Visualisation of complex functions on Riemann sphere
| LEADER | caa a22 4500 | ||
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| 001 | 605541329 | ||
| 003 | CHVBK | ||
| 005 | 20210128100915.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00371-014-0928-3 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00371-014-0928-3 | ||
| 245 | 0 | 0 | |a Visualisation of complex functions on Riemann sphere |h [Elektronische Daten] |c [Miroslava Valíková, Pavel Chalmovianský] |
| 520 | 3 | |a The notion of a multi-valued function is frequent in complex analysis and related fields. A graph of such a function helps to inspect the function, however, the methods working with single-valued functions can not be applied directly. To visualize such a type of function, its Riemann surface is often used as a domain of the function. On such a surface, a multi-valued function behaves like a single-valued function. In our paper, we give a quick overview of the proposed method of visualization of a single-valued complex function over its Riemann sphere. Then, we pass to the adaptation of this method on the visualization of a multi-valued complex function. Our method uses absolute value and argument of the function to create the graph in 3D space over the Riemann sphere. Such a graph provides an overview of the function behavior over its whole domain, the amount and the position of its branch points, as well as poles and zeros and their multiplicity. We have also created an algorithm for adaptive grid which provides higher density of vertices in areas with higher curvature of the graph. The algorithm eliminates the alias in places where the branches are joined together. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Riemann surfaces |2 nationallicence | |
| 690 | 7 | |a Multi-valued function |2 nationallicence | |
| 690 | 7 | |a Visualization |2 nationallicence | |
| 690 | 7 | |a Singular points |2 nationallicence | |
| 700 | 1 | |a Valíková |D Miroslava |u Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia |4 aut | |
| 700 | 1 | |a Chalmovianský |D Pavel |u Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia |4 aut | |
| 773 | 0 | |t The Visual Computer |d Springer Berlin Heidelberg |g 31/2(2015-02-01), 141-154 |x 0178-2789 |q 31:2<141 |1 2015 |2 31 |o 371 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00371-014-0928-3 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00371-014-0928-3 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Valíková |D Miroslava |u Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Chalmovianský |D Pavel |u Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t The Visual Computer |d Springer Berlin Heidelberg |g 31/2(2015-02-01), 141-154 |x 0178-2789 |q 31:2<141 |1 2015 |2 31 |o 371 | ||