From 87e7ad3a3d237715ca0566826f2be7ded913125f Mon Sep 17 00:00:00 2001 From: Tyler Hallada Date: Sat, 1 Feb 2020 17:46:15 -0500 Subject: [PATCH] New blog post: icosahedrons and hexspheres in rust --- ...ing-icosahedrons-and-hexspheres-in-rust.md | 757 ++++++++++++++++++ img/blog/bad_hexsphere_normals.png | Bin 0 -> 372129 bytes img/blog/dodecahedron_in_icosahedron.png | Bin 0 -> 54170 bytes img/blog/hexagon_fan.png | Bin 0 -> 258583 bytes img/blog/hexagon_fan_construct.png | Bin 0 -> 351079 bytes img/blog/hexagon_fan_triangle_selected.png | Bin 0 -> 261260 bytes img/blog/hexagon_tiling.png | Bin 0 -> 619021 bytes img/blog/hexsphere_colored_3.png | Bin 0 -> 173444 bytes img/blog/icosahedron_colored_1.png | Bin 0 -> 100337 bytes img/blog/icosahedron_colored_3.png | Bin 0 -> 240133 bytes 10 files changed, 757 insertions(+) create mode 100644 _posts/2020-02-01-generating-icosahedrons-and-hexspheres-in-rust.md create mode 100755 img/blog/bad_hexsphere_normals.png create mode 100644 img/blog/dodecahedron_in_icosahedron.png create mode 100755 img/blog/hexagon_fan.png create mode 100755 img/blog/hexagon_fan_construct.png create mode 100755 img/blog/hexagon_fan_triangle_selected.png create mode 100755 img/blog/hexagon_tiling.png create mode 100755 img/blog/hexsphere_colored_3.png create mode 100755 img/blog/icosahedron_colored_1.png create mode 100755 img/blog/icosahedron_colored_3.png diff --git a/_posts/2020-02-01-generating-icosahedrons-and-hexspheres-in-rust.md b/_posts/2020-02-01-generating-icosahedrons-and-hexspheres-in-rust.md new file mode 100644 index 0000000..1f5cab7 --- /dev/null +++ b/_posts/2020-02-01-generating-icosahedrons-and-hexspheres-in-rust.md @@ -0,0 +1,757 @@ +--- +title: "Generating icosahedrons and hexspheres in Rust" +layout: post +--- + +I've been trying to learn [Rust](https://www.rust-lang.org/) lately, the hot new +systems programming language. One of the projects I wanted to tackle with the +speed of Rust was generating 3D polyhedron shapes. Specifically, I wanted to +implement something like the [Three.js +`IcosahedronGeometry`](https://threejs.org/docs/#api/en/geometries/IcosahedronGeometry) +in Rust. If you try to generate +[icosahedron](https://en.wikipedia.org/wiki/Icosahedron)s in Three.js over any +detail level over 5 the whole browser will slow to a crawl. I think we can do +better in Rust! + +Furthermore, I wanted to generate a hexsphere: a sphere composed of hexagon +faces and 12 pentagon faces, otherwise known as a truncated icosahedron or the +[Goldberg polyhedron](https://en.wikipedia.org/wiki/Goldberg_polyhedron). The +shape would be ideal for a game since (almost) every tile would have the same +area and six sides to defend or attack from. There's a few [Javascript projects +for generating hexspheres](https://www.robscanlon.com/hexasphere/). Most of them +generate the shape by starting with a subdivided icosahedron and then truncating +the sides into hexagons. Though, there [exist other methods for generating the +hexsphere +shape](https://stackoverflow.com/questions/46777626/mathematically-producing-sphere-shaped-hexagonal-grid). + +**Play around with all of these shapes in your browser at: +[https://www.hallada.net/planet/](https://www.hallada.net/planet/).** + +So, how would we go about generating a hexsphere from scratch? + + + +### The Icosahedron Seed + +To start our sculpture, we need our ball of clay. The most basic shape that we +start with can be defined by its 20 triangle faces and 12 vertices: the regular +icosahedron. If you've ever played Dungeons and Dragons, this is the 20-sided +die. + +To define this basic shape in Rust, we first need to define a few structs. The +most basic unit we need is a 3D vector which describes a single point in 3D +space with a X, Y, and Z float values. I could have defined this myself, but to +avoid having to implement a bunch of vector operations (like add, subtract, +multiply, etc.) I chose to import +[`Vector3`](https://docs.rs/cgmath/0.17.0/cgmath/struct.Vector3.html) from the +[cgmath