From fb6b8aa33cbbe0d46d858c192f43b036f8b291ab Mon Sep 17 00:00:00 2001
From: root <>
Date: Thu, 24 Apr 2025 12:39:51 +0000
Subject: [PATCH 01/10] adjust constant
---
sketch.js | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/sketch.js b/sketch.js
index 362e59f..e89068d 100644
--- a/sketch.js
+++ b/sketch.js
@@ -35,7 +35,7 @@ function move_charges() {
charges[i].position,
charges[j].position,
);
- const acceleration_mag = 1 / displacement.mag() * 0.005;
+ const acceleration_mag = 1 / displacement.mag() * 0.001;
let ai = displacement.copy().normalize().mult(acceleration_mag);
let aj = p5.Vector.mult(ai, -1);
project_onto_plane(ai, charges[i].position);
From 6cbdb04786b381c948abd4f6b82d802f9de373b7 Mon Sep 17 00:00:00 2001
From: root <>
Date: Fri, 25 Apr 2025 08:56:49 +0000
Subject: [PATCH 02/10] move charge repelling stuff to its own file
---
index.html | 1 +
sketch.js | 42 +-----------------------------------------
thomson-problem.js | 44 ++++++++++++++++++++++++++++++++++++++++++++
3 files changed, 46 insertions(+), 41 deletions(-)
create mode 100644 thomson-problem.js
diff --git a/index.html b/index.html
index cf15339..6129f5f 100644
--- a/index.html
+++ b/index.html
@@ -16,6 +16,7 @@ body {
<body>
<main>
</main>
+<script src="thomson-problem.js"></script>
<script src="sketch.js"></script>
</body>
</html>
diff --git a/sketch.js b/sketch.js
index e89068d..cf036fc 100644
--- a/sketch.js
+++ b/sketch.js
@@ -19,52 +19,12 @@ function draw() {
make_lights();
if (physics) {
- move_charges();
+ move_charges(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() * 0.001;
- let ai = displacement.copy().normalize().mult(acceleration_mag);
- let aj = p5.Vector.mult(ai, -1);
- project_onto_plane(ai, charges[i].position);
- project_onto_plane(aj, charges[j].position);
- charges[i].acceleration.add(ai);
- charges[j].acceleration.add(aj);
- }
- }
- for (let i = 0; i < charges.length; i += 1) {
- let charge = charges[i];
- charge.velocity = charge.velocity.add(charge.acceleration);
- //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`
-/// Mutates `v`
-function project_onto_plane(v, unit_vector) {
- let v_proj = project_onto_unit_vector(v, unit_vector);
- v.sub(v_proj)
-}
-
function make_charges(n) {
charges = [];
for (let i = 0; i < n; i += 1) {
diff --git a/thomson-problem.js b/thomson-problem.js
new file mode 100644
index 0000000..0cbbdaa
--- /dev/null
+++ b/thomson-problem.js
@@ -0,0 +1,44 @@
+function move_charges(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,
+ );
+ let acceleration_mag = 1 / displacement.mag() * 0.001;
+ let ai;
+ if (acceleration_mag === Infinity) {
+ ai = createVector(random(-1, 1), random(-1, 1), random(-1, 1));
+ } else {
+ ai = displacement.copy();
+ }
+ ai = ai.normalize().mult(acceleration_mag);
+ let aj = p5.Vector.mult(ai, -1);
+ project_onto_plane(ai, charges[i].position);
+ project_onto_plane(aj, charges[j].position);
+ charges[i].acceleration.add(ai);
+ charges[j].acceleration.add(aj);
+ }
+ }
+ for (let i = 0; i < charges.length; i += 1) {
+ let charge = charges[i];
+ charge.velocity = charge.velocity.add(charge.acceleration);
+ 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`
+/// Mutates `v`
+function project_onto_plane(v, unit_vector) {
+ let v_proj = project_onto_unit_vector(v, unit_vector);
+ v.sub(v_proj)
+}
From c20044c4598e99f095fc56cfb7711d24794f54a9 Mon Sep 17 00:00:00 2001
From: root <>
Date: Fri, 25 Apr 2025 08:58:35 +0000
Subject: [PATCH 03/10] skeleton
---
sketch.js | 43 ++++++++++++++++++++++++++++++++++---------
1 file changed, 34 insertions(+), 9 deletions(-)
diff --git a/sketch.js b/sketch.js
index cf036fc..65842a6 100644
--- a/sketch.js
+++ b/sketch.js
