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25. KONFERENCE O GEOMETRII A POČÍTAČOVÉ GRAFICE Oldřich Hykš LINEAR PERSPECTIVE IN PAINTING – A TOOL SUPPORTING GEOMETRIC EDUCATION Abstract The paper discusses a motivation for geometric education of students of technical universities and secondary schools, as well as other interested persons. It presents a study material which combines the exposition of basic principles and methods of geometric representations with commentaries and pictorial documentation of the historical development. This approach is based on the analogy between particular phases of perspective knowledge in the history and the gradual development of student’s knowledge, which facilitates the study. Linear perspective, painting 1 Introduction Keywords The objective of the contribution is to present a study material Birth and Applications of Linear Perspective in Painting [3] which represents a complement to standard lessons on geometry at technical universities and secondary schools. Its principal aim is to motivate students – coming usually without any previous knowledge of geometric projections – for some effort to understand and master the basic principles of linear perspective and methods of its practical applications. At present, in the days of attractive graphical computer programs, many students consider the study of these topics to be purposeless and it is necessary to persuade them of the sense of geometric education and the importance of the knowledge they earn there. For this purpose, the excursion into the history of painting is a convenient tool that can help students to become aware of the importance of geometric methods and of possible consequences of ignorance in this field. Concurrently, the material was created as an alternative to many of present publications devoted to linear perspective that are usually attractive, contain large colour reproductions, but follow the way of entertaining the reader rather than tasking his mind with a “useless” theory. It tries to remain attractive to motivate a today reader withal teaching him the necessary 89
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Katedra matematiky Fakulty stavebn
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Programový výbor konference: Doc.
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OBSAH TABLE OF CONTENTS
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Table of Contents Petr Kahánek, Al
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Table of Contents Daniela Velichov
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PLENÁRNÍ PŘEDNÁŠKY PLENARY LEC
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František Kuřina sítě čtyřdim
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František Kuřina Kombinace těcht
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František Kuřina 3 Matematika a v
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František Kuřina řešení je alt
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Gunter Weiss should show an own sci
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Gunter Weiss “industrial reality
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Gunter Weiss 5 “e-learning Geomet
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Gunter Weiss In the following some
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Gunter Weiss screen. This made it f
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REFERÁTY CONFERENCE PAPERS
Page 38 and 39: Eva Baranová, Kamil Maleček S a a
Page 40 and 41: Eva Baranová, Kamil Maleček extr
Page 42 and 43: Eva Baranová, Kamil Maleček Obrá
Page 44 and 45: ÊÓÞÔ×ÑÓ×ÓÙÖÒÔÞ×Ñ Å
Page 46 and 47: ÞÓÓÑÓÒÒ×ÓÙÖÒ×ÓÙÊ´
Page 48 and 49: ÔÖØÓÑØÓÔÓÝÙ×ÓÙÖÓÚ
Page 50 and 51: Bohumír Bastl The second reason fo
Page 52 and 53: Bohumír Bastl 4 3 2 1 0 2 4 0 2 4
Page 54 and 55: Bohumír Bastl the package that bot
Page 56 and 57: Zuzana Benáková x B y z B B = u c
Page 58 and 59: Zuzana Benáková Obrázek 4: třet
Page 60 and 61: Michal Benes Since des t 2 = ds 2 +
Page 62 and 63: Michal Benes The latter condition i
Page 64 and 65: Michal Benes 4 Innitesimal deformat
Page 66 and 67: Michal Benes where , 1, 2, ¢1, ¢2
Page 68 and 69: Milan Bořík, Vojtěch Honzík sys
Page 70 and 71: Milan Bořík, Vojtěch Honzík Dá
Page 72 and 73: Milan Bořík, Vojtěch Honzík Obr
Page 74 and 75: Jaromír Dobrý Example 2 Let’s c
Page 76 and 77: Jaromír Dobrý M ϕ ϕ(M) ϑ V {o}
Page 78 and 79: Jaromír Dobrý It is obvious from
Page 80 and 81: Henryk Gliński distortion coeffici
Page 82 and 83: Henryk Gliński polynomial. The coe
Page 84 and 85: ÊÓÑÒÀõ ÎÖÚÑÓúÒÓÔÖÓ
Page 86 and 87: ÊÓÑÒÀõ ÃõÒÐÓÝ´ÚÞÇÖ
Page 90 and 91: Oldřich Hykš foundations and simp
Page 92 and 93: Oldřich Hykš The choice of the tr
Page 94 and 95: Oldřich Hykš discussed together w
Page 96 and 97: Petr Kahánek, Alexej Kolcun 2 Tria
Page 98 and 99: Petr Kahánek, Alexej Kolcun of thi
Page 100 and 101: Petr Kahánek, Alexej Kolcun Now we
Page 102 and 103: Petr Kahánek, Alexej Kolcun In the
Page 104 and 105: Mária Kmeťová Bernsteinove polyn
Page 106 and 107: Mária Kmeťová H 0 O H 1 V 1 V 2
Page 108 and 109: Mária Kmeťová Na obrázku 5 je k
Page 110 and 111: Mária Kmeťová 6 Záver Program E
Page 112 and 113: Milada Kočandrlová Pro body X eli
Page 114 and 115: Milada Kočandrlová Podmínku cykl
Page 116 and 117: Milada Kočandrlová 6 Homotetický
Page 118 and 119: Jiří Kosinka medial axis transfor
Page 120 and 121: Jiří Kosinka Figure 3: Asymptotic
Page 122 and 123: Jiří Kosinka a) b) Figure 4: a) F
Page 124 and 125: Iva Křivková • body (např. Bri
Page 126 and 127: Iva Křivková V trojrozměrném eu
Page 128 and 129: Iva Křivková asymptoty). V tomto
Page 130 and 131: Karolína Kundrátová myslíme roz
Page 132 and 133: Karolína Kundrátová Bázové fun
Page 134 and 135: Karolína Kundrátová Obr. 2: Kři
Page 136 and 137: Miroslav Lávička of this article
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Miroslav Lávička if 〈x, x〉 M
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Miroslav Lávička n: x - x = 0 0 4
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Miroslav Lávička 5 Conclusion In
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Pavel Leischner Věta 1 (ptolemaiov
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Pavel Leischner Věta 2 (Ptolemaiov
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Pavel Leischner Literatura [1] Enge
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Ivana Linkeová Je-li hodnota výra
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Ivana Linkeová jednotkové váhy.
