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Commit 787fd66

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Carlos Martin
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Moved math helper functions for hyperbolic space to mathlib.js
1 parent 7d9a5a2 commit 787fd66

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3 files changed

+106
-122
lines changed

3 files changed

+106
-122
lines changed

‎hyperbolic/hyperbolic.html

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Original file line numberDiff line numberDiff line change
@@ -1,6 +1,7 @@
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<!DOCTYPE html>
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<html>
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<body>
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<script src="mathlib.js"></script>
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<script src="hyperbolic.js"></script>
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</body>
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</html>

‎hyperbolic/hyperbolic.js

-122
Original file line numberDiff line numberDiff line change
@@ -1,125 +1,3 @@
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var dimensions = 2;
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/* Returns the sum of two vectors */
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function sum(vector1, vector2) {
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var result = [];
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for (var i = 0; i < dimensions; ++i) {
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result[i] = vector1[i] + vector2[i];
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}
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return result;
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}
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/* Returns the difference of two vectors */
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function difference(vector1, vector2) {
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return sum(vector1, scale(vector2, -1));
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}
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/* Returns the metric tensor */
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function get_metric(position) {
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var factor = 1;
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for (var i = 0; i < dimensions; ++i) {
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factor -= position[i] * position[i];
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}
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var result = [];
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for (var i = 0; i < dimensions; ++i) {
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result[i] = [];
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for (var j = 0; j < dimensions; ++j) {
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if (i == j) {
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result[i][j] = 1/(factor * factor);
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} else {
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result[i][j] = 0;
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}
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}
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}
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return result;
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}
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/* Returns the connection coefficients (Christoffel symbols) */
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function get_connection(position) {
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var factor = 1;
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for (var i = 0; i < dimensions; ++i) {
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factor -= position[i] * position[i];
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}
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var result = [];
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for (var i = 0; i < dimensions; ++i) {
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result[i] = [];
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for (var j = 0; j < dimensions; ++j) {
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result[i][j] = [];
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for (var k = 0; k < dimensions; ++k) {
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result[i][j][k] = 0;
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if (i == k) result[i][j][k] += position[j];
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if (i == j) result[i][j][k] += position[k];
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if (j == k) result[i][j][k] -= position[i];
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result[i][j][k] *= 2/factor;
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}
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}
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}
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return result;
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}
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/* Returns a raycast */
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function get_ray(position, velocity, steps) {
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var positions = [];
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positions[0] = position;
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positions[1] = sum(position, velocity);
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for (var step = 0; step < steps; ++step) {
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positions[step + 2] = [];
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var connection = get_connection(positions[step + 1]);
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for (var i = 0; i < dimensions; ++i) {
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positions[step + 2][i] = 2 * positions[step + 1][i] - positions[step][i];
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for (var j = 0; j < dimensions; ++j) {
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for (var k = 0; k < dimensions; ++k) {
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positions[step + 2][i] -= connection[i][j][k] * (positions[step + 1][j] - positions[step][j]) * (positions[step + 1][k] - positions[step][k]);
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}
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}
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}
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}
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return positions;
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}
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/* Returns the product of a vector and a scalar */
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function scale(vector, scalar) {
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var result = [];
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for (var i = 0; i < dimensions; ++i) {
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result[i] = vector[i] * scalar;
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}
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return result;
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}
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/* Returns the inner product of two vectors */
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function inner(vector1, vector2, metric) {
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var result = 0;
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for (var i = 0; i < dimensions; ++i) {
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for (var j = 0; j < dimensions; ++j) {
96-
result += metric[i][j] * vector1[i] * vector2[j];
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}
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}
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return result;
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}
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/* Returns the norm of a vector */
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function norm(vector, metric) {
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return Math.sqrt(inner(vector, vector, metric));
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}
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var canvas = document.createElement('canvas');
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canvas.width = 500;
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canvas.height = 500;

‎hyperbolic/mathlib.js

+105
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,105 @@
1+
var dimensions = 2;
2+
3+
/* Returns the sum of two vectors */
4+
function sum(vector1, vector2) {
5+
var result = [];
6+
for (var i = 0; i < dimensions; ++i) {
7+
result[i] = vector1[i] + vector2[i];
8+
}
9+
return result;
10+
}
11+
12+
/* Returns the difference of two vectors */
13+
function difference(vector1, vector2) {
14+
return sum(vector1, scale(vector2, -1));
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}
16+
17+
/* Returns the metric tensor */
18+
function get_metric(position) {
19+
var factor = 1;
20+
for (var i = 0; i < dimensions; ++i) {
21+
factor -= position[i] * position[i];
22+
}
23+
24+
var result = [];
25+
for (var i = 0; i < dimensions; ++i) {
26+
result[i] = [];
27+
for (var j = 0; j < dimensions; ++j) {
28+
if (i == j) {
29+
result[i][j] = 1/(factor * factor);
30+
} else {
31+
result[i][j] = 0;
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}
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}
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}
35+
return result;
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}
37+
38+
/* Returns the connection coefficients (Christoffel symbols) */
39+
function get_connection(position) {
40+
var factor = 1;
41+
for (var i = 0; i < dimensions; ++i) {
42+
factor -= position[i] * position[i];
43+
}
44+
45+
var result = [];
46+
for (var i = 0; i < dimensions; ++i) {
47+
result[i] = [];
48+
for (var j = 0; j < dimensions; ++j) {
49+
result[i][j] = [];
50+
for (var k = 0; k < dimensions; ++k) {
51+
result[i][j][k] = 0;
52+
if (i == k) result[i][j][k] += position[j];
53+
if (i == j) result[i][j][k] += position[k];
54+
if (j == k) result[i][j][k] -= position[i];
55+
result[i][j][k] *= 2/factor;
56+
}
57+
}
58+
}
59+
return result;
60+
}
61+
62+
/* Returns a raycast */
63+
function get_ray(position, velocity, steps) {
64+
var positions = [];
65+
positions[0] = position;
66+
positions[1] = sum(position, velocity);
67+
for (var step = 0; step < steps; ++step) {
68+
positions[step + 2] = [];
69+
var connection = get_connection(positions[step + 1]);
70+
for (var i = 0; i < dimensions; ++i) {
71+
positions[step + 2][i] = 2 * positions[step + 1][i] - positions[step][i];
72+
for (var j = 0; j < dimensions; ++j) {
73+
for (var k = 0; k < dimensions; ++k) {
74+
positions[step + 2][i] -= connection[i][j][k] * (positions[step + 1][j] - positions[step][j]) * (positions[step + 1][k] - positions[step][k]);
75+
}
76+
}
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}
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}
79+
return positions;
80+
}
81+
82+
/* Returns the product of a vector and a scalar */
83+
function scale(vector, scalar) {
84+
var result = [];
85+
for (var i = 0; i < dimensions; ++i) {
86+
result[i] = vector[i] * scalar;
87+
}
88+
return result;
89+
}
90+
91+
/* Returns the inner product of two vectors */
92+
function inner(vector1, vector2, metric) {
93+
var result = 0;
94+
for (var i = 0; i < dimensions; ++i) {
95+
for (var j = 0; j < dimensions; ++j) {
96+
result += metric[i][j] * vector1[i] * vector2[j];
97+
}
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}
99+
return result;
100+
}
101+
102+
/* Returns the norm of a vector */
103+
function norm(vector, metric) {
104+
return Math.sqrt(inner(vector, vector, metric));
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}

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