custom charge magnitude
also: s/charge/particle to reduce confusion
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3 changed files with 54 additions and 48 deletions
20
index.html
20
index.html
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@ -86,16 +86,16 @@ aside > container > div {
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<button id="button-surface-earth" onclick="set_surface(SURFACE_EARTH)">Earth</button>
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</div>
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<div>
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<button onclick="make_charges(0);faces=[]">0</button>
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<button onclick="make_charges(1);faces=[]">1</button>
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<button onclick="make_charges(2);faces=[]">2</button>
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<button onclick="make_charges(3);faces=[]">3</button>
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<button onclick="make_charges(4);faces=[]">4</button>
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<button onclick="make_charges(5);faces=[]">5</button>
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<button onclick="make_charges(6);faces=[]">6</button>
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<button onclick="make_charges(7);faces=[]">7</button>
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<button onclick="make_charges(8);faces=[]">8</button>
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<button onclick="make_charges(9);faces=[]">9</button>
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<button onclick="make_particles(0);faces=[]">0</button>
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<button onclick="make_particles(1);faces=[]">1</button>
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<button onclick="make_particles(2);faces=[]">2</button>
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<button onclick="make_particles(3);faces=[]">3</button>
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<button onclick="make_particles(4);faces=[]">4</button>
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<button onclick="make_particles(5);faces=[]">5</button>
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<button onclick="make_particles(6);faces=[]">6</button>
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<button onclick="make_particles(7);faces=[]">7</button>
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<button onclick="make_particles(8);faces=[]">8</button>
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<button onclick="make_particles(9);faces=[]">9</button>
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</div>
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</container>
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</aside>
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48
sketch.js
48
sketch.js
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@ -1,7 +1,7 @@
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let camera;
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let red;
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let charges = [];
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let particles = [];
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let faces = [];
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let sphere_radius;
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@ -14,6 +14,7 @@ let surface = SURFACE_CIRCLES;
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let physics = false;
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let skeleton = false;
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let polytope = false;
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let charge = -1;
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let buttons_surface;
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let checkbox_physics;
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@ -70,9 +71,9 @@ function draw() {
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camera.centerZ = 0;
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make_lights();
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if (physics) move_charges(charges, 8e-4);
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if (physics) move_particles(particles, 8e-4);
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draw_charges(sphere_radius);
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draw_particles(sphere_radius);
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if (skeleton) draw_skeleton(sphere_radius);
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if (polytope) {
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if (physics || faces.length === 0) find_faces();
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@ -88,27 +89,27 @@ function face_dist_sq([v1, v2, v3]) {
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function find_faces() {
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faces = [];
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for (let i = 2; i < charges.length; i += 1) {
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for (let i = 2; i < particles.length; i += 1) {
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for (let j = 1; j < i; j += 1) {
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for (let k = 0; k < j; k += 1) {
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// Check if p1 p2 p3 form a face of the convex polytope
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// enclosing all vertices ...
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const p1 = charges[i].position;
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const p2 = charges[j].position;
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const p3 = charges[k].position;
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const p1 = particles[i].position;
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const p2 = particles[j].position;
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const p3 = particles[k].position;
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const normal = p5.Vector.sub(p2, p1).cross(p5.Vector.sub(p3, p1));
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// ... by checking if the other vertices are on the same
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// side of the plane generated by p1 p2 p3
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let plane_separates_vertices = false;
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let euler_formula = false;
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for (let r = 1; r < charges.length; r += 1) {
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for (let r = 1; r < particles.length; r += 1) {
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for (let s = 0; s < r; s += 1) {
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if (
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r === i || r === j || r === k ||
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s === i || s === j || s === k
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) continue;
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const q1 = charges[r].position;
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const q2 = charges[s].position;
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const q1 = particles[r].position;
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const q2 = particles[s].position;
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// Let l(t) := q1 + (q2 - q1) * t.