@@ -1,12 +1,13 @@
let charges = [];
-let sphere_mode = 'circles';
let sphere_radius = 200;
let physics = false;
+let earth = false;
+let skeleton = false;
function preload() {
- earth = loadImage("atlas1.jpg");
+ earth_image = loadImage("atlas1.jpg");
}
function setup() {
@@ -21,10 +22,32 @@ function draw() {
if (physics) {
move_charges(charges);
}
+ if (skeleton) {
+ draw_skeleton(sphere_radius);
+ }
draw_charges(sphere_radius);
draw_sphere(sphere_radius, 25);
}
+function draw_skeleton(radius) {
+ push();
+ noStroke();
+ fill(0xff);
+ sphere(4);
+ stroke(0xbf);
+ for (let charge of charges) {
+ line(
+ 0,
+ 0,
+ 0,
+ charge.position.x * radius,
+ charge.position.y * radius,
+ charge.position.z * radius,
+ );
+ }
+ pop();
+}
+
function make_charges(n) {
charges = [];
for (let i = 0; i < n; i += 1) {
@@ -71,7 +94,7 @@ function draw_sphere(radius, n_axis_circles) {
rotateX(TAU / 4);
draw_circles(
radius,
- sphere_mode === 'earth' ? 2 : n_axis_circles,
+ earth ? 2 : n_axis_circles,
color(0x00, 0x9f, 0xff),
color(0xff, 0x9f, 0x00),
);
@@ -80,17 +103,17 @@ function draw_sphere(radius, n_axis_circles) {
rotateY(TAU / 4);
draw_circles(
radius,
- sphere_mode === 'earth' ? 2 : n_axis_circles,
+ earth ? 2 : n_axis_circles,
color(0xff, 0x00, 0xff),
color(0x00, 0xff, 0x00),
);
pop();
- if (sphere_mode === 'earth') {
+ if (earth) {
noStroke();
noFill();
tint(0xff, 0x9f);
- texture(earth);
+ texture(earth_image);
push();
rotateY(TAU / 4);
sphere(radius);
@@ -127,10 +150,12 @@ function make_lights() {
}
function keyPressed() {
- if (key == 'd') {
- sphere_mode = sphere_mode === 'earth' ? 'circles' : 'earth';
- } else if (key == ' ') {
+ if (key == ' ') {
physics = !physics;
+ } else if (key == 'd') {
+ earth = !earth;
+ } else if (key == 'f') {
+ skeleton = !skeleton;
} else if (key >= '0' && key <= '9') {
make_charges(int(key));
}
From 620896fb49506ae8357c9f9048d73808eebed4bc Mon Sep 17 00:00:00 2001
From: root <>
Date: Fri, 25 Apr 2025 14:47:03 +0000
Subject: [PATCH 04/10] begin drawing faces
---
sketch.js | 50 +++++++++++++++++++++++++++++++++++++++++++++++++-
1 file changed, 49 insertions(+), 1 deletion(-)
diff --git a/sketch.js b/sketch.js
index 65842a6..479ebf8 100644
--- a/sketch.js
+++ b/sketch.js
@@ -5,6 +5,10 @@ let sphere_radius = 200;
let physics = false;
let earth = false;
let skeleton = false;
+let planes = false;
+
+let red;
+let yellow;
function preload() {
earth_image = loadImage("atlas1.jpg");
@@ -12,6 +16,8 @@ function preload() {
function setup() {
createCanvas(600, 600, WEBGL);
+ red = color(0xbf, 0x00, 0x00);
+ yellow = color(0xff, 0xff, 0x00);
}
function draw() {
@@ -25,6 +31,41 @@ function draw() {
if (skeleton) {
draw_skeleton(sphere_radius);
}
+
+ 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));
+ 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);
+ 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);
+ vertex(v1.x, v1.y, v1.z);
+ vertex(v2.x, v2.y, v2.z);
+ vertex(v3.x, v3.y, v3.z);
+ endShape();
+ pop();
+ } else {
+ for (let charge of charges) {
+ charge.color = red;
+ }
+ }
+
draw_charges(sphere_radius);
draw_sphere(sphere_radius, 25);
}
@@ -67,6 +108,7 @@ function make_charges(n) {
position: position,
velocity: createVector(),
acceleration: createVector(),
+ color: red,
});
}
}
@@ -74,8 +116,8 @@ function make_charges(n) {
function draw_charges(radius) {
push();
noStroke();
- ambientMaterial(0xbf, 0x00, 0x00);
for (let charge of charges.values()) {
+ ambientMaterial(charge.color);
let position = charge.position.copy();
position.mult(radius);
push();
@@ -156,7 +198,13 @@ function keyPressed() {
earth = !earth;
} else if (key == 'f') {
skeleton = !skeleton;
+ } else if (key == 'g') {
+ planes = !planes;
