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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title>MathBox - Scatterplot</title>
<script src="./vendor/mathbox-bundle.min.js"></script>
<link rel="stylesheet" href="./vendor/mathbox.css" />
<meta name="viewport" content="initial-scale=1, maximum-scale=1" />
</head>
<body>
<script>
// D3Q27 lattice node model
var ortho = 10000;
mathbox = mathBox({
plugins: ["core", "controls", "cursor", "mathbox"],
controls: {
klass: THREE.OrbitControls,
},
camera: {
fov: (Math.atan(1 / ortho) * 360) / π,
near: ortho / 4,
far: ortho * 4,
},
});
if (mathbox.fallback) throw "WebGL not supported";
three = mathbox.three;
three.renderer.setClearColor(new THREE.Color(255, 255, 255), 1.0);
var colors = {
red: 0xff4136, // red
yellow: 0xffdc00, // yellow
blue: 0x0074d9, // blue
orange: 0xff851b, // orange
purple: 0xb10dc9, // purple
green: 0x2ecc40, // green
brown: 0x654321, // brown
};
// Place camera
var camera = mathbox
.set({
focus: ortho,
scale: 720,
})
.camera({
proxy: true,
position: [ortho / 3, ortho / 1.8, ortho * 1.6],
rotation: [0, 0, 0],
});
var view = mathbox.cartesian({
range: [
[-4, 4],
[-4, 4],
[-4, 4],
],
scale: [1, 1, 1],
});
// mathbox.set({ scale: 200, focus: 1 });
let ex = [
0,
1,
-1,
0,
0,
0,
0,
1,
-1,
1,
-1,
1,
-1,
1,
-1,
0,
0,
0,
0,
1,
-1,
1,
-1,
1,
-1,
1,
-1,
];
let ey = [
0,
0,
0,
1,
-1,
0,
0,
1,
1,
-1,
-1,
0,
0,
0,
0,
1,
-1,
1,
-1,
1,
1,
-1,
-1,
1,
1,
-1,
-1,
];
let ez = [
0,
0,
0,
0,
0,
1,
-1,
0,
0,
0,
0,
1,
1,
-1,
-1,
1,
1,
-1,
-1,
1,
1,
1,
1,
-1,
-1,
-1,
-1,
];
let e = [];
for (var i = 1; i < 27; i++) {
e.push([0, 0, 0]); // start point
e.push([ex[i] * 4, ez[i] * 4, ey[i] * 4]); // end point
}
// Right
view
.volume({
data: [
[ex[1] * 4, ez[1] * 4, ey[1] * 4],
[ex[9] * 4, ez[9] * 4, ey[9] * 4],
[ex[21] * 4, ez[21] * 4, ey[21] * 4],
[ex[11] * 4, ez[11] * 4, ey[11] * 4],
[ex[13] * 4, ez[13] * 4, ey[13] * 4],
[ex[25] * 4, ez[25] * 4, ey[25] * 4],
[ex[9] * 4, ez[9] * 4, ey[9] * 4],
[ex[7] * 4, ez[7] * 4, ey[7] * 4],
[ex[19] * 4, ez[19] * 4, ey[19] * 4],
[ex[11] * 4, ez[11] * 4, ey[11] * 4],
[ex[13] * 4, ez[13] * 4, ey[13] * 4],
[ex[23] * 4, ez[23] * 4, ey[23] * 4],
[ex[23] * 4, ez[23] * 4, ey[23] * 4],
[ex[19] * 4, ez[19] * 4, ey[19] * 4],
[ex[19] * 4, ez[19] * 4, ey[19] * 4],
],
width: 4,
height: 4,
depth: 4,
channels: 3,
items: 1,
live: false,
})
.line({ color: colors.brown, width: 4, opacity: 0.5 });
// Left
view
.volume({
data: [
[ex[2] * 4, ez[2] * 4, ey[2] * 4],
[ex[10] * 4, ez[10] * 4, ey[10] * 4],
[ex[22] * 4, ez[22] * 4, ey[22] * 4],
[ex[12] * 4, ez[12] * 4, ey[12] * 4],
[ex[14] * 4, ez[14] * 4, ey[14] * 4],
[ex[26] * 4, ez[26] * 4, ey[26] * 4],
[ex[10] * 4, ez[10] * 4, ey[10] * 4],
[ex[8] * 4, ez[8] * 4, ey[8] * 4],