crate](https://crates.io/crates/cgmath). + +The next struct we need is `Triangle`. This will define a face between three +vertices: + +```rust +#[derive(Debug)] +pub struct Triangle { + pub a: usize, + pub b: usize, + pub c: usize, +} + +impl Triangle { + fn new(a: usize, b: usize, c: usize) -> Triangle { + Triangle { a, b, c } + } +} +``` + +We use `usize` for the three points of the triangle because they are indices +into a [`Vec`](https://doc.rust-lang.org/std/vec/struct.Vec.html) of `Vector3`s. + +To keep these all together, I'll define a `Polyhedron` struct: + +```rust +#[derive(Debug)] +pub struct Polyhedron { + pub positions: Vec, + pub cells: Vec, +} +``` + +With this, we can define the regular icosahedron: + +```rust +impl Polyhedron { + pub fn regular_isocahedron() -> Polyhedron { + let t = (1.0 + (5.0 as f32).sqrt()) / 2.0; + Polyhedron { + positions: vec![ + Vector3::new(-1.0, t, 0.0), + Vector3::new(1.0, t, 0.0), + Vector3::new(-1.0, -t, 0.0), + Vector3::new(1.0, -t, 0.0), + Vector3::new(0.0, -1.0, t), + Vector3::new(0.0, 1.0, t), + Vector3::new(0.0, -1.0, -t), + Vector3::new(0.0, 1.0, -t), + Vector3::new(t, 0.0, -1.0), + Vector3::new(t, 0.0, 1.0), + Vector3::new(-t, 0.0, -1.0), + Vector3::new(-t, 0.0, 1.0), + ], + cells: vec![ + Triangle::new(0, 11, 5), + Triangle::new(0, 5, 1), + Triangle::new(0, 1, 7), + Triangle::new(0, 7, 10), + Triangle::new(0, 10, 11), + Triangle::new(1, 5, 9), + Triangle::new(5, 11, 4), + Triangle::new(11, 10, 2), + Triangle::new(10, 7, 6), + Triangle::new(7, 1, 8), + Triangle::new(3, 9, 4), + Triangle::new(3, 4, 2), + Triangle::new(3, 2, 6), + Triangle::new(3, 6, 8), + Triangle::new(3, 8, 9), + Triangle::new(4, 9, 5), + Triangle::new(2, 4, 11), + Triangle::new(6, 2, 10), + Triangle::new(8, 6, 7), + Triangle::new(9, 8, 1), + ], + } + } +} + +``` + +### JSON Serialization + +To prove this works, we need to be able to output our shape to some format that +will be able to be rendered. Coming from a JS background, I'm only familiar with +rendering shapes with WebGL. So, I need to be able to serialize the shape to +JSON so I can load it in JS. + +There's an amazing library in Rust called +[serde](https://crates.io/crates/serde) that will make this very +straightforward. We just need to import it and `impl Serialize` for all of our +structs. + +The JSON structure we want will look like this. This is what Three.js expects +when initializing +[`BufferGeometry`](https://threejs.org/docs/#api/en/core/BufferGeometry). + +```json +{ + "positions": [ + [ + -0.8506508, + 0, + 0.5257311 + ], + ... + ], + "cells": [ + [ + 0, + 1, + 2, + ], + ... + ], +} +``` + +For the `"cells"` array, we'll need to serialize `Triangle` into an array of 3 +integer arrays: + +```rust +impl Serialize for Triangle { + fn serialize(&self, serializer: S) -> Result + where + S: Serializer, + { + let vec_indices = vec![self.a, self.b, self.c]; + let mut seq = serializer.serialize_seq(Some(vec_indices.len()))?; + for index in vec_indices { + seq.serialize_element(&index)?; + } + seq.end() + } +} +``` + +I had some trouble serializing the `cgmath::Vector3` to an array, so I made my +own type that wrapped `Vector3` that could be serialized to an array of 3 +floats. + +```rust +#[derive(Debug)] +pub struct ArraySerializedVector(pub Vector3); + +impl Serialize for ArraySerializedVector { + fn serialize(&self, serializer: S) -> Result + where + S: Serializer, + { + let values = vec![self.0.x, self.0.y, self.0.z]; + let mut seq = serializer.serialize_seq(Some(values.len()))?; + for value in values { + seq.serialize_element(&value)?; + } + seq.end() + } +} +``` + +And now `Polyhedron` needs to use this new type and implement `Serialize` for +the whole shape to get serialized: + +```rust +#[derive(Serialize, Debug)] +pub struct Polyhedron { + pub positions: Vec, + pub cells: Vec, +} +``` + +The actual serialization is done with: + +```rust +fn write_to_json_file(polyhedron: Polyhedron, path: &Path) { + let mut json_file = File::create(path).expect("Can't create file"); + let json = serde_json::to_string(&polyhedron).expect("Problem serializing"); + json_file + .write_all(json.as_bytes()) + .expect("Can't write to file"); +} +``` + +On the JS side, the `.json` file can be read and simply fed into either Three.js +or [regl](https://github.com/regl-project/reg) to be rendered in WebGL ([more on +that later](#rendering-in-webgl-with-regl)). + +![Regular Icosahedron](/img/blog/icosahedron_colored_1.png) + +## Subdivided Icosahedron + +Now, we need to take our regular icosahedron and subdivide its faces N number of +times to generate an icosahedron with a detail level of N. + +I pretty much copied must of [the subdividing code from +Three.js](https://github.com/mrdoob/three.js/blob/34dc2478c684066257e4e39351731a93c6107ef5/src/geometries/PolyhedronGeometry.js#L90) +directly into Rust. + +I won't bore you with the details here, you can find the function +[here](https://github.com/thallada/icosahedron/blob/9643757df245e29f5ecfbb25f9a2c06b3a4e1217/src/lib.rs#L160-L205). + +![Subdivided Icosahedron](/img/blog/icosahedron_colored_3.png) + +### Truncated Icosahedron + +Now we get to the meat of this project. Transforming an icosahedron into a +hexsphere by +[truncating](https://en.wikipedia.org/wiki/Truncation_%28geometry%29) the points +of the icosahedron into hexagon and pentagon faces. + +You can imagine this operation as literally cutting off the points of the +subdivided icosahedron at exactly the midpoint between the point and it's six or +five neighboring points. + +![Image of biggest dodecahedron inside +icosahedron](/img/blog/dodecahedron_in_icosahedron.png) +([image source](http://www.oz.nthu.edu.tw/~u9662122/DualityProperty.html)) + +In this image you can see the regular icosahedron (0 subdivisions) in wireframe +with a yellow shape underneath which is the result of all 12 points truncated to +12 pentagon faces, in other words: the [regular +dodecahedron](https://en.wikipedia.org/wiki/Dodecahedron). + +You can see that the points of the new pentagon faces will be the exact center +of the original triangular faces. It should now make sense why truncating a +shape with 20 faces of 3 edges each results in a shape with 12 faces of 5 edges +each. Each pair multiplied still equals 60. + +#### Algorithm + +There are many different algorithms you could use to generate the truncated +shape, but this is roughly what I came up with: + +1. Store a map of every icosahedron vertex to faces composed from that vertex + (`vert_to_faces`). + +2. Calculate and cache the [centroid](https://en.wikipedia.org/wiki/Centroid) of + every triangle in the icosahedron (`triangle_centroids`). + +3. For every vertex in the original icosahedron: + +4. Find the center point between all of centroids of all of the faces for that + vertex (`center_point`). This is essentially the original icosahedron point + but lowered towards the center of the polygon since it will eventually be the + center of a new flat hexagon face. + + ![hexagon center point in red with original icosahedron faces fanning + out](/img/blog/hexagon_fan.png) + +5. For every triangle face composed from the original vertex: + + ![hexagon fan with selected triangle face in + blue](/img/blog/hexagon_fan_triangle_selected.png) + +6. Sort the vertices of the triangle face so there is a vertex `A` in the center + of the fan like in the image, and two other vertices `B` and `C` at the edges + of the hexagon. + +7. Find the centroid of the selected face. This will be one of the five or six + points of the new pentagon or hexagon (in brown in diagram below: + `triangleCentroid`). + +8. Find the mid point between `AB` and `AC` (points `midAB` and `midAC` in + diagram). + +9. With these mid points and the face centroid, we now have two new triangles + (in orange below) that form one-fifth or one-sixth of the final pentagon or + hexagon face. Add the points of the triangle to the `positions` array. Add + the two new triangles composed from those vertices as indexes into the + `positions` array to the `cells` array. We need