1 files changed, 131 insertions, 0 deletions
diff --git a/js/hypersphere.js b/js/hypersphere.js
new file mode 100644
index 0000000..d34a74d
--- /dev/null
+++ b/js/hypersphere.js
@@ -0,0 +1,131 @@
+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);
+            }
+        }
+    }
+    
+    
+}