Odpověď z MediaWiki API
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{
"compare": {
"fromid": 1,
"fromrevid": 1,
"fromns": 0,
"fromtitle": "Hlavn\u00ed strana",
"toid": 2,
"torevid": 2,
"tons": 0,
"totitle": "Geometrie/Afinn\u00ed transformace sou\u0159adnic",
"*": "<tr><td colspan=\"2\" class=\"diff-lineno\" id=\"mw-diff-left-l1\">\u0158\u00e1dek 1:</td>\n<td colspan=\"2\" class=\"diff-lineno\">\u0158\u00e1dek 1:</td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\"><strong>MediaWiki byla \u00fasp\u011b\u0161n\u011b nainstalov\u00e1na</del>.<del class=\"diffchange diffchange-inline\"></strong></del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Geometrie|Geometrick\u00e9]] transformace jsou jedn\u011bmi z nej\u010dast\u011bji pou\u017e\u00edvan\u00fdch operac\u00ed v po\u010d\u00edta\u010dov\u00e9 grafice. Mezi afinn\u00ed operace pat\u0159\u00ed posunut\u00ed, ot\u00e1\u010den\u00ed, zm\u011bna m\u011b\u0159\u00edtka, zkosen\u00ed a operace vznikl\u00e9 jejich skl\u00e1d\u00e1n\u00edm</ins>.</div></td></tr>\n<tr><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-deleted\"><br></td><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-added\"><br></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>[<del class=\"diffchange diffchange-inline\">https://www.mediawiki</del>.<del class=\"diffchange diffchange-inline\">org/wiki/Special:MyLanguage/Help:Contents U\u017eivatelsk\u00e1 p\u0159\u00edru\u010dka] v\u00e1m napov\u00ed</del>, <del class=\"diffchange diffchange-inline\">jak pou\u017e\u00edvat MediaWiki</del>.</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Vyj\u00e1d\u0159en\u00ed ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">''Afinn\u00ed transformace'' jsou vyj\u00e1d\u0159eny vztahem ''P' '' = ''P'' '''A''', kde ''P'' je bodem, kter\u00fd transformujeme matic\u00ed '''A'''. Plat\u00ed ''P' '' = [x' y' w'] = ''P'' '''A''' = </ins>[<ins class=\"diffchange diffchange-inline\">x y w] '''A'''</ins>. <ins class=\"diffchange diffchange-inline\">Matice '''A''' reprezentuje jednotliv\u00e9 transformace</ins>, <ins class=\"diffchange diffchange-inline\">kter\u00e9 mohou b\u00fdt i skl\u00e1d\u00e1ny</ins>.</div></td></tr>\n<tr><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-deleted\"><br></td><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-added\"><br></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>== <del class=\"diffchange diffchange-inline\">Za\u010d\u00edn\u00e1me </del>==</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Geometrick\u00e9 afinn\u00ed transformace sou\u0159adnic n\u00e1m umo\u017e\u0148uj\u00ed bod ''P'' posunout, oto\u010dit nebo zm\u011bnit jeho m\u011b\u0159\u00edtko (t\u00fdk\u00e1 se objekt\u016f, z t\u011bchto bod\u016f slo\u017een\u00fdch).</ins></div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">* </del>[<del class=\"diffchange diffchange-inline\">https:</del>//<del class=\"diffchange diffchange-inline\">www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org/wiki/Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Manual:Configuration_settings Nastaven\u00ed konfigurace</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">* </del>[<del class=\"diffchange diffchange-inline\">https:</del>//<del class=\"diffchange diffchange-inline\">www.mediawiki.org</del>/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage/Manual</del>:<del class=\"diffchange diffchange-inline\">FAQ \u010casto kladen\u00e9 ot\u00e1zky </del>o <del class=\"diffchange diffchange-inline\">MediaWiki</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Podrobn\u011bj\u0161\u00ed rozeps\u00e1n\u00ed t\u011bchto transformac\u00ed a jejich skl\u00e1d\u00e1n\u00ed viz n\u00ed\u017ee.