Rendering of Large Scale Terrain

Tato práce pojednává o renderování rozsáhlého terénu. V první části je popsána teorie renderování terénu a konkrétních LOD technik. Dále jsou v této části stručně popsány tři zajímavé moderní algoritmy. Hlavní důraz je kladen na popis algoritmu Geometry Clipmaps i s jeho optimalizací GPU-Based Geometry Clipmaps. Implementace tohoto optimalizovaného algoritmu je podrobně popsána v následujících kapitolách. Hlavní výhodou tohoto algoritmu je inkrementální aktualizace vertex textur a přesun zátěže z CPU na GPU. Poslední část je zaměřena na testování výkonu implementovaného algoritmu a porovnává výsledky s různým nastavením kvality výsledného terénu.This thesis deals with rendering of large scale terrain. The first part describes theory of terrain rendering and particular level of detail techniques. Three modern intriguing algorithms are briefly depicted after this theoretical part. Main work insists on description of Geometry Clipmaps algorithm along with its optimized version GPU-Based Geometry Clipmaps. Implementation of this optimized algorithm is depicted in detail. Main advantage of this approach is incremental update of vertex data, which allows to offload overhead from CPU to GPU. In the last chapter performance of my implementation is analysed using simple benchmark.

Graphical Library for Educational Purposes

Práce se zabývá návrhem a vývojem grafické knihovny vhodné pro výuku programování na stedních školách a ukazuje použití této knihovny pro vizualizaci algoritmu na funkci sinus. Dále popisuje knihovny pro práci s grafickým výstupem a srovnává dobe známé multimediální knihovny.This thesis is focused on projecting and developing graphical library for educational purposes at high schools. And shows usage of this library for visualization of sinus function algorithm. Further describes graphical libraries and compares well known multimedia libraries.

On 2-arc-transitivity of Cayley graphs

AbstractThe classification of 2-arc-transitive Cayley graphs of cyclic groups, given in (J. Algebra. Combin. 5 (1996) 83–86) by Alspach, Conder, Xu and the author, motivates the main theme of this article: the study of 2-arc-transitive Cayley graphs of dihedral groups. First, a previously unknown infinite family of such graphs, arising as covers of certain complete graphs, is presented, leading to an interesting property of Singer cycles in the group PGL(2,q), q an odd prime power, among others. Second, a structural reduction theorem for 2-arc-transitive Cayley graphs of dihedral groups is proved, putting us—modulo a possible existence of such graphs among regular cyclic covers over a small family of certain bipartite graphs—a step away from a complete classification of such graphs. As a byproduct, a partial description of 2-arc-transitive Cayley graphs of abelian groups with at most three involutions is also obtained

On vertex symmetric digraphs

AbstractIt is proved that if p is a prime, k and m⩽p are positive integers, and I is a vertex symmetric diagraph of order pk or mp, then Γ has an automorphism all of whose orbits have cardinality p. Vertex symmetric graphs of order 2p such that 2p−1 is not the square of a composite integer and vertex symmetric digraphs of order pk are characterised