polyhedron alg progress: face separates vertices

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

sketch.js

@@ -33,33 +33,60 @@ function draw() {
   }
 
   if (planes) {
-    let p = charges[0];
+    let p_charge = charges[0];
-    let a = charges[1];
+    let a_charge = charges[1];
-    let b = charges[2];
+    let b_charge = charges[2];
-    p.color = yellow;
+    p_charge.color = yellow;
-    a.color = yellow;
+    a_charge.color = yellow;
-    b.color = yellow;
+    b_charge.color = yellow;
-    let n = p5.Vector.sub(p.position, a.position).cross(p5.Vector.sub(p.position, b.position));
+    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,
+      0, 0, 0,
-      n.x*sphere_radius,n.y*sphere_radius,n.z*sphere_radius,
+      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 v1 = p5.Vector.mult(p, sphere_radius);
-    const v2 = p5.Vector.mult(a.position, sphere_radius);
+    const v2 = p5.Vector.mult(a, sphere_radius);
-    const v3 = p5.Vector.mult(b.position, 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;