</ins></div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">* [https:</del>//<del class=\"diffchange diffchange-inline\">lists.wikimedia.org</del>/<del class=\"diffchange diffchange-inline\">postorius</del>/<del class=\"diffchange diffchange-inline\">lists</del>/<del class=\"diffchange diffchange-inline\">mediawiki-announce</del>.<del class=\"diffchange diffchange-inline\">lists</del>.<del class=\"diffchange diffchange-inline\">wikimedia</del>.<del class=\"diffchange diffchange-inline\">org</del>/ <del class=\"diffchange diffchange-inline\">E-mailov\u00e1 konference ozn\u00e1men\u00ed MediaWiki]</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">* [https</del>:/<del class=\"diffchange diffchange-inline\">/www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Localisation#Translation_resources P\u0159eklad MediaWiki </del>do <del class=\"diffchange diffchange-inline\">va\u0161eho jazyka]</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Afinn\u00ed geometrick\u00e9 transformace sou\u0159adnic ==</ins></div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">* </del>[<del class=\"diffchange diffchange-inline\">https</del>://www.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org/wiki/Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage/Manual:Combating_spam Nau\u010dte se bojovat se spamem na va\u0161\u00ed wiki</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==</ins>= <ins class=\"diffchange diffchange-inline\">Posunut\u00ed </ins>===</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Transformace posunut\u00ed nebo tak\u00e9 translace ''(move, translation)'' bodu ''P</ins>[<ins class=\"diffchange diffchange-inline\">X, Y]'' je ur\u010dena vektorem posunut\u00ed</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">p=(X_T, Y_T)=(X' - X, Y' - Y)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"></math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Aplikac\u00ed t\u00e9to transformace na bod ''P'' z\u00edsk\u00e1me bod ''P' '' o sou\u0159adnic\u00edch</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">X'=X+X_T</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"></math><br </ins>/<ins class=\"diffchange diffchange-inline\">></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Y'=Y+Y_T</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Maticov\u00e9 vyj\u00e1d\u0159en\u00ed transformace posunut\u00ed m\u00e1 pro homogenn\u00ed sou\u0159adnice tvar</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">A_T=</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\begin{bmatrix} 1 & 0 & 0\\\\ 0 & 1 & 0\\\\ X_T & Y_T & 1 \\end{bmatrix}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"></math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Soubor:Move02</ins>.<ins class=\"diffchange diffchange-inline\">svg|r\u00e1m|st\u0159ed|Obr</ins>.<ins class=\"diffchange diffchange-inline\">1</ins>: <ins class=\"diffchange diffchange-inline\">Posunut\u00ed - \u010cerven\u00e1 k\u0159ivka je v\u00fdsledkem posunut\u00ed p\u016fvodn\u00ed modr\u00e9 k\u0159ivky o vektor ''a''<sup>\u2192<</ins>/<ins class=\"diffchange diffchange-inline\">sup>.]</ins>]</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Ot\u00e1\u010den\u00ed ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Ot\u00e1\u010den\u00edm ''(rotation)'' bodu ''P'' kolem po\u010d\u00e1tku soustavy sou\u0159adnic O=</ins>[<ins class=\"diffchange diffchange-inline\">0,0] o orientovan\u00fd \u00fahel \u03b1 z\u00edsk\u00e1me bod ''P' '' o sou\u0159adnic\u00edch</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">X'=Xcos\\alpha -Ysin\\alpha</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><</ins>/<ins class=\"diffchange diffchange-inline\">math><br </ins>/<ins class=\"diffchange diffchange-inline\">></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Y'=Xsin\\alpha +Ycos \\alpha</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Maticov\u00e9 vyj\u00e1d\u0159en\u00ed transformace ot\u00e1\u010den\u00ed m\u00e1 pro homogenn\u00ed sou\u0159adnice tvar</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">A_R=</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\begin{bmatrix} cos\\alpha & -sin\\alpha & 0\\\\ sin\\alpha & cos\\alpha & 0\\\\ 0 & 0 & 1 \\end{bmatrix}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Soubor</ins>:<ins class=\"diffchange diffchange-inline\">Rotate (1).svg|r\u00e1m|st\u0159ed|Obr.2</ins>: <ins class=\"diffchange diffchange-inline\">Oto\u010den\u00ed - \u010cerven\u00e1 k\u0159ivka je v\u00fdsledkem oto\u010den\u00ed p\u016fvodn\u00ed modr\u00e9 k\u0159ivky </ins>o <ins class=\"diffchange diffchange-inline\">180<sup>0</sup>.]</ins>]</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Zm\u011bna m\u011b\u0159\u00edtka ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Zm\u011bna m\u011b\u0159\u00edtka ''(scale, zoom)'' je zm\u011bnou velikosti objektu ve sm\u011bru sou\u0159adnicov\u00fdch os. Pokud je absolutn\u00ed hodnota koeficientu m\u011b\u0159\u00edtkov\u00e1n\u00ed v intervalu (0, 1), doch\u00e1z\u00ed ke zmen\u0161en\u00ed transformovan\u00e9ho objektu.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Je-li absolutn\u00ed hodnota koeficientu v\u011bt\u0161\u00ed ne\u017e jedna, dojde k prodlou\u017een\u00ed, je-li znam\u00e9nko z\u00e1porn\u00e9, doch\u00e1z\u00ed k prodlou\u017een\u00ed \u010di zmen\u0161en\u00ed v opa\u010dn\u00e9m sm\u011bru.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Rovnice pro zm\u011bnu m\u011b\u0159\u00edtka bodu ''P'' maj\u00ed tvar</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">X'=S_xX</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><</ins>/<ins class=\"diffchange diffchange-inline\">math><br </ins>/<ins class=\"diffchange diffchange-inline\">></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Y'=S_yY</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">kde S<sub>x<</ins>/<ins class=\"diffchange diffchange-inline\">sub> je koeficient zm\u011bny m\u011b\u0159\u00edtka ve sm\u011bru sou\u0159adnicov\u00e9 osy ''x'' a S<sub>y<</ins>/<ins class=\"diffchange diffchange-inline\">sub> je koeficient zm\u011bny m\u011b\u0159\u00edtka ve sm\u011bru sou\u0159adnicov\u00e9 osy ''y''.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Odpov\u00eddaj\u00edc\u00ed transforma\u010dn\u00ed matice m\u00e1 pro homogenn\u00ed sou\u0159adnice tvar</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">A_{S}=</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\begin{bmatrix} S_x & 0 & 0\\\\ 0 & S_y & 0\\\\ 0 & 0 & 1 \\end{bmatrix}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"></math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Image:Scale</ins>.<ins class=\"diffchange diffchange-inline\">svg|r\u00e1m|st\u0159ed|Obr</ins>.<ins class=\"diffchange diffchange-inline\">3: Zm\u011bna m\u011b\u0159\u00edtka - \u010cerven\u00e1 k\u0159ivka je v\u00fdsledkem zv\u011bt\u0161en\u00ed p\u016fvodn\u00ed modr\u00e9 k\u0159ivky, zelen\u00e1 pak jej\u00edm zmen\u0161en\u00edm</ins>.<ins class=\"diffchange diffchange-inline\"><br </ins>/<ins class=\"diffchange diffchange-inline\">></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u010cerven\u00e1 k\u0159ivka</ins>: <ins class=\"diffchange diffchange-inline\">Scale X = Scale Y = 1,2<br </ins>/<ins class=\"diffchange diffchange-inline\">></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Zelen\u00e1 k\u0159ivka: Scale X = Scale Y = 0,45]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Skl\u00e1d\u00e1n\u00ed transformac\u00ed ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">P\u0159i postupn\u00e9m aplikov\u00e1n\u00ed transformac\u00ed na bod ''P'' z\u00e1le\u017e\u00ed na po\u0159ad\u00ed, v jak\u00e9m se transformace prov\u00e1d\u011bj\u00ed.