Created
May 20, 2018 11:11
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let mathjs = require("mathjs"); | |
function getRandomPointOnSphere() { | |
let o = 2 * Math.PI * Math.random(); | |
let a = Math.acos(2 * Math.random() - 1); | |
return { o, a }; | |
} | |
function polarToCarth(o) { | |
let x = Math.sin(o.o) * Math.cos(o.a); | |
let y = Math.sin(o.o) * Math.sin(o.a); | |
let z = Math.cos(o.o); | |
return [x, y, z]; | |
} | |
function run() { | |
let [x1, y1, z1] = polarToCarth(getRandomPointOnSphere()); | |
let [x2, y2, z2] = polarToCarth(getRandomPointOnSphere()); | |
let [x3, y3, z3] = polarToCarth(getRandomPointOnSphere()); | |
let [x4, y4, z4] = polarToCarth(getRandomPointOnSphere()); | |
let x = 0; | |
let y = 0; | |
let z = 0; | |
let d0 = mathjs.det([ | |
[x1, y1, z1, 1], | |
[x2, y2, z2, 1], | |
[x3, y3, z3, 1], | |
[x4, y4, z4, 1] | |
]); | |
let d1 = mathjs.det([ | |
[x, y, z, 1], | |
[x2, y2, z2, 1], | |
[x3, y3, z3, 1], | |
[x4, y4, z4, 1] | |
]); | |
let d2 = mathjs.det([ | |
[x1, y1, z1, 1], | |
[x, y, z, 1], | |
[x3, y3, z3, 1], | |
[x4, y4, z4, 1] | |
]); | |
let d3 = mathjs.det([ | |
[x1, y1, z1, 1], | |
[x2, y2, z2, 1], | |
[x, y, z, 1], | |
[x4, y4, z4, 1] | |
]); | |
let d4 = mathjs.det([ | |
[x1, y1, z1, 1], | |
[x2, y2, z2, 1], | |
[x3, y3, z3, 1], | |
[x, y, z, 1] | |
]); | |
if ( | |
(d0 >= 0 && d1 >= 0 && d2 >= 0 && d3 >= 0 && d4 >= 0) || | |
(d0 < 0 && d1 < 0 && d2 < 0 && d3 < 0 && d4 < 0) | |
) { | |
return true; | |
} else { | |
return false; | |
} | |
} | |
let yes = 0; | |
let no = 0; | |
for (var i = 0; i < 1000000; i++) { | |
if (i % 1000 == 0) { | |
console.log(i); | |
} | |
if (run()) { | |
yes++; | |
} else { | |
no++; | |
} | |
} | |
console.log(yes, no, yes / 1000000); |
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