Published
Edited
Nov 28, 2020
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Math
// Make a list of plane meshes for Calabi-Yau Manifold
calabiYau = function(n, a) {
function coordinate(x, y, n, k1, k2, a) {
const z1 = math.multiply(
math.exp(math.complex(0, 2*math.PI*k1/n)),
math.pow(math.cos(math.complex(x, y)), 2/n)
);
const z2 = math.multiply(
math.exp(math.complex(0, 2*math.PI*k2/n)),
math.pow(math.sin(math.complex(x, y)), 2/n)
);
return new THREE.Vector3(z1.re, z2.re, z1.im*math.cos(a) + z2.im*math.sin(a));
}
const dx = math.PI/10;
const dy = math.PI/10;
const meshes = [];
d3.cross(d3.range(n), d3.range(n)).forEach(k => {
d3.range(0, math.PI/2, dx).forEach(x => {
d3.range(-math.PI/2, math.PI/2, dy).forEach(y => {
const data = [
{"x": x, "y": y },
{"x": x+dx, "y": y },
{"x": x+dx, "y": y+dy},
{"x": x, "y": y+dy},
];
meshes.push(normalRect(
...data.map(d => coordinate(d.x, d.y, n, k[0], k[1], a))
));
});
});
});
return meshes;
};
// Make a Plane mesh with Normal Material
normalRect = function(v1, v2, v3, v4) {
// material
const normalMaterial = new THREE.MeshNormalMaterial({
side: THREE.DoubleSide
})
// mesh
return rect(v1, v2, v3, v4, normalMaterial);
}
// Make a Plane mesh with specified Material
rect = function(v1, v2, v3, v4, material) {
const planeGeometry = new THREE.Geometry();
// add vertices
[v1, v2, v3, v4].forEach(v => planeGeometry.vertices.push(v));
// add faces
planeGeometry.faces.push(new THREE.Face3(0, 1, 2));
planeGeometry.faces.push(new THREE.Face3(2, 3, 0));
planeGeometry.computeFaceNormals();
// mesh
const plane = new THREE.Mesh( planeGeometry, material );
return plane;
}
scene = {
const scene = new THREE.Scene();
scene.background = new THREE.Color(0xffffff);
calabiYau(exponent, projection).forEach(m => scene.add(m));
return scene;
}
camera = {
const fov = 45;
const aspect = width / height;
const near = 1;
const far = 1000;
const camera = new THREE.PerspectiveCamera(fov, aspect, near, far);
camera.position.set(7, 0, 0)
camera.lookAt(new THREE.Vector3(0, 0, 0));
return camera;
}
height = 500
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