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catmullClark.html
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<!DOCTYPE html>
<html lang="cs-cz">
<head>
<meta charset="UTF-8">
<meta content="width=device-width, initial-scale=1.0" name="viewport">
<title>Catmull-Clark subdivision</title>
<script charset="UTF-8" src="jsxgraphcore.js" type="text/javascript"></script>
<link href="jsxgraph.css" rel="stylesheet" type="text/css"/>
<link href="darkModeStyle.css" rel="stylesheet" type="text/css"/>
<link href="appletStyle.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<header>
<div class="header1"><h1>Catmull-Clark subdivision</h1></div>
<div class="user-toggle">
<div class="[ visually-hidden ][ js-mode-status ]" role="status"></div>
<button class="[ toggle-button ] [ js-mode-toggle ]">
<span class="[ toggle-button__text ] [ js-mode-toggle-text ]">Tmavý režim</span>
<span aria-hidden="true" class="toggle-button__icon"></span>
</button>
</div>
<script charset="UTF-8" src="darkMode.js" type="text/javascript"></script>
</header>
<p>
<div class='jxgbox' id='jxgbox1' style='float: left; width:300px; height:300px;'></div>
<div class='jxgbox' id='jxgbox2' style='float: left; width:300px; height:300px;'></div>
<div class='jxgbox' id='jxgbox3' style='float: left; width:300px; height:300px;'></div>
<div class='jxgbox' id='jxgbox4' style='float: left; width:300px; height:300px;'></div>
<script type='text/javascript'>
var velZarovnani = 4;
var zarovnani = [-velZarovnani, velZarovnani, velZarovnani, -velZarovnani]
var board = JXG.JSXGraph.initBoard('jxgbox1', {
boundingbox: zarovnani,
showNavigation: false,
showCopyright: false,
keepaspectratio: true,
zoom: {enabled: false},
pan: {enabled: false},
axis: true,
width: 700,
height: 400
});
var board2 = JXG.JSXGraph.initBoard('jxgbox2', {
boundingbox: zarovnani,
showNavigation: false,
showCopyright: false,
keepaspectratio: true,
zoom: {enabled: false},
pan: {enabled: false},
axis: true,
width: 700,
height: 400
});
var board3 = JXG.JSXGraph.initBoard('jxgbox3', {
boundingbox: zarovnani,
showNavigation: false,
showCopyright: false,
keepaspectratio: true,
zoom: {enabled: false},
pan: {enabled: false},
axis: true,
width: 700,
height: 400
});
var board4 = JXG.JSXGraph.initBoard('jxgbox4', {
boundingbox: zarovnani,
showNavigation: false,
showCopyright: false,
keepaspectratio: true,
zoom: {enabled: false},
pan: {enabled: false},
axis: true,
width: 700,
height: 400
});
var matice = [
[[-3, 3], [3, 3]],
[[-3, -3], [3, -3]]
];
var p = []; //body (points)
var p2 = [];
var p3 = [];
var p4 = [];
var l = []; //čáry (lines)
var l2 = [];
var l3 = [];
var l4 = [];
var prumerBodu = function (bodA, bodB, bodC, bodD, korekce) {
if (korekce) {
return [(bodA[0] + bodB[0] + bodC[0] + bodD[0]*korekce) / 4, (bodA[1] + bodB[1] + bodC[1] + bodD[1]*korekce) / 4];
} else if (bodD) {
return [(bodA[0] + bodB[0] + bodC[0] + bodD[0]) / 4, (bodA[1] + bodB[1] + bodC[1] + bodD[1]) / 4];
} else if (bodC) {
return [(bodA[0] + bodB[0] + bodC[0]) / 3, (bodA[1] + bodB[1] + bodC[1]) / 3];
} else if (bodB) {
return [(bodA[0] + bodB[0]) / 2, (bodA[1] + bodB[1]) / 2];
} else {
return [bodA[0], bodA[1]];
}
};
var pocetBodu = function (matice) {
var pocitadlo = 0;
for (var i = 0; i < matice.length; i++) {
pocitadlo = pocitadlo + matice[i].length;
}
return pocitadlo;
};
var soucetBodu = function (matice) {
var soucet = [0, 0];
for (var i = 0; i < matice.length; i++) {
for (var j = 0; j < matice[i].length; j++) {
