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var WIDTH = 500;
var HEIGHT = 500;
var z_angle = 4*Math.PI/9;
var w_angle = 2*Math.PI/3;
var matrix = [[Math.cos(0), Math.sin(0)], [Math.cos(2*Math.PI/9), Math.sin(2*Math.PI/9)], [Math.cos(z_angle), Math.sin(z_angle)], [Math.cos(w_angle), Math.sin(w_angle)]];
var quality = 5;
var speed = 0.2;
var coordinatesSize = 4;
var topLeft = [-coordinatesSize/2, +coordinatesSize/2];
var topRight = [+coordinatesSize/2, +coordinatesSize/2];
var bottomLeft = [-coordinatesSize/2, -coordinatesSize/2];
var bottomRight = [+coordinatesSize/2, -coordinatesSize/2];
var origin;
$(function()
{
$("#chq").click(function()
{
quality = $("#quality").val();
})
})
function convertCoordinates(coords)
{
var x = map(coords[0], topLeft[0], topRight[0], 0, width);
var y = map(coords[1], topLeft[1], bottomLeft[1], 0, width);
return [x, y];
}
function transform(vector)
{
var ans = [];
for (var i = 0; i < matrix[0].length; i++)
{
ans.push(0);
}
for (var i = 0; i < matrix.length; i++)
{
for (var j = 0; j < matrix[i].length; j++)
{
ans[j] += vector[i] * matrix[i][j];
}
}
return convertCoordinates(ans);
}
function pointOnSphere(r,s,t)
{
var x = r * Math.cos(s) * Math.sin(t);
var y = r * Math.sin(s) * Math.sin(t);
var z = r * Math.cos(t);
return [x,y,z];
}
function pointOnHyperSphere(r,s,t,u)
{
var x = r * Math.cos(s);
var y = r * Math.sin(s) * Math.cos(t);
var z = r * Math.sin(s) * Math.sin(t) * Math.cos(u);
var w = r * Math.sin(s) * Math.sin(t) * Math.sin(u);
return [x,y,z,w];
}
function setup()
{
createCanvas(500, 500);
origin = [width/2, height/2];
}
function draw()
{
background(255);
ellipseMode(CENTER);
var xVal = map(mouseX, 0, width, 0, 2*Math.PI);
matrix[0] = [Math.cos(xVal), Math.sin(xVal)];
var yVal = map(mouseY, 0, height, 0, 2*Math.PI);
matrix[1] = [Math.cos(yVal), Math.sin(yVal)];
if (keyIsDown(LEFT_ARROW))
{
z_angle -= speed;
}
if (keyIsDown(RIGHT_ARROW))
{
z_angle += speed;
}
if (keyIsDown(DOWN_ARROW))
{
w_angle -= speed;
}
if (keyIsDown(UP_ARROW))
{
w_angle += speed;
}
matrix[2] = [Math.cos(z_angle), Math.sin(z_angle)];
matrix[3] = [Math.cos(w_angle), Math.sin(w_angle)];
var i_hat = convertCoordinates(matrix[0]);
var j_hat = convertCoordinates(matrix[1]);
var k_hat = convertCoordinates(matrix[2]);
var l_hat = convertCoordinates(matrix[3]);
strokeWeight(2);
stroke(255, 0, 0);
line(origin[0], origin[1], i_hat[0], i_hat[1]);
stroke(0, 255, 0);
line(origin[0], origin[1], j_hat[0], j_hat[1]);
stroke(0, 0, 255);
line(origin[0], origin[1], k_hat[0], k_hat[1]);
stroke(0, 255, 255);
line(origin[0], origin[1], l_hat[0], l_hat[1]);
fill(157, 0, 255);
noStroke();
for (var s = 0; s < 2*Math.PI; s += 1/quality)
{
for (var t = 0; t < 2*Math.PI; t += 1/quality)
{
for (var u = 0; u < 2*Math.PI; u += 1/quality)
{
var transformed = transform(pointOnHyperSphere(1, s, t, u));
ellipse(transformed[0], transformed[1], 1, 1);
}
}
}
}
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