - 68 PG - 8 SN - 1787-5021 UR - https://m2.mtmt.hu/api/publication/2995391 ID - 2995391 AB - A geometric Hermite arc is a cubic curve in the plane that is specified by its endpoints along with unit tangent vectors and signed curvatures at them. This problem has already been solved by means of numerical procedures. Based on projective geometric considerations, we deduce the problem to finding the base points of a pencil of conics, that reduces the original quartic problem to a cubic one that easier can exactly be solved. A simple solvability criterion is also provided. © 2015, Eszterhazy Karoly College. All rights reserved. LA - English DB - MTMT ER - TY - JOUR AU - Hoffmann, Miklós AU - Juhász, Imre AU - Károlyi, Gyula TI - A control point based curve with two exponential shape parameters JF - BIT NUMERICAL MATHEMATICS J2 - BIT VL - 54 PY - 2014 IS - 3 SP - 691 EP - 710 PG - 20 SN - 0006-3835 DO - 10.1007/s10543-014-0468-2 UR - https://m2.mtmt.hu/api/publication/2701166 ID - 2701166 N1 - Cited By :9 Export Date: 22 February 2023 Correspondence Address: Hoffmann, M.; Eszterházy Károly University College, Leányka str. 4, Hungary Funding details: European Commission, EC Funding details: Australian Research Council, ARC Funding details: Hungarian Scientific Research Fund, OTKA, OTKA NN102029 Funding details: European Social Fund, ESF Funding text 1: This research was carried out as a part of the TAMOP-4.2.1.B-10/2/KONV-2010-0001 project with support by the European Union, co-financed by the European Social Fund. The third author was supported by the Australian Research Council and by Hungarian Scientific Research Grant OTKA NN102029. AB - A generalization of a recently developed trigonometric Bézier curve is presented in this paper. The set of original basis functions are generalized also for non-trigonometric functions, and essential properties, such as linear independence, nonnegativity and partition of unity are proved. The new curve-contrary to the original one-can be defined by arbitrary number of control points meanwhile it preserves the properties of the original curve. © 2014 Springer Science+Business Media Dordrecht. LA - English DB - MTMT ER - TY - CHAP AU - Juhász, Imre AU - Róth, Ágoston-István ED - Szirmay-Kalos, László ED - Renner, Gábor TI - A generalization of the Overhauser spline T2 - VII. Magyar Számítógépes Grafika és Geometria Konferencia PB - Neumann János Számítógép-tudományi Társaság CY - Budapest SN - 9786155036088 PY - 2014 SP - 52 EP - 59 PG - 8 UR - https://m2.mtmt.hu/api/publication/2547772 ID - 2547772 LA - English DB - MTMT ER -