to compose the pentagon or + hexagon out of triangles because in graphics everything is a triangle, and + this is the simplest way to tile either shape with triangles: + + ![hexagon fan ](/img/blog/hexagon_fan_construct.png) + +10. Go to step 5 until all faces of the icosahedron vertex have been visited. + Save indices to all new triangles in the `cells` array, which now form a + complete pentagon or hexagon face, to the `faces` array. + + ![hexagons tiling on icosahedron faces](/img/blog/hexagon_tiling.png) + +11. Go to step 3 until all vertices in the icosahedron have been visited. The + truncated icosahedron is now complete. + +![colored hexsphere of detail level 3](/img/blog/hexsphere_colored_3.png) + +#### Code + +The `truncate` function calls out to a bunch of other functions, so [here's a +link to the function within the context of the whole +file](https://github.com/thallada/icosahedron/blob/9643757df245e29f5ecfbb25f9a2c06b3a4e1217/src/lib.rs#L227). + +### Calculating Normals + +It took me a surprisingly long time to figure out how to compute +[normals](https://en.wikipedia.org/wiki/Normal_(geometry)) for the truncated +icosahedron. I tried just using an out-of-the-box solution like +[angle-normals](https://github.com/mikolalysenko/angle-normals/blob/master/angle-normals.js) +which could supposedly calculate the normal vectors for you, but they came out +all wrong. + +![hexsphere with bad normals](/img/blog/bad_hexsphere_normals.png) + +So, I tried doing it myself. Most tutorials on computing normal vectors for a +mesh assume that it is tiled in a particular way. But, my algorithm spins around +icosahedron points in all different directions, and so the triangle points are +not uniformly in clockwise or counter-clockwise order. + +I could have sorted these points into the correct order, but I found it easier +to instead just detect when the normal was pointing the wrong way and just +invert it. + +```rust +pub fn compute_triangle_normals(&mut self) { + let origin = Vector3::new(0.0, 0.0, 0.0); + for i in 0..self.cells.len() { + let vertex_a = &self.positions[self.cells[i].a].0; + let vertex_b = &self.positions[self.cells[i].b].0; + let vertex_c = &self.positions[self.cells[i].c].0; + + let e1 = vertex_a - vertex_b; + let e2 = vertex_c - vertex_b; + let mut no = e1.cross(e2); + + // detect and correct inverted normal + let dist = vertex_b - origin; + if no.dot(dist) < 0.0 { + no *= -1.0; + } + + let normal_a = self.normals[self.cells[i].a].0 + no; + let normal_b = self.normals[self.cells[i].b].0 + no; + let normal_c = self.normals[self.cells[i].c].0 + no; + + self.normals[self.cells[i].a] = ArraySerializedVector(normal_a); + self.normals[self.cells[i].b] = ArraySerializedVector(normal_b); + self.normals[self.cells[i].c] = ArraySerializedVector(normal_c); + } + + for normal in self.normals.iter_mut() { + *normal = ArraySerializedVector(normal.0.normalize()); + } +} +``` + +### Assigning Random Face Colors + +Finally, all that's left to generate is the face colors. The only way I could +figure out how to individually color a shape's faces in WebGL was to pass a +color per vertex. The issue with this is that each vertex of the generated +shapes could be shared between many different faces. + +How can we solve this? At the cost of memory, we can just duplicate a vertex +every time it's used by a different triangle. That way no vertex is shared. + +This can be done after a shape has been generated with shared vertices. + +```rust +pub fn unique_vertices(&mut self, other: Polyhedron) { + for triangle in other.cells { + let vertex_a = other.positions[triangle.a].0; + let vertex_b = other.positions[triangle.b].0; + let vertex_c = other.positions[triangle.c].0; + let normal_a = other.normals[triangle.a].0; + let normal_b = other.normals[triangle.b].0; + let normal_c = other.normals[triangle.c].0; + + self.positions.push(ArraySerializedVector(vertex_a)); + self.positions.push(ArraySerializedVector(vertex_b)); + self.positions.push(ArraySerializedVector(vertex_c)); + self.normals.push(ArraySerializedVector(normal_a)); + self.normals.push(ArraySerializedVector(normal_b)); + self.normals.push(ArraySerializedVector(normal_c)); + self.colors + .push(ArraySerializedVector(Vector3::new(1.0, 1.0, 1.0))); + self.colors + .push(ArraySerializedVector(Vector3::new(1.0, 1.0, 1.0))); + self.colors + .push(ArraySerializedVector(Vector3::new(1.0, 1.0, 1.0))); + let added_index = self.positions.len() - 1; + self.cells + .push(Triangle::new(added_index - 2, added_index - 1, added_index)); + } + self.faces = other.faces; +} +``` + +With unique vertices, we can now generate a random color per face with the [rand +crate](https://crates.io/crates/rand). + + +```rust +pub fn assign_random_face_colors(&mut self) { + let mut rng = rand::thread_rng(); + for i in 0..self.faces.len() { + let face_color = Vector3::new(rng.gen(), rng.gen(), rng.gen()); + + for c in 0..self.faces[i].len() { + let face_cell = &self.cells[self.faces[i][c]]; + + self.colors[face_cell.a] = ArraySerializedVector(face_color); + self.colors[face_cell.b] = ArraySerializedVector(face_color); + self.colors[face_cell.c] = ArraySerializedVector(face_color); + } + } +} +``` + +### Binary Serialization + +Now that we have to duplicate vertices for individual face colors, the size of +our JSON outputs are getting quite big: + +| File | Size | +|---|---| +| icosahedron_r1_d6.json | 28 MB | +| icosahedron_r1_d7.json | 113 MB | +| hexsphere_r1_d5.json | 42 MB | +| hexsphere_r1_d6.json | 169 MB | + +Since all of our data is just floating point numbers, we could reduce the size +of the output considerably by using a binary format instead. + +I used the [byteorder](https://docs.rs/byteorder/1.3.2/byteorder/) crate to +write out all of the `Vec`s in my `Polyhedron` struct to a binary file in +little-endian order. + +The binary format is laid out as: + +1. 1 32 bit unsigned integer specifying the number of vertices (`V`) +2. 1 32 bit unsigned integer specifying the number of triangles (`T`) +3. `V` * 3 number of 32 bit floats for every vertex's x, y, and z coordinate +4. `V` * 3 number of 32 bit floats for the normals of every vertex +5. `V` * 3 number of 32 bit floats for the color of every vertex +6. `T` * 3 number of 32 bit unsigned integers for the 3 indices into the vertex + array that make every triangle + +The `write_to_binary_file` function which does all that is +[here](https://github.com/thallada/icosahedron/blob/9643757df245e29f5ecfbb25f9a2c06b3a4e1217/src/bin.rs#L13). + +That's a lot better: + +| File | Size | +|---|---| +| icosahedron_r1_d6.bin | 9.8 MB | +| icosahedron_r1_d7.bin | 11 MB | +| hexsphere_r1_d5.bin | 14 MB | +| hexsphere_r1_d6.bin | 58 MB | + +On the JavaScript side, the binary files can be read into `Float32Array`s like +this: + +```javascript +fetch(binaryFile) + .then(response => response.arrayBuffer()) + .then(buffer => { + let reader = new DataView(buffer); + let numVertices = reader.getUint32(0, true); + let numCells = reader.getUint32(4, true); + let shape = { + positions: new Float32Array(buffer, 8, numVertices * 3), + normals: new Float32Array(buffer, numVertices * 12 + 8, numVertices * 3), + colors: new Float32Array(buffer, numVertices * 24 + 8, numVertices * 3), + cells: new Uint32Array(buffer, numVertices * 36 + 8, numCells * 3), + }) +``` + +### Rendering in WebGL with Regl + +I was initially rendering the shapes with Three.js but switched to +[regl](https://github.com/regl-project/regl) because it seemed like a more +direct abstraction over WebGL. It makes setting up a WebGL renderer incredibly +easy compared to all of the dozens cryptic function calls you'd have to +otherwise use. + +This is pretty much all of the rendering code using regl in my [3D hexsphere and +icosahedron viewer project](https://github.com/thallada/planet). + +```javascript +const drawShape = hexsphere => regl({ + vert: ` + precision mediump float; + uniform mat4 projection, view; + attribute vec3 position, normal, color; + varying vec3 fragNormal, fragPosition, fragColor; + void main() { + fragNormal = normal; + fragPosition = position; + fragColor = color; + gl_Position = projection * view * vec4(position, 1.0); + }`, + + frag: ` + precision mediump float; + struct Light { + vec3 color; + vec3 position; + }; + uniform Light lights[1]; + varying vec3 fragNormal, fragPosition, fragColor; + void main() { + vec3 normal = normalize(fragNormal); + vec3 light = vec3(0.1, 0.1, 0.1); + for (int i = 0; i < 1; i++) { + vec3 lightDir = normalize(lights[i].position - fragPosition); + float diffuse = max(0.0, dot(lightDir, normal)); + light += diffuse * lights[i].color; + } + gl_FragColor = vec4(fragColor * light, 1.0); + }`, + + attributes: { + position: hexsphere.positions, + normal: hexsphere.normals, + color: hexsphere.colors, + }, + elements: hexsphere.cells, + uniforms: { + "lights[0].color": [1, 1, 1], + "lights[0].position": ({ tick }) => { + const t = 0.008 * tick + return [ + 1000 * Math.cos(t), + 1000 * Math.sin(t), + 1000 * Math.sin(t) + ] + }, + }, +}) +``` + +I also imported [regl-camera](https://github.com/regl-project/regl-camera) which +handled all of the complex viewport code for me. + +It was fairly easy to get a simple renderer working quickly in regl, but I +couldn't find many examples of more complex projects using regl. Unfortunately, +the project looks a bit unmaintained these days as well. If I'm going to +continue with rendering in WebGL, I think I will try out +[Babylon.js](https://www.babylonjs.com/) instead. + +### Running in WebAssembly + +Since rust can be compiled down to wasm and then run in the browser, I briefly +tried getting the project to run completely in the browser. + +The [wasm-pack](https://github.com/rustwasm/wasm-pack) tool made it pretty easy +to get started. My main struggle was figuring out an efficient way to get the +megabytes of generated shape data into the JavaScript context so it could be +rendered in WebGL. + +The best I could come up with was to export all of my structs into flat +`Vec`s and then create `Float32Array`s from the JS side that are views into +wasm's memory. + +To export: + +```rust +pub fn fill_exports(&mut self) { + for position in &self.positions { + self.export_positions.push(position.0.x); + self.export_positions.push(position.0.y); + self.export_positions.push(position.0.z); + } + for normal in &self.normals { + self.export_normals.push(normal.0.x); + self.export_normals.push(normal.0.y); + self.export_normals.push(normal.0.z); + } + for color in &self.colors { + self.export_colors.push(color.0.x); + self.export_colors.push(color.0.y); + self.export_colors.push(color.0.z); + } + for cell in &self.cells { + self.export_cells.push(cell.a as u32); + self.export_cells.push(cell.b as u32); + self.export_cells.push(cell.c as u32); + } +} +``` + +And then the wasm `lib.rs`: + +```rust +use byteorder::{LittleEndian, WriteBytesExt}; +use js_sys::{Array, Float32Array, Uint32Array}; +use wasm_bindgen::prelude::*; +use web_sys::console; + +mod icosahedron; + +#[cfg(feature = "wee_alloc")] +#[global_allocator] +static ALLOC: wee_alloc::WeeAlloc = wee_alloc::WeeAlloc::INIT; + +#[wasm_bindgen(start)] +pub fn main_js() -> Result<(), JsValue> { + #[cfg(debug_assertions)] + console_error_panic_hook::set_once(); + + Ok(()) +} + +#[wasm_bindgen] +pub struct Hexsphere { + positions: Float32Array, + normals: Float32Array, + colors: Float32Array, + cells: Uint32Array, +} + +#[wasm_bindgen] +pub fn shape_data() -> Result { + let radius = 1.0; + let detail = 7; + let mut hexsphere = icosahedron::Polyhedron::new_truncated_isocahedron(radius, detail); + hexsphere.compute_triangle_normals(); + let mut unique_hexsphere = icosahedron::Polyhedron::new(); + unique_hexsphere.unique_vertices(hexsphere); + unique_hexsphere.assign_random_face_colors(); + unique_hexsphere.fill_exports(); + + let positions = unsafe { Float32Array::view(&unique_hexsphere.export_positions) }; + let normals = unsafe { Float32Array::view(&unique_hexsphere.export_normals) }; + let colors = unsafe { Float32Array::view(&unique_hexsphere.export_colors) }; + let