soucet[0] += matice[i][j][0];
soucet[1] += matice[i][j][1];
}
}
return soucet;
};
var prevodPole1D2D = function (matice) {
//var vysledek = [[[], []], [[], []]];
var vysledek;
if (matice.length === 4) {
vysledek = [[[], []], [[], []]];
}
var pocitadlo = 0;
for (var i = 0; i < (matice.length / 2); i++) {
for (var j = 0; j < (matice.length / 2); j++) {
vysledek[i][j] = matice[pocitadlo];
pocitadlo++;
}
}
return vysledek;
};
var rozdelMaticiNa4 = function (matice, kterouMatici) {
if (matice.length === 3) {
switch (kterouMatici) {
case 0:
return [[matice[0][0], matice[0][1]], [matice[1][0], matice[1][1]]];
case 1:
return [[matice[0][1], matice[0][2]], [matice[1][1], matice[1][2]]];
case 2:
return [[matice[1][0], matice[1][1]], [matice[2][0], matice[2][1]]];
case 3:
return [[matice[1][1], matice[1][2]], [matice[2][1], matice[2][2]]];
default:
return [
[[matice[0][0], matice[0][1]], [matice[1][0], matice[1][1]]],
[[matice[0][1], matice[0][2]], [matice[1][1], matice[1][2]]],
[[matice[1][0], matice[1][1]], [matice[2][0], matice[2][1]]],
[[matice[1][1], matice[1][2]], [matice[2][1], matice[2][2]]]
];
}
} else {
return [
[[matice[0][0], matice[0][1], matice[0][2]], [matice[1][0], matice[1][1], matice[1][2]], [matice[2][0], matice[2][1], matice[2][2]]],
[[matice[0][2], matice[0][3], matice[0][4]], [matice[1][2], matice[1][3], matice[1][4]], [matice[2][2], matice[2][3], matice[2][4]]],
[[matice[2][0], matice[2][1], matice[2][2]], [matice[3][0], matice[3][1], matice[3][2]], [matice[4][0], matice[4][1], matice[4][2]]],
[[matice[2][2], matice[2][3], matice[2][4]], [matice[3][2], matice[3][3], matice[3][4]], [matice[4][2], matice[4][3], matice[4][4]]]
];
}
};
var zapisBody = function () {
var pocitadlo = 0;
for (var i = 0; i < matice.length; i++) {
for (var j = 0; j < matice[i].length; j++) {
matice[i][j][0] = p[pocitadlo].X();
matice[i][j][1] = p[pocitadlo].Y();
pocitadlo++;
}
}
};
var vykresliBody = function (board, matice, p, zamek) {
for (var i = 0; i < matice.length; i++) {
for (var j = 0; j < matice[i].length; j++) {
p.push(board.create('point', [matice[i][j][0], matice[i][j][1]], {
name: '',
fixed: zamek, label: {visible: false}
}));
}
}
};
var smazBody = function (board, p) {
board.suspendUpdate();
var i = p.length;
while (i >= 0) {
board.removeObject(p[p.length - i]);
i--;
}
p = [];
board.unsuspendUpdate();
};
var vykresliCary = function (board, matice, l) {
for (var i = 1; i < matice.length; i++) {
for (var j = 1; j < matice[i].length; j++) {
l.push(board.create('segment', [[matice[i - 1][j - 1][0], matice[i - 1][j - 1][1]], [matice[i - 1][j][0], matice[i - 1][j][1]]], {
strokeOpacity: 1,
fixed: true
}));
l.push(board.create('segment', [[matice[i - 1][j - 1][0], matice[i - 1][j - 1][1]], [matice[i][j - 1][0], matice[i][j - 1][1]]], {
strokeOpacity: 1,
fixed: true
}));
l.push(board.create('segment', [[matice[i][j - 1][0], matice[i][j - 1][1]], [matice[i][j][0], matice[i][j][1]]], {
strokeOpacity: 1,
fixed: true
}));
l.push(board.create('segment', [[matice[i - 1][j][0], matice[i - 1][j][1]], [matice[i][j][0], matice[i][j][1]]], {
strokeOpacity: 1,
fixed: true
}))
}
}
};
var smazCary = function (board, l) {
board.suspendUpdate();
var i = l.length;
while (i >= 0) {
board.removeObject(l[l.length - i]);
i--;
}
l = [];
board.unsuspendUpdate();
};
var vypocetF = function (matice) {
var pocetB = pocetBodu(matice);
var soucet = soucetBodu(matice);
if (matice.length < 3) {
// F - vrchol (středový)