[ex[20] * 4, ez[20] * 4, ey[20] * 4],
[ex[12] * 4, ez[12] * 4, ey[12] * 4],
[ex[14] * 4, ez[14] * 4, ey[14] * 4],
[ex[24] * 4, ez[24] * 4, ey[24] * 4],
[ex[24] * 4, ez[24] * 4, ey[24] * 4],
[ex[20] * 4, ez[20] * 4, ey[20] * 4],
[ex[20] * 4, ez[20] * 4, ey[20] * 4],
],
width: 4,
height: 4,
depth: 4,
channels: 3,
items: 1,
live: false,
})
.line({ color: colors.brown, width: 4, opacity: 0.5 });
// Front
view
.volume({
data: [
[ex[3] * 4, ez[3] * 4, ey[3] * 4],
[ex[7] * 4, ez[7] * 4, ey[7] * 4],
[ex[19] * 4, ez[19] * 4, ey[19] * 4],
[ex[15] * 4, ez[15] * 4, ey[15] * 4],
[ex[17] * 4, ez[17] * 4, ey[17] * 4],
[ex[23] * 4, ez[23] * 4, ey[23] * 4],
[ex[23] * 4, ez[23] * 4, ey[23] * 4],
[ex[24] * 4, ez[24] * 4, ey[24] * 4],
[ex[24] * 4, ez[24] * 4, ey[24] * 4],
[ex[20] * 4, ez[20] * 4, ey[20] * 4],
[ex[19] * 4, ez[19] * 4, ey[19] * 4],
[ex[7] * 4, ez[7] * 4, ey[7] * 4],
[ex[8] * 4, ez[8] * 4, ey[8] * 4],
[ex[3] * 4, ez[3] * 4, ey[3] * 4],
[ex[3] * 4, ez[3] * 4, ey[3] * 4],
[ex[8] * 4, ez[8] * 4, ey[8] * 4],
[ex[20] * 4, ez[20] * 4, ey[20] * 4],
[ex[15] * 4, ez[15] * 4, ey[15] * 4],
[ex[17] * 4, ez[17] * 4, ey[17] * 4],
[ex[24] * 4, ez[24] * 4, ey[24] * 4],
[ex[17] * 4, ez[17] * 4, ey[17] * 4],
[ex[17] * 4, ez[17] * 4, ey[17] * 4],
],
width: 4,
height: 4,
depth: 4,
channels: 3,
items: 1,
live: false,
})
.line({ color: colors.brown, width: 4, opacity: 0.5 });
// Back
view
.volume({
data: [
[ex[4] * 4, ez[4] * 4, ey[4] * 4],
[ex[9] * 4, ez[9] * 4, ey[9] * 4],
[ex[21] * 4, ez[21] * 4, ey[21] * 4],
[ex[16] * 4, ez[16] * 4, ey[16] * 4],
[ex[4] * 4, ez[4] * 4, ey[4] * 4],
[ex[18] * 4, ez[18] * 4, ey[18] * 4],
[ex[25] * 4, ez[25] * 4, ey[25] * 4],
[ex[9] * 4, ez[9] * 4, ey[9] * 4],
[ex[4] * 4, ez[4] * 4, ey[4] * 4],
[ex[10] * 4, ez[10] * 4, ey[10] * 4],
[ex[26] * 4, ez[26] * 4, ey[26] * 4],
[ex[18] * 4, ez[18] * 4, ey[18] * 4],
[ex[16] * 4, ez[16] * 4, ey[16] * 4],
[ex[22] * 4, ez[22] * 4, ey[22] * 4],
[ex[16] * 4, ez[16] * 4, ey[16] * 4],
[ex[22] * 4, ez[22] * 4, ey[22] * 4],
[ex[10] * 4, ez[10] * 4, ey[10] * 4],
[ex[9] * 4, ez[9] * 4, ey[9] * 4],
[ex[4] * 4, ez[4] * 4, ey[4] * 4],
[ex[16] * 4, ez[16] * 4, ey[16] * 4],
[ex[16] * 4, ez[16] * 4, ey[16] * 4],
[ex[4] * 4, ez[4] * 4, ey[4] * 4],
[ex[10] * 4, ez[10] * 4, ey[10] * 4],
[ex[10] * 4, ez[10] * 4, ey[10] * 4],
[ex[22] * 4, ez[22] * 4, ey[22] * 4],
[ex[16] * 4, ez[16] * 4, ey[16] * 4],
[ex[16] * 4, ez[16] * 4, ey[16] * 4],
[ex[21] * 4, ez[21] * 4, ey[21] * 4],
[ex[25] * 4, ez[25] * 4, ey[25] * 4],
[ex[18] * 4, ez[18] * 4, ey[18] * 4],
[ex[18] * 4, ez[18] * 4, ey[18] * 4],
],
width: 4,
height: 4,
depth: 4,
channels: 3,
items: 1,
live: false,
})
.line({ color: colors.brown, width: 4, opacity: 0.5 });
// Top
view
.volume({
data: [
[ex[15] * 4, ez[15] * 4, ey[15] * 4],