cells = unsafe { Uint32Array::view(&unique_hexsphere.export_cells) }; + + Ok(Array::of4(&positions, &normals, &colors, &cells)) +} +``` + +With wasm-pack, I could import the wasm package, run the `shape_data()` +function, and then read the contents as any other normal JS array. + +```javascript +let rust = import("../pkg/index.js") +rust.then(module => { + const shapeData = module.shape_data() + const shape = { + positions: shapeData[0], + normals: shapeData[1], + colors: shapeData[2], + cells: shapeData[3], + } + ... +}) +``` + +I could side-step the issue of transferring data from Rust to JavaScript +entirely by programming literally everything in WebAssembly. But the bindings +from rust wasm to the WebGL API are still way too complicated compared to just +using regl. Plus, I'd have to implement my own camera from scratch. + +### The Stats + +So how much faster is Rust than JavaScript in generating icosahedrons and +hexspheres? + +Here's how long it took with generating shapes in JS with Three.js in Firefox +vs. in native Rust with a i5-2500K 3.3 GHz CPU. + +| Shape | JS generate time | Rust generate time | +|---|---|---| +| Icosahedron detail 6 | 768 ms | 28.23 ms | +| Icosahedron detail 7 | 4.25 s | 128.81 ms | +| Hexsphere detail 6 | 11.37 s | 403.10 ms | +| Hexsphere detail 7 | 25.49 s | 1.85 s | + +So much faster! + + +### Todo + +* Add a process that alters the shape post-generation. Part of the reason why I + decided to fan the hexagon faces with so many triangles is that it also allows + me to control the height of the faces better. This could eventually allow me + to create mountain ranges and river valleys on a hexsphere planet. Stretching + and pulling the edges of the polygon faces in random directions could add + variation and make for a more organic looking hexsphere. + +* Conversely, it would be nice to be able to run a process post-generation that + could reduce the number of triangles by tiling the hexagons more efficiently + when face elevation isn't needed. + +* Add parameters to the generation that allows generating sections of the + hexsphere / icosahedron. This will be essential for rendering very detailed + polyhedrons since at a certain detail level it becomes impossible to render + the entire shape at once. + + In WebGL, figure out what part of the shape is in the current viewport and + pass these parameters to the generation. + +* Render the shapes in a native Rust graphics library instead of WebGL. I'm + curious how much slower WebGL is making things. + +* Parallelize the generation. Right now the generation is very CPU bound and + each subdivide/truncate iteration is mostly independent from each other, so I + think I could get some decent speed-up by allowing the process to run on + multiple cores. Perhaps the [rayon](https://github.com/rayon-rs/rayon) crate + could make this pretty straightforward. + +* Find some way to avoid unique vertices. The size of the shape is *much* bigger + because of this. There might be a way to keep shared vertices while also + having a separate color per face by using texture mapping. + +* In the renderer, implement face selection (point and click face and show an + outline around selected face). + +* In the renderer, implement fly-to-face zooming: given a face, fly the camera + around the sphere in an orbit and then zoom in on the face. diff --git a/img/blog/bad_hexsphere_normals.png b/img/blog/bad_hexsphere_normals.png new file mode 100755 index 0000000000000000000000000000000000000000..6bcb45610f0a99c9c833c38579de9c0bb115ebc4 GIT binary patch literal 372129 zcmeFY^4GvZ1ffZJ^@MYTTaeIJftdx^j0Q( zG>z$=)YksTmieqTM0$4o)KtCdyBgy?j{EpBwhL^i*&)wIA+E3EH|N6Jbf8zfy z8AdF;R|l|R*$VPxe!d+;4cx6aK3(%;r0f$)MBf>MtJCyV&rEv4ICvHCqkg(Q=8e^W z8MMmj^~b55yj3kE(^fUtB?H=Yudr_3{iFZf>)KbEIGUus$WxiqM)V4(w8-~CiWs9} zh!g=5``4h!-PMQy%?IMZe1bvT7t1%>o&I{O0hH z=pwn zisY@Besfk;JHA>U_S``7ODrNH@YBII!&&H&>P6M6+a1>L0iXU0UF`qH5bw8l8zp9jj<`G7JefC~i($ts2$@?%%MIC0Hcxviu5prVm=dIP9>!w~Fy64y 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