soucet[0] = (1 / pocetB) * soucet[0];
soucet[1] = (1 / pocetB) * soucet[1];
} else {
var matRozdelena = rozdelMaticiNa4(matice);
for (var i = 0; i < matRozdelena.length; i++) {
soucet[i] = vypocetF(matRozdelena[i]);
}
soucet = prevodPole1D2D(soucet);
}
return soucet;
};
var vypocetE = function (matice, fVrchol) {
var vysledek = [];
vysledek.splice(matice);
if (matice.length < 3) {
var vysledekA = [((matice[0][0][0] + matice[0][1][0]) / 2), ((matice[0][0][1] + matice[0][1][1]) / 2)];
var vysledekB = [((matice[0][0][0] + matice[1][0][0]) / 2), ((matice[0][0][1] + matice[1][0][1]) / 2)];
var vysledekC = [((matice[0][1][0] + matice[1][1][0]) / 2), ((matice[0][1][1] + matice[1][1][1]) / 2)];
var vysledekD = [((matice[1][0][0] + matice[1][1][0]) / 2), ((matice[1][0][1] + matice[1][1][1]) / 2)];
vysledek = [[vysledekA, vysledekB], [vysledekC, vysledekD]];
} else {
var matRozdelena = rozdelMaticiNa4(matice);
for (var i = 0; i < matRozdelena.length; i++) {
vysledek[i] = vypocetE(matRozdelena[i]);
}
vysledek = prevodPole1D2D(vysledek);
}
return vysledek;
};
var vypocetV = function (matice, matE, matF) {
var pocetBoduMatice = pocetBodu(matice);
var n = pocetBoduMatice, q = [], r = [], s = [];
// (Q - průměr okolních F bodů)/4 + 2*(R - průměr okolních středových E bodů)/4 + (S - původní vrchol)/4
if (pocetBoduMatice === 4) {
var vysledekA = [matice[0][0][0] / pocetBoduMatice + 2 * ((matE[0][1][0] + matE[0][0][0]) / 2) / pocetBoduMatice + (matice[0][0][0] * (pocetBoduMatice - 3)) / pocetBoduMatice,
matice[0][0][1] / pocetBoduMatice + 2 * ((matE[0][1][1] + matE[0][0][1]) / 2) / pocetBoduMatice + (matice[0][0][1] * (pocetBoduMatice - 3)) / pocetBoduMatice];
var vysledekB = [matice[0][1][0] / pocetBoduMatice + 2 * ((matE[0][0][0] + matE[1][0][0]) / 2) / pocetBoduMatice + (matice[0][1][0] * (pocetBoduMatice - 3)) / pocetBoduMatice,
matice[0][1][1] / pocetBoduMatice + 2 * ((matE[0][0][1] + matE[1][0][1]) / 2) / pocetBoduMatice + (matice[0][1][1] * (pocetBoduMatice - 3)) / pocetBoduMatice];
var vysledekC = [matice[1][0][0] / pocetBoduMatice + 2 * ((matE[0][1][0] + matE[1][1][0]) / 2) / pocetBoduMatice + (matice[1][0][0] * (pocetBoduMatice - 3)) / pocetBoduMatice,
matice[1][0][1] / pocetBoduMatice + 2 * ((matE[0][1][1] + matE[1][1][1]) / 2) / pocetBoduMatice + (matice[1][0][1] * (pocetBoduMatice - 3)) / pocetBoduMatice];
var vysledekD = [matice[1][1][0] / pocetBoduMatice + 2 * ((matE[1][0][0] + matE[1][1][0]) / 2) / pocetBoduMatice + (matice[1][1][0] * (pocetBoduMatice - 3)) / pocetBoduMatice,
matice[1][1][1] / pocetBoduMatice + 2 * ((matE[1][0][1] + matE[1][1][1]) / 2) / pocetBoduMatice + (matice[1][1][1] * (pocetBoduMatice - 3)) / pocetBoduMatice];
return [[vysledekA, vysledekB],
[vysledekC, vysledekD]];
}
};
var provedSubdivision = function (matice) {
var fVrchol = vypocetF(matice);
var eVrchol = vypocetE(matice, fVrchol);
var vVrchol = vypocetV(matice, eVrchol, fVrchol);
return [[vVrchol[0][0], eVrchol[0][0], vVrchol[0][1]],
[eVrchol[0][1], fVrchol, eVrchol[1][0]],
[vVrchol[1][0], eVrchol[1][1], vVrchol[1][1]]];
};
var provedSubdivision2 = function (matice) {
var fVrchol = vypocetF(matice);
var eVrchol = vypocetE(matice, fVrchol);
var rozdelenaMatice = rozdelMaticiNa4(matice);
var prevedenaMatice = prevodPole1D2D(rozdelenaMatice);
var vVrchol = [[], []];
for (var i = 0; i < (matice.length / 2); i++) {
for (var j = 0; j < (matice.length / 2); j++) {
vVrchol[i][j] = vypocetV(prevedenaMatice[i][j], eVrchol[i][j], fVrchol[i][j]);//???
