physics simulation

sketch.js

@@ -1,9 +1,10 @@
-let charges = new Map();
-let counter = 0;
+let charges = [];
 
 let sphere_mode = 'circles';
 let sphere_radius = 200;
 
+let physics = false;
+
 function preload() {
   earth = loadImage("atlas1.jpg");
 }
@@ -17,15 +18,59 @@ function draw() {
   background(50);
 
   make_lights();
-  draw_sphere(sphere_radius, 25);
+  if (physics) {
+    move_charges();
+  }
   draw_charges(sphere_radius);
+  draw_sphere(sphere_radius, 25);
+}
+
+function move_charges() {
+  for (charge of charges) {
+    charge.acceleration.setMag(0);
+  }
+  for (let i = 0; i < charges.length; i += 1) {
+    for (let j = 0; j < i; j += 1) {
+      const displacement = p5.Vector.sub(
+        charges[i].position,
+        charges[j].position,
+      );
+      const acceleration_mag = 1 / displacement.mag() * 0.005;
+      let ai = displacement.copy().normalize().mult(acceleration_mag);
+      let aj = p5.Vector.mult(ai, -1);
+      let ai_norm = project_onto_plane(ai, charges[i].position);
+
+      let aj_norm = project_onto_plane(aj, charges[j].position);
+
+      charges[i].acceleration.add(ai_norm);
+      charges[j].acceleration.add(aj_norm);
+    }
+  }
+  for (let i = 0; i < charges.length; i += 1) {
+    let charge = charges[i];
+    charge.velocity = charge.velocity.add(charge.acceleration);
+    //charge.velocity = project_onto_plane(charge.velocity, charge.position);
+    charge.position = charge.position.add(charge.velocity);
+    charge.position.normalize();
+  }
+}
+
+function project_onto_unit_vector(v, unit_vector) {
+  let size = p5.Vector.dot(v, unit_vector);
+  return p5.Vector.mult(unit_vector, size);
+}
+
+/// Project `v` onto the plane normal to `unit_vector`
+function project_onto_plane(v, unit_vector) {
+  let v_proj = project_onto_unit_vector(v, unit_vector);
+  return v.sub(v_proj)
 }
 
 function make_charges(n) {
-  charges.clear();
+  charges = [];
   for (let i = 0; i < n; i += 1) {
     let position;
-    if (i == 0) {
+    if (i === 0) {
       position = createVector(0, -1, 0);
     } else {
       const lat = random(-TAU / 4, TAU / 4);
@@ -36,8 +81,11 @@ function make_charges(n) {
         cos(lat) * sin(lon),
       );
     }
-    charges.set(counter, position);
-    counter += 1;
+    charges.push({
+      position: position,
+      velocity: createVector(),
+      acceleration: createVector(),
+    });
   }
 }
 
@@ -46,7 +94,7 @@ function draw_charges(radius) {
   noStroke();
   ambientMaterial(0xbf, 0x00, 0x00);
   for (let charge of charges.values()) {
-    let position = charge.copy();
+    let position = charge.position.copy();
     position.mult(radius);
     push();
     translate(position.x, position.y, position.z);
@@ -122,6 +170,8 @@ function make_lights() {
 function keyPressed() {
   if (key == 'd') {
     sphere_mode = sphere_mode === 'earth' ? 'circles' : 'earth';
+  } else if (key == ' ') {
+    physics = !physics;
   } else if (key >= '0' && key <= '9') {
     make_charges(int(key));
   }