[ex[5] * 4, ez[5] * 4, ey[5] * 4],
[ex[16] * 4, ez[16] * 4, ey[16] * 4],
[ex[21] * 4, ez[21] * 4, ey[21] * 4],
[ex[11] * 4, ez[11] * 4, ey[11] * 4],
[ex[5] * 4, ez[5] * 4, ey[5] * 4],
[ex[12] * 4, ez[12] * 4, ey[12] * 4],
[ex[11] * 4, ez[11] * 4, ey[11] * 4],
[ex[19] * 4, ez[19] * 4, ey[19] * 4],
[ex[20] * 4, ez[20] * 4, ey[20] * 4],
[ex[12] * 4, ez[12] * 4, ey[12] * 4],
[ex[12] * 4, ez[12] * 4, ey[12] * 4],
[ex[11] * 4, ez[11] * 4, ey[11] * 4],
[ex[11] * 4, ez[11] * 4, ey[11] * 4],
],
width: 4,
height: 4,
depth: 4,
channels: 3,
items: 1,
live: false,
})
.line({ color: colors.brown, width: 4, opacity: 0.5 });
// Bottom
view
.volume({
data: [
[ex[17] * 4, ez[17] * 4, ey[17] * 4],
[ex[6] * 4, ez[6] * 4, ey[6] * 4],
[ex[18] * 4, ez[18] * 4, ey[18] * 4],
[ex[25] * 4, ez[25] * 4, ey[25] * 4],
[ex[13] * 4, ez[13] * 4, ey[13] * 4],
[ex[14] * 4, ez[14] * 4, ey[14] * 4],
[ex[14] * 4, ez[14] * 4, ey[14] * 4],
[ex[24] * 4, ez[24] * 4, ey[24] * 4],
[ex[23] * 4, ez[23] * 4, ey[23] * 4],
[ex[13] * 4, ez[13] * 4, ey[13] * 4],
[ex[13] * 4, ez[13] * 4, ey[13] * 4],
[ex[14] * 4, ez[14] * 4, ey[14] * 4],
[ex[14] * 4, ez[14] * 4, ey[14] * 4],
[ex[13] * 4, ez[13] * 4, ey[13] * 4],
],
width: 4,
height: 4,
depth: 4,
channels: 3,
items: 1,
live: false,
})
.line({ color: colors.brown, width: 4, opacity: 0.5 });
// Center
var vector = view
.array({
data: [[0, 0, 0]],
width: 1,
channels: 3,
items: 2,
})
.point({
color: colors.red,
size: 30,
})
.text({
aligned: true,
data: ["0"],
})
.label({
offset: [20, 10],
zIndex: 1,
color: "black",
size: 20
});
// nearest neighbors
let nn = e.slice(0, 12);
var vector = view
.array({
data: nn,
width: nn.length,
channels: 3,
items: 2,
})
.vector({
end: true,
width: 8,
color: colors.green,
})
.text({
items: 2,
data: ["", "1", "", "2", "", "3", "", "4", "", "5", "", "6"],
})
.label({
offset: [10, 10],
zIndex: 1,
color: "black",
size: 20
});
// next-nearest neighbors
let nnn = e.slice(12, 36);
var vector = view
.array({
data: nnn,
width: nnn.length,
channels: 3,
items: 2,
})
.vector({
end: true,
width: 8,
color: colors.blue,
})
.text({
items: 2,
data: [
"",
"7",
"",
"8",
"",
"9",
"",
"10",
"",
"11",
"",
"12",
"",
"13",
"",
"14",
"",
"15",
"",
"16",
"",
"17",
"",
"18",
],
})
.label({
offset: [10, 10],
zIndex: 1,
color: "black",
size: 20
});
// next to next-nearest neighbors
let nnnn = e.slice(36, 52);
var vector = view
.array({
data: nnnn,
width: nnnn.length,
channels: 3,
items: 2,
live: false,
})
.vector({
end: true,
width: 8,
color: colors.purple,
})
.text({
aligned: false,
items: 2,
data: [
"",
"19",
"",
"20",
"",
"21",
"",
"22",
"",
"23",
"",
"24",
"",
"25",
"",
"26",
],
})
.label({
offset: [10, 10],
zIndex: 1,
color: "black",
size: 20
});
</script>
</body>
</html>