} else if (key >= '0' && key <= '9') {
make_charges(int(key));
}
}
+
+// TODO draw faces
+// algorithm: choose 3 vertices until 2-partition of other vertices has one empty set
+// done when V - E + F = 2. V is known. count E and F while creating faces
From 838eae2cbf198548d4e6c37865badac8dd25c440 Mon Sep 17 00:00:00 2001
From: root <>
Date: Fri, 25 Apr 2025 14:59:51 +0000
Subject: [PATCH 05/10] 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 | 51 +++++++++++++++++++++++++++++++++++++++------------
1 file changed, 39 insertions(+), 12 deletions(-)
diff --git a/sketch.js b/sketch.js
index 479ebf8..f97897e 100644
--- a/sketch.js
+++ b/sketch.js
@@ -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;
From cec27160f4e75883f5353ebf273f3b092b6609a4 Mon Sep 17 00:00:00 2001
From: root <>
Date: Fri, 25 Apr 2025 17:14:31 +0000
Subject: [PATCH 06/10] convex polyhedron
---
sketch.js | 149 ++++++++++++++++++++++++++++++------------------------
1 file changed, 83 insertions(+), 66 deletions(-)
diff --git a/sketch.js b/sketch.js
index f97897e..db98094 100644
--- a/sketch.js
+++ b/sketch.js
@@ -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) {
From 34e1de68f1913d0c737aa2589b4981c78c556c3a Mon Sep 17 00:00:00 2001
From: root <>
Date: Sat, 26 Apr 2025 04:08:10 +0000
Subject: [PATCH 07/10] hide sphere; euler's forumla trick; cache faces
---
sketch.js | 68 ++++++++++++++++++++++++++++++++++++-------------------
1 file changed, 45 insertions(+), 23 deletions(-)
diff --git a/sketch.js b/sketch.js
index db98094..1d684e6 100644
--- a/sketch.js
+++ b/sketch.js
@@ -2,13 +2,18 @@ let camera;
let red;
let charges = [];
+let faces = [];
let sphere_radius = 200;
+const SURFACE_NONE = 0;
+const SURFACE_CIRCLES = 1;
+const SURFACE_EARTH = 2;
+
+let surface = SURFACE_CIRCLES;
let physics = false;
-let earth = false;
let skeleton = false;
-let planes = false;
+let polyhedron = false;
function preload() {
@@ -16,11 +21,15 @@ function preload() {
}
function setup() {
- createCanvas(600, 600, WEBGL);
+ createCanvas(windowWidth, windowHeight, WEBGL);
camera = createCamera();
red = color(0xbf, 0x00, 0x00);
}
+function windowResized() {
+ resizeCanvas(windowWidth, windowHeight);
+}
+
function draw() {
orbitControl();
background(50);
@@ -29,9 +38,12 @@ function draw() {
if (physics) move_charges(charges);
draw_charges(sphere_radius);
- draw_sphere(sphere_radius, 25);
if (skeleton) draw_skeleton(sphere_radius);
- if (planes) draw_planes(sphere_radius);
+ if (polyhedron) {
+ if (physics || faces.length === 0) find_faces();
+ draw_faces(sphere_radius);
+ }
+ draw_sphere(sphere_radius, 25);
}
function face_dist_sq([v1, v2, v3]) {
@@ -39,8 +51,8 @@ function face_dist_sq([v1, v2, v3]) {
return createVector(camera.eyeX, camera.eyeY, camera.eyeZ).sub(center).magSq();
};
-function draw_planes(radius) {
- let faces = [];
+function find_faces() {
+ 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) {
@@ -53,6 +65,7 @@ function draw_planes(radius) {
// ... by checking if the other vertices are on the same
// side of the plane generated by p1 p2 p3
let plane_separates_vertices = false;
+ let euler_formula = false;
for (let r = 1; r < charges.length; r += 1) {
for (let s = 0; s < r; s += 1) {
if (
@@ -85,30 +98,32 @@ function draw_planes(radius) {
);
plane_separates_vertices ||= t >= 0 && t <= 1;
if (plane_separates_vertices) break;
+ euler_formula ||= charges.length * 2 - faces.length == 4;
+ if (euler_formula) break;
}
- if (plane_separates_vertices) break;
+ if (plane_separates_vertices || euler_formula) break;
}
+ if (euler_formula) return;
if (!plane_separates_vertices) {
- faces.push([
- p5.Vector.mult(p1, radius),
- p5.Vector.mult(p2, radius),
