caa a22 4500 605541329 CHVBK 20210128100915.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00371-014-0928-3 doi (NATIONALLICENCE)springer-10.1007/s00371-014-0928-3 Visualisation of complex functions on Riemann sphere [Elektronische Daten] [Miroslava Valíková, Pavel Chalmovianský] 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. Springer-Verlag Berlin Heidelberg, 2014 Riemann surfaces nationallicence Multi-valued function nationallicence Visualization nationallicence Singular points nationallicence Valíková Miroslava Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia aut Chalmovianský Pavel Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia aut The Visual Computer Springer Berlin Heidelberg 31/2(2015-02-01), 141-154 0178-2789 31:2<141 2015 31 371 https://doi.org/10.1007/s00371-014-0928-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00371-014-0928-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Valíková Miroslava Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia aut NATIONALLICENCE 700 1- Chalmovianský Pavel Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia aut NATIONALLICENCE 773 0- The Visual Computer Springer Berlin Heidelberg 31/2(2015-02-01), 141-154 0178-2789 31:2<141 2015 31 371