}
}
var vyslednaMatice = [
[vVrchol[0][0][0][0], eVrchol[0][0][0][0], prumerBodu(vVrchol[0][0][0][1], vVrchol[0][1][0][0], matice[0][1], matice[0][1]), eVrchol[0][1][0][0], vVrchol[0][1][0][1]],
[eVrchol[0][0][0][1], fVrchol[0][0], eVrchol[0][0][1][0], fVrchol[0][1], eVrchol[0][1][1][0]],
[prumerBodu(vVrchol[0][0][1][0], vVrchol[1][0][0][0], matice[1][0], matice[1][0]), eVrchol[0][0][1][1], matice[1][1], eVrchol[0][1][1][1], prumerBodu(vVrchol[0][1][1][1], vVrchol[1][1][0][1], matice[1][2], matice[1][2])],
[eVrchol[1][0][0][1], fVrchol[1][0], eVrchol[1][0][1][0], fVrchol[1][1], eVrchol[1][1][1][0]],
[vVrchol[1][0][1][0], eVrchol[1][0][1][1], prumerBodu(vVrchol[1][0][1][1], vVrchol[1][1][1][0], matice[2][1], matice[2][1]), eVrchol[1][1][1][1], vVrchol[1][1][1][1]]
];
return vyslednaMatice;
};
var provedSubdivision3 = function (matice) {
var rozdelenaMatice = rozdelMaticiNa4(matice);
var fVrchol = [];
var eVrchol = [];
var vCM = [];
for (var i = 0; i < rozdelenaMatice.length; i++) {
fVrchol[i] = vypocetF(rozdelenaMatice[i]);
eVrchol[i] = vypocetE(rozdelenaMatice[i], fVrchol[i]);
vCM[i] = provedSubdivision2(rozdelenaMatice[i]);
}
var vyslednaMatice = [];
for (var i = 0; i < 10; i++) {
if (i < 5) {
vyslednaMatice[i] = vCM[0][i].concat(vCM[1][i]);
} else {
vyslednaMatice[i] = vCM[2][i - 5].concat(vCM[3][i - 5]);
}
}
var stred = prumerBodu(vyslednaMatice[4][4], vyslednaMatice[4][5], vyslednaMatice[5][4], vyslednaMatice[5][5]);
var vrch = prumerBodu(vyslednaMatice[0][4], vyslednaMatice[0][5], matice[0][2], matice[0][2], 1.1);
var leva = prumerBodu(vyslednaMatice[4][0], vyslednaMatice[5][0], matice[2][0], matice[2][0], 1.1);
var prava = prumerBodu(vyslednaMatice[4][9], vyslednaMatice[5][9], matice[2][4], matice[2][4], 1.1);
var spodek = prumerBodu(vyslednaMatice[9][4], vyslednaMatice[9][5], matice[4][2], matice[4][2], 1.1);
for (var i = 0; i < 10; i++) {
vyslednaMatice[i][4] = prumerBodu(vyslednaMatice[i][4], vyslednaMatice[i][5]);
vyslednaMatice[4][i] = prumerBodu(vyslednaMatice[4][i], vyslednaMatice[5][i]);
}
for (var i = 0; i < 10; i++) {
vyslednaMatice[i].splice(5, 1);
}
vyslednaMatice.splice(5, 1);
vyslednaMatice[4][4] = stred;
vyslednaMatice[0][4] = vrch;
vyslednaMatice[4][0] = leva;
vyslednaMatice[4][8] = prava;
vyslednaMatice[8][4] = spodek;
return vyslednaMatice;
};
var provedHlavni = function (){
vykresliCary(board, matice, l);
var mat2 = provedSubdivision(matice);
vykresliBody(board2, mat2, p2, true);
vykresliCary(board2, mat2, l2);
var mat3 = provedSubdivision2(mat2);
vykresliBody(board3, mat3, p3, true);
vykresliCary(board3, mat3, l3);
var mat4 = provedSubdivision3(mat3);
vykresliBody(board4, mat4, p4, true);
vykresliCary(board4, mat4, l4);
};
var smazHlavni = function (){
smazCary(board, l);
smazCary(board2, l2);
smazBody(board2, p2);
smazCary(board3, l3);
smazBody(board3, p3);
smazCary(board4, l4);
smazBody(board4, p4);
}
down = function (e) {
};
up = function (e) {
zapisBody(board, p);
smazHlavni();
provedHlavni();
};
board.on('down', down);
board.on('up', up);
vykresliBody(board, matice, p);
provedHlavni();
</script>
</p>
</body>
</html>