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Ivana Linkeová funkce jsou pro u 0
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Dalibor Martišek systémech, je po
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Dalibor Martišek Zvládneme-li pra
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Dalibor Martišek (což je jednoduc
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Katarína Mészárosová vedcov nov
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Katarína Mészárosová Obrázok 1
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Katarína Mészárosová Analogicky
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Katarína Mészárosová pocit krá
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Martin Němec do databáze, popří
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Martin Němec Obrázek 3: Modul pro
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Martin Němec Literatura [1] J. Ziv
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Stanislav Olivík 2 Hledání odraz
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Stanislav Olivík S 1 Q i+2 P Q Q i
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Stanislav Olivík Metoda popsaná v
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Anna Porazilová Table 1 shows the
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Anna Porazilová respective sum of
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Anna Porazilová Figure 4a. Demonst
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Anna Porazilová precisely (figure
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LenkaPospíšilová výpočtupřija
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LenkaPospíšilová > evolute:=proc
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LenkaPospíšilová Soustavatečenp
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Radka Pospíšilová Pro získání
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Radka Pospíšilová Obrázek 2: Uk
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Jana Procházková 2 Derivative of
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Jana Procházková now we continue
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Jana Procházková Figure 1: Tangen
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Marie Provazníková SO(n) je topol
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Marie Provazníková qiq −1 = −
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Marie Provazníková Potom máme do
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Jana Přívratská ponechává nedo
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Jana Přívratská Z 16 klasických
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Adam Rużyczka During those years,
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Adam Rużyczka % 100 90 80 70 60 50
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Adam Rużyczka Table 3 presents com
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Ivo Serba Obr. 1. Princip geometric
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Ivo Serba výplň rohů = vloop( vp
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Ivo Serba . Obr. 7. Příklad tří
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Ivo Serba Literatura [1] Cline, M.:
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Tomáš Staudek vizualizací prosto
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Tomáš Staudek - Matematické mode
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Tomáš Staudek - Stíny (měkké,
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Zbyněk Šír circular arcs share o
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Zbyněk Šír In addition to the hi
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JiříŠrubař Jetakézřejmé,žen
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JiříŠrubař cházejícístředys
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JiříŠrubař |LS|=|OS|, |TS|= 1 2
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Diana Šteflová 2 Digitální foto
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Diana Šteflová Organizační prav
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Vladimír Tichý Definice a označe
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Vladimír Tichý Případy 2 až 4
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Vladimír Tichý V tomto konkrétn
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Světlana Tomiczková Figure 1: Are
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Světlana Tomiczková follows: 1. B
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Světlana Tomiczková ∫ [x 2 (s(t
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Margita Vajsáblová Křovák zostr
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Margita Vajsáblová 3 Použitie ku
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Margita Vajsáblová Obrázok 4: Gr
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Jiří Vaníček technického směr
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Jiří Vaníček Vzhledem k nasazen
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Jiří Vaníček politiky a má zvy
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Jiří Vaníček tedy které úlohy
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Jana Vecková 2 Algoritmus navrhova
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Jana Vecková Obrázek 5: Porovnán
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Daniela Velichová 2 Dvojosové rot
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Daniela Velichová Obrázok 3: Dvoj
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Daniela Velichová Skupina IB1 - Cy
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Daniela Velichová Parametrické ro
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Šárka Voráčová also available
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Šárka Voráčová efficiency is p
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Šárka Voráčová 5 Conclusion Ma
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Edita Vranková (intM∩intN=∅).
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Edita Vranková translations). This
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Edita Vranková From all previous s
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Edita Vranková References [1] Bíl
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Radek Výrut Další postup využí
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Radek Výrut Nyní si podrobněji p
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Radek Výrut [3] I. K. Lee, M. S. K
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Lucie Zrůstová Náplň deskriptiv
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Lucie Zrůstová V roce 1951 byla z
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Lucie Zrůstová Školní rok Zimn
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Mária Zvariková, Zuzana Juščák
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Antonina Żaba An attempt to find a
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Antonina Żaba Figure 2: Drawing fr
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Antonina Żaba element) are include
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Antonina Żaba but look slantwise a
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Antonina Żaba Figure 2: Drawing 56
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Antonina Żaba In S. Ignazio Church
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25. KONFERENCE O GEOMETRII A POČÍ
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Seznam účastníků Milena Foglaro
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Alexej Kolcun Akademie věd České
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Seznam účastníků Dagmar Mannhei
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Seznam účastníků Radka Pospíš
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Seznam účastníků Jaroslav Škra
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Edita Vranková Trnavská univerzit
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ELKAN, spol. s r.o. Výhradní dist
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