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Je rozd\u00edl, jestli\u017ee bod posuneme a pot\u00e9 oto\u010d\u00edme okolo po\u010d\u00e1tku sou\u0159adnicov\u00e9ho syst\u00e9mu, nebo zda bod nejprve oto\u010d\u00edme a pot\u00e9 provedeme transformaci posunut\u00ed.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Transformaci vzniklou slo\u017een\u00edm z v\u00edce transformac\u00ed lze vyj\u00e1d\u0159it jedinou matic\u00ed, kterou z\u00edsk\u00e1me postupn\u00fdm n\u00e1soben\u00edm matic, reprezentuj\u00edc\u00edch d\u00edl\u010d\u00ed transformace.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Proto\u017ee z\u00e1le\u017e\u00ed na po\u0159ad\u00ed transformac\u00ed, z\u00e1le\u017e\u00ed i na po\u0159ad\u00ed n\u00e1soben\u00ed matic. Jeliko\u017e pou\u017e\u00edv\u00e1me z\u00e1pis ''P'=P'''A''' '', mus\u00edme matice reprezentuj\u00edc\u00ed jednotliv\u00e9 transformace n\u00e1sobit zprava.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Plat\u00ed, \u017ee pokud n\u00e1sob\u00edme transforma\u010dn\u00ed matici, matic\u00ed k n\u00ed inverzn\u00ed, dostaneme p\u016fvodn\u00ed (netransformovan\u00e9) sou\u0159adnice</ins>. <ins class=\"diffchange diffchange-inline\">Jinak \u0159e\u010deno inverzn\u00ed transformace je reprezentov\u00e1na inverzn\u00ed matic\u00ed</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">''P\u0159\u00edklad''</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Odvozen\u00ed transforma\u010dn\u00ed matice pro ot\u00e1\u010den\u00ed o \u00fahel \u03b1 okolo bodu R[x<sub>R<</ins>/<ins class=\"diffchange diffchange-inline\">sub></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">,y<sub>R<</ins>/<ins class=\"diffchange diffchange-inline\">sub>]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Operaci provedeme n\u00e1sleduj\u00edc\u00edm zp\u016fsobem</ins>: <ins class=\"diffchange diffchange-inline\">bod ''R'' nejprve p\u0159em\u00edst\u00edme pomoc\u00ed matice '''A'''<sub>M</sub> do po\u010d\u00e1tku sou\u0159adnicov\u00e9ho syst\u00e9mu, pot\u00e9 provedeme oto\u010den\u00ed o \u00fahel \u03b1 pomoc\u00ed matice '''A'''<sub>R<</ins>/<ins class=\"diffchange diffchange-inline\">sub> a nakonec bod p\u0159em\u00edst\u00edme zp\u011bt </ins>do <ins class=\"diffchange diffchange-inline\">p\u016fvodn\u00ed polohy inverzn\u00ed matice '''A'''<sup>-1</sup><sub>M</sub>. V\u0161e provedeme tak, \u017ee vytvo\u0159\u00edme matici, kter\u00e1 vznikne slo\u017een\u00edm matic vyjad\u0159uj\u00edc\u00edch v\u0161echny t\u0159i operace. V\u00fdsledn\u00e1 matice je sou\u010din</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">A=A_MA_RA_M^{-1}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"></math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">''(Pozn. V\u00fd\u0161e uveden\u00e9 vztahy a vzorce jsou vzta\u017eeny ke 2D. Jejich 3D verze jsou podobn\u00e9 a z nich lehce odvoditeln\u00e9.)''</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Auto\u0159i ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Tento text vypracovali studenti </ins>[<ins class=\"diffchange diffchange-inline\">http</ins>://www.<ins class=\"diffchange diffchange-inline\">inf</ins>.<ins class=\"diffchange diffchange-inline\">upol.cz Univerzity Palack\u00e9ho v Olomouci] katedry Matematick\u00e9 informatiky jako z\u00e1po\u010dtov\u00fd \u00fakol do p\u0159edm\u011btu Po\u010d\u00edta\u010dov\u00e1 geometrie.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Kategorie</ins>:<ins class=\"diffchange diffchange-inline\">Geometrie|Afinn\u00ed transformace sou\u0159adnic]</ins>]</div></td></tr>\n"
}
}