- p5.Vector.mult(p3, radius),
- ]);
+ faces.push([p1, p2, p3]);
}
}
}
}
+}
+
+function draw_faces(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) {
+ for ([p1, p2, p3] of faces) {
fill(0xbf, 0x7f);
beginShape(TRIANGLES);
- vertex(v1.x, v1.y, v1.z);
- vertex(v2.x, v2.y, v2.z);
- vertex(v3.x, v3.y, v3.z);
+ vertex(p1.x * radius, p1.y * radius, p1.z * radius);
+ vertex(p2.x * radius, p2.y * radius, p2.z * radius);
+ vertex(p3.x * radius, p3.y * radius, p3.z * radius);
endShape();
}
pop();
@@ -176,11 +191,14 @@ function draw_sphere(radius, n_axis_circles) {
stroke(0x3f);
noFill();
+ if (surface === SURFACE_NONE) n_axis_circles = 0;
+ else if (surface === SURFACE_EARTH) n_axis_circles = 2;
+
push();
rotateX(TAU / 4);
draw_circles(
radius,
- earth ? 2 : n_axis_circles,
+ n_axis_circles,
color(0x00, 0x9f, 0xff),
color(0xff, 0x9f, 0x00),
);
@@ -189,13 +207,13 @@ function draw_sphere(radius, n_axis_circles) {
rotateY(TAU / 4);
draw_circles(
radius,
- earth ? 2 : n_axis_circles,
+ n_axis_circles,
color(0xff, 0x00, 0xff),
color(0x00, 0xff, 0x00),
);
pop();
- if (earth) {
+ if (surface === SURFACE_EARTH) {
noStroke();
noFill();
tint(0xff, 0x9f);
@@ -239,16 +257,20 @@ function keyPressed() {
if (key == ' ') {
physics = !physics;
} else if (key == 'd') {
- earth = !earth;
+ surface = (surface + 1) % 3;
} else if (key == 'f') {
skeleton = !skeleton;
} else if (key == 'g') {
- planes = !planes;
+ polyhedron = !polyhedron;
} else if (key >= '0' && key <= '9') {
- make_charges(int(key));
+ make_charges(Math.pow(int(key), 2));
+ faces = [];
}
}
// TODO draw faces
// algorithm: choose 3 vertices until 2-partition of other vertices has one empty set
// done when V - E + F = 2. V is known. count E and F while creating faces
+// when the graph is finished: E = F * 3 / 2
+// V - E + F = V - F * 3 / 2 + F = V - F / 2
+// V * 2 - F = 4
From d0be92d50ecd336643879a793964a178edb8f01a Mon Sep 17 00:00:00 2001
From: root <>
Date: Sat, 26 Apr 2025 04:12:55 +0000
Subject: [PATCH 08/10] charges should not have earth texture, lol
---
sketch.js | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/sketch.js b/sketch.js
index 1d684e6..cbc9252 100644
--- a/sketch.js
+++ b/sketch.js
@@ -214,11 +214,11 @@ function draw_sphere(radius, n_axis_circles) {
pop();
if (surface === SURFACE_EARTH) {
+ push();
noStroke();
noFill();
tint(0xff, 0x9f);
texture(earth_image);
- push();
rotateY(TAU / 4);
sphere(radius);
pop();
From e51d5df1dc684062d4b23ff59fdfce1e11d155f3 Mon Sep 17 00:00:00 2001
From: root <>
Date: Sat, 26 Apr 2025 04:15:57 +0000
Subject: [PATCH 09/10] cleanup
---
sketch.js | 9 +--------
1 file changed, 1 insertion(+), 8 deletions(-)
diff --git a/sketch.js b/sketch.js
index cbc9252..1d3cb0a 100644
--- a/sketch.js
+++ b/sketch.js
@@ -263,14 +263,7 @@ function keyPressed() {
} else if (key == 'g') {
polyhedron = !polyhedron;
} else if (key >= '0' && key <= '9') {
- make_charges(Math.pow(int(key), 2));
+ make_charges(int(key));
faces = [];
}
}
-
-// TODO draw faces
-// algorithm: choose 3 vertices until 2-partition of other vertices has one empty set
-// done when V - E + F = 2. V is known. count E and F while creating faces
-// when the graph is finished: E = F * 3 / 2
-// V - E + F = V - F * 3 / 2 + F = V - F / 2
-// V * 2 - F = 4
From eeb1beaea3d8ade3e5c835df68973bcaac7cf34a Mon Sep 17 00:00:00 2001
From: root <>
Date: Sat, 26 Apr 2025 04:20:00 +0000
Subject: [PATCH 10/10] fix: firefox scrollbar
---
index.html | 1 +
1 file changed, 1 insertion(+)
diff --git a/index.html b/index.html
index 6129f5f..ff66bc9 100644
--- a/index.html
+++ b/index.html
@@ -10,6 +10,7 @@ body {
padding: 0;
margin: 0;
background-color: #1b1b1b;
+ overflow-y: hidden;
}
</style>
</head>