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convex polyhedron

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root 2025-04-25 17:14:31 +00:00
parent 838eae2cbf
commit cec27160f4
1 changed files with 83 additions and 66 deletions
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149
sketch.js
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@ -1,3 +1,6 @@
let camera;
let red;
let charges = [];
let sphere_radius = 200;
@ -7,8 +10,6 @@ let earth = false;
let skeleton = false;
let planes = false;
let red;
let yellow;
function preload() {
earth_image = loadImage("atlas1.jpg");
@ -16,8 +17,8 @@ function preload() {
function setup() {
createCanvas(600, 600, WEBGL);
camera = createCamera();
red = color(0xbf, 0x00, 0x00);
yellow = color(0xff, 0xff, 0x00);
}
function draw() {
@ -25,76 +26,92 @@ function draw() {
background(50);
make_lights();
if (physics) {
move_charges(charges);
}
if (skeleton) {
draw_skeleton(sphere_radius);
}
if (physics) move_charges(charges);
if (planes) {
let p_charge = charges[0];
let a_charge = charges[1];
let b_charge = charges[2];
p_charge.color = yellow;
a_charge.color = yellow;
b_charge.color = yellow;
let p = p_charge.position;
let a = a_charge.position;
let b = b_charge.position;
let n = p5.Vector.sub(p, a).cross(p5.Vector.sub(p, b));
n.normalize(); // unnecessary
push();
strokeWeight(5);
stroke(0x7f);
line(
0, 0, 0,
n.x * sphere_radius, n.y * sphere_radius, n.z * sphere_radius,
)
fill(0xff);
strokeWeight(3);
stroke(0x00);
draw_charges(sphere_radius);
draw_sphere(sphere_radius, 25);
if (skeleton) draw_skeleton(sphere_radius);
if (planes) draw_planes(sphere_radius);
}
function face_dist_sq([v1, v2, v3]) {
const center = p5.Vector.add(v1, v2).add(v3).mult(1 / 3);
return createVector(camera.eyeX, camera.eyeY, camera.eyeZ).sub(center).magSq();
};
function draw_planes(radius) {
let faces = [];
for (let i = 2; i < charges.length; i += 1) {
for (let j = 1; j < i; j += 1) {
for (let k = 0; k < j; k += 1) {
// Check if p1 p2 p3 form a face of the convex polyhedron
// enclosing all vertices ...
const p1 = charges[i].position;
const p2 = charges[j].position;
const p3 = charges[k].position;
const normal = p5.Vector.sub(p2, p1).cross(p5.Vector.sub(p3, p1));
// ... by checking if the other vertices are on the same
// side of the plane generated by p1 p2 p3
let plane_separates_vertices = false;
for (let r = 1; r < charges.length; r += 1) {
for (let s = 0; s < r; s += 1) {
if (
r === i || r === j || r === k ||
s === i || s === j || s === k
) continue;
const q1 = charges[r].position;
const q2 = charges[s].position;
// Let l(t) := q1 + (q2 - q1) * t.
// L := { l(t) : 0 <= t <= 1 } is the line segment
// between q1 and q2. L intersects the plane
// generated by p1 p2 p3 iff l(t) intersects with
// the plane for some 0 <= t <= 1.
//
// If L intersects the plane, q1 and q2 are on
// opposite sides of the plane generated by p1 p2 p3,
// so p1 p2 p3 can't be a face. If we want the
// polyhedron to be convex. Which we do.
//
// A point k is on the plane generated by p1 p2 p3 iff
// dot(k - p1, normal) = 0. Let n := normal.
//
// dot(l(t) - p1, n) = 0
// iff dot(q1 + (q2 - q1) * t - p1, n) = 0
// iff dot(q1 - p1, n) + dot(q2 - q2, n) * t = 0
// iff t = dot(p1 - q1, n) / dot(q2 - q2, n)
const t = (
p5.Vector.dot(p5.Vector.sub(p1, q1), normal) /
p5.Vector.dot(p5.Vector.sub(q2, q1), normal)
);
plane_separates_vertices ||= t >= 0 && t <= 1;
if (plane_separates_vertices) break;
}
if (plane_separates_vertices) break;
}
if (!plane_separates_vertices) {
faces.push([
p5.Vector.mult(p1, radius),
p5.Vector.mult(p2, radius),
p5.Vector.mult(p3, radius),
]);
}
}
}
}
// fix OpenGL stacking alpha behaviour
faces.sort((a, b) => face_dist_sq(b) - face_dist_sq(a));
push();
strokeWeight(2);
stroke(0x00);
for ([v1, v2, v3] of faces) {
fill(0xbf, 0x7f);
beginShape(TRIANGLES);
const v1 = p5.Vector.mult(p, sphere_radius);
const v2 = p5.Vector.mult(a, sphere_radius);
const v3 = p5.Vector.mult(b, sphere_radius);
vertex(v1.x, v1.y, v1.z);
vertex(v2.x, v2.y, v2.z);
vertex(v3.x, v3.y, v3.z);
endShape();
pop();
for (let i = 4; i < charges.length; i += 1) {
for (let j = 3; j < i; j += 1) {
push();
const u = charges[i].position;
const v = charges[j].position;
const t = p5.Vector.dot(p5.Vector.sub(p, u), n) / p5.Vector.dot(p5.Vector.sub(v, u), n);
const intersects_plane = t >= 0 && t <= 1;
if (intersects_plane) {
stroke(0xff, 0x1f, 0x00);
} else {
stroke(0x00, 0xff, 0x00);
}
strokeWeight(3);
line(
charges[i].position.x * sphere_radius,
charges[i].position.y * sphere_radius,
charges[i].position.z * sphere_radius,
charges[j].position.x * sphere_radius,
charges[j].position.y * sphere_radius,
charges[j].position.z * sphere_radius,
);
pop();
}
}
} else {
for (let charge of charges) {
charge.color = red;
}
}
draw_charges(sphere_radius);
draw_sphere(sphere_radius, 25);
pop();
}
function draw_skeleton(radius) {