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 - JOUR AU - Róth, Ágoston-István TI - Control point based exact description of trigonometric/hyperbolic curves, surfaces and volumes JF - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS J2 - J COMPUT APPL MATH VL - 290 PY - 2015 IS - C SP - 74 EP - 91 PG - 18 SN - 0377-0427 DO - 10.1016/j.cam.2015.05.003 UR - https://m2.mtmt.hu/api/publication/3096980 ID - 3096980 LA - English DB - MTMT ER - TY - JOUR AU - Róth, Ágoston-István TI - Control point based exact description of curves and surfaces, in extended Chebyshev spaces JF - COMPUTER AIDED GEOMETRIC DESIGN J2 - COMPUT AIDED GEOM D VL - 40 PY - 2015 SP - 40 EP - 58 PG - 19 SN - 0167-8396 DO - 10.1016/j.cagd.2015.09.005 UR - https://m2.mtmt.hu/api/publication/3096977 ID - 3096977 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 - TY - JOUR AU - Juhász, Imre AU - Róth, Ágoston-István TI - A scheme for interpolation with trigonometric spline curves JF - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS J2 - J COMPUT APPL MATH VL - 263 PY - 2014 SP - 246 EP - 261 PG - 16 SN - 0377-0427 DO - 10.1016/j.cam.2013.12.034 UR - https://m2.mtmt.hu/api/publication/2516029 ID - 2516029 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Juhász, Imre AU - Róth, Ágoston-István TI - A class of generalized B-spline curves JF - COMPUTER AIDED GEOMETRIC DESIGN J2 - COMPUT AIDED GEOM D VL - 30 PY - 2013 IS - 1 SP - 85 EP - 115 PG - 31 SN - 0167-8396 DO - 10.1016/j.cagd.2012.06.007 UR - https://m2.mtmt.hu/api/publication/2145302 ID - 2145302 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Róth, Ágoston-István AU - Juhász, Imre TI - Constrained surface interpolation by means of a genetic algorithm JF - COMPUTER-AIDED DESIGN J2 - COMPUT AIDED DESIGN VL - 43 PY - 2011 IS - 9 SP - 1194 EP - 1210 PG - 17 SN - 0010-4485 DO - 10.1016/j.cad.2011.05.002 UR - https://m2.mtmt.hu/api/publication/1766889 ID - 1766889 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Róth, Ágoston-István AU - Juhász, Imre TI - Control point based exact description of a class of closed curves and surfaces JF - COMPUTER AIDED GEOMETRIC DESIGN J2 - COMPUT AIDED GEOM D VL - 27 PY - 2010 IS - 2 SP - 179 EP - 201 PG - 23 SN - 0167-8396 DO - 10.1016/j.cagd.2009.11.005 UR - https://m2.mtmt.hu/api/publication/1771591 ID - 1771591 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Juhász, Imre AU - Róth, Ágoston-István TI - Closed rational trigonometric curves and surfaces JF - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS J2 - J COMPUT APPL MATH VL - 234 PY - 2010 IS - 8 SP - 2390 EP - 2404 PG - 15 SN - 0377-0427 DO - 10.1016/j.cam.2010.03.009 UR - https://m2.mtmt.hu/api/publication/1368892 ID - 1368892 LA - English DB - MTMT ER - TY - CHAP AU - Róth, Ágoston-István AU - Juhász, Imre ED - Szirmay-Kalos, László ED - Renner, Gábor TI - Interpolation with cyclic curves and surfaces T2 - V. Magyar Számítógépes Grafika és Geometria Konferencia PB - Neumann János Számítógép-tudományi Társaság CY - Budapest SN - 9789634215912 PY - 2010 SP - 58 EP - 64 PG - 7 UR - https://m2.mtmt.hu/api/publication/1300490 ID - 1300490 LA - English DB - MTMT ER -