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polyhedron alg progress: face separates vertices

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the algorithm so far:
- select 3 vertices
- draw a triangle between them
- for all vertex pairs (non-triangle vertices):
-- draw a line between them
-- if line intersects with triangle plane, red
-- otherwise, green

if the line is red the two vertices are on other sides of the
triangle plane, and this triangle can't be a face, because we
want the polyhedron to be convex

to demo: press 9, press g, press space; press 9 over and over
This commit is contained in:
root 2025-04-25 14:59:51 +00:00
parent 620896fb49
commit 838eae2cbf
1 changed files with 39 additions and 12 deletions
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51
sketch.js
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@ -33,33 +33,60 @@ function draw() {
}
if (planes) {
let p = charges[0];
let a = charges[1];
let b = charges[2];
p.color = yellow;
a.color = yellow;
b.color = yellow;
let n = p5.Vector.sub(p.position, a.position).cross(p5.Vector.sub(p.position, b.position));
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,
0, 0, 0,
n.x * sphere_radius, n.y * sphere_radius, n.z * sphere_radius,
)
fill(0xff);
strokeWeight(3);
stroke(0x00);
beginShape(TRIANGLES);
const v1 = p5.Vector.mult(p.position, sphere_radius);
const v2 = p5.Vector.mult(a.position, sphere_radius);
const v3 = p5.Vector.mult(b.position, sphere_radius);
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;