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// L := { l(t) : 0 <= t <= 1 } is the line segment
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// between q1 and q2. L intersects the plane
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@ -133,7 +134,7 @@ function find_faces() {
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);
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plane_separates_vertices ||= t >= 0 && t <= 1;
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if (plane_separates_vertices) break;
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euler_formula ||= charges.length * 2 - faces.length == 4;
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euler_formula ||= particles.length * 2 - faces.length == 4;
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if (euler_formula) break;
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}
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if (plane_separates_vertices || euler_formula) break;
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@ -170,21 +171,21 @@ function draw_skeleton(radius) {
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fill(0xff);
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sphere(4);
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stroke(0xbf);
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for (let charge of charges) {
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for (let particle of particles) {
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line(
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0,
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0,
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0,
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charge.position.x * radius,
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charge.position.y * radius,
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charge.position.z * radius,
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particle.position.x * radius,
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particle.position.y * radius,
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particle.position.z * radius,
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);
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}
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pop();
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}
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function make_charges(n) {
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charges = [];
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function make_particles(n) {
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particles = [];
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for (let i = 0; i < n; i += 1) {
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let position;
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if (i === 0) {
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@ -192,21 +193,22 @@ function make_charges(n) {
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} else {
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position = p5.Vector.random3D();
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}
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charges.push({
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particles.push({
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position: position,
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velocity: createVector(),
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acceleration: createVector(),
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charge: charge,
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color: red,
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});
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}
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}
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function draw_charges(radius) {
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function draw_particles(radius) {
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push();
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noStroke();
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for (let charge of charges.values()) {
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ambientMaterial(charge.color);
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let position = charge.position.copy();
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for (let particle of particles) {
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ambientMaterial(particle.color);
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let position = particle.position.copy();
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position.mult(radius);
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push();
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translate(position.x, position.y, position.z);
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@ -292,7 +294,7 @@ function keyPressed() {
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} else if (key == 'g') {
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toggle_polytope();
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} else if (key >= '0' && key <= '9') {
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make_charges(int(key));
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make_particles(int(key));
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faces = [];
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}
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}
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@ -1,14 +1,18 @@
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function move_charges(charges, force_constant) {
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for (let charge of charges) {
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charge.acceleration.setMag(0);
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function move_particles(particles, force_constant) {
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for (let particle of particles) {
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particle.acceleration.setMag(0);
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}
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for (let i = 0; i < charges.length; i += 1) {
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for (let i = 0; i < particles.length; i += 1) {
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for (let j = 0; j < i; j += 1) {
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const displacement = p5.Vector.sub(
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charges[i].position,
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charges[j].position,
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particles[i].position,
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particles[j].position,
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);
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const force_mag = (
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particles[i].charge * particles[j].charge
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/ displacement.magSq()
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* force_constant
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);
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const force_mag = 1 / displacement.magSq() * force_constant;
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// XXX possible extension: divide by charge's mass
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const ai_mag = force_mag;
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const aj_mag = force_mag;
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@ -23,16 +27,16 @@ function move_charges(charges, force_constant) {
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}
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ai.mult(ai_mag);
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aj.mult(aj_mag);
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project_onto_plane(ai, charges[i].position);
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project_onto_plane(aj, charges[j].position);
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charges[i].acceleration.add(ai);
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charges[j].acceleration.add(aj);
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project_onto_plane(ai, particles[i].position);
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project_onto_plane(aj, particles[j].position);
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particles[i].acceleration.add(ai);
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particles[j].acceleration.add(aj);
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}
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}
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for (let charge of charges) {
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charge.velocity = charge.velocity.add(charge.acceleration);
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charge.position = charge.position.add(charge.velocity);
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charge.position.normalize();
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for (let particle of particles) {
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particle.velocity = particle.velocity.add(particle.acceleration);
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particle.position = particle.position.add(particle.velocity);
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particle.position.normalize();
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}
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}
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