├── .yarnrc.yml ├── .github ├── FUNDING.yml └── workflows │ └── ci.yml ├── .gitignore ├── test ├── cube.glb ├── cube.obj └── test.js ├── assets ├── correct.png └── incorrect.png ├── .yarn └── install-state.gz ├── renovate.json ├── Cargo.toml ├── LICENSE ├── package.json ├── src └── lib.rs ├── README.md ├── Cargo.lock └── yarn.lock /.yarnrc.yml: -------------------------------------------------------------------------------- 1 | nodeLinker: node-modules 2 | -------------------------------------------------------------------------------- /.github/FUNDING.yml: -------------------------------------------------------------------------------- 1 | github: [donmccurdy] 2 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | .cache 2 | dist 3 | node_modules 4 | pkg 5 | target 6 | -------------------------------------------------------------------------------- /test/cube.glb: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/donmccurdy/mikktspace-wasm/HEAD/test/cube.glb -------------------------------------------------------------------------------- /assets/correct.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/donmccurdy/mikktspace-wasm/HEAD/assets/correct.png -------------------------------------------------------------------------------- /assets/incorrect.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/donmccurdy/mikktspace-wasm/HEAD/assets/incorrect.png -------------------------------------------------------------------------------- /.yarn/install-state.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/donmccurdy/mikktspace-wasm/HEAD/.yarn/install-state.gz -------------------------------------------------------------------------------- /renovate.json: -------------------------------------------------------------------------------- 1 | { 2 | "$schema": "https://docs.renovatebot.com/renovate-schema.json", 3 | "extends": [ 4 | "local>donmccurdy/renovate-config" 5 | ] 6 | } 7 | -------------------------------------------------------------------------------- /Cargo.toml: -------------------------------------------------------------------------------- 1 | [package] 2 | name = "mikktspace" 3 | version = "1.1.0" 4 | authors = ["Don McCurdy "] 5 | description = "MikkTSpace vertex tangent calculation, in Web Assembly." 6 | license = "MIT" 7 | repository = "https://github.com/donmccurdy/mikktspace-wasm" 8 | edition = "2018" 9 | 10 | [lib] 11 | crate-type = ["cdylib"] 12 | 13 | [dependencies] 14 | wasm-bindgen = "0.2" 15 | mikktspace = "0.3" 16 | nalgebra = "0.33.0" 17 | # Debug only. 18 | console_error_panic_hook = { version = "0.1" } 19 | 20 | [profile.release] 21 | opt-level = 's' 22 | -------------------------------------------------------------------------------- /.github/workflows/ci.yml: -------------------------------------------------------------------------------- 1 | name: build 2 | on: [push, pull_request] 3 | jobs: 4 | build: 5 | runs-on: ubuntu-latest 6 | strategy: 7 | matrix: 8 | node-version: [20.x] 9 | env: 10 | CI: true 11 | steps: 12 | # Setup. 13 | - uses: actions/checkout@v5 14 | - uses: actions-rs/toolchain@v1 15 | with: 16 | toolchain: stable 17 | - uses: jetli/wasm-pack-action@v0.4.0 18 | - name: Use Node.js ${{ matrix.node-version }} 19 | uses: actions/setup-node@v4 20 | with: 21 | node-version: ${{ matrix.node-version }} 22 | 23 | # Build. 24 | - run: corepack enable 25 | - run: yarn install 26 | - run: yarn dist 27 | 28 | # Test. 29 | - run: yarn test 30 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | The MIT License (MIT) 2 | 3 | Copyright (c) 2021 Don McCurdy 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /package.json: -------------------------------------------------------------------------------- 1 | { 2 | "name": "mikktspace", 3 | "version": "1.1.1", 4 | "description": "MikkTSpace vertex tangent calculation, in Web Assembly", 5 | "author": "Don McCurdy ", 6 | "license": "MIT", 7 | "repository": "github:donmccurdy/mikktspace-wasm", 8 | "main": "dist/main/mikktspace_main.js", 9 | "module": "dist/module/mikktspace_module.js", 10 | "types": "dist/module/mikktspace_module.d.ts", 11 | "sideEffects": false, 12 | "scripts": { 13 | "dist": "yarn dist:main && yarn dist:module && find dist/main -type f ! -name 'mikktspace*' -delete && find dist/module -type f ! -name 'mikktspace*' -delete", 14 | "dist:module": "wasm-pack build --release --target bundler --out-dir dist/module --out-name mikktspace_module", 15 | "dist:main": "wasm-pack build --release --target nodejs --out-dir dist/main --out-name mikktspace_main", 16 | "dist:debug": "wasm-pack build --dev --target nodejs --out-dir dist/main --out-name mikktspace_main", 17 | "clean": "rm dist/main* && rm dist/module*", 18 | "test": "tape test/test.js | tap-spec", 19 | "preversion": "yarn dist && yarn test", 20 | "postversion": "git push && git push --tags && npm publish" 21 | }, 22 | "keywords": [ 23 | "mikktspace", 24 | "tangents", 25 | "tangent-space", 26 | "three.js", 27 | "threejs", 28 | "webgl", 29 | "webgpu" 30 | ], 31 | "files": [ 32 | "README.md", 33 | "LICENSE", 34 | "package.json", 35 | "dist/", 36 | "mikktspace.d.ts" 37 | ], 38 | "devDependencies": { 39 | "@gltf-transform/core": "4.2.1", 40 | "@gltf-transform/functions": "4.2.1", 41 | "tap-spec": "5.0.0", 42 | "tape": "5.9.0" 43 | }, 44 | "packageManager": "yarn@4.10.3" 45 | } 46 | -------------------------------------------------------------------------------- /test/cube.obj: -------------------------------------------------------------------------------- 1 | v 0.5 -0.5 0.5 2 | v 0.5 -0.5 -0.5 3 | v 0.5 0.5 -0.5 4 | v 0.5 0.5 0.5 5 | v 0.5 0 0 6 | v -0.5 0.5 0.5 7 | v -0.5 0.5 -0.5 8 | v -0.5 -0.5 -0.5 9 | v -0.5 -0.5 0.5 10 | v -0.5 0 0 11 | v 0.5 0.5 0.5 12 | v 0.5 0.5 -0.5 13 | v -0.5 0.5 -0.5 14 | v -0.5 0.5 0.5 15 | v 0 0.5 0 16 | v -0.5 -0.5 0.5 17 | v -0.5 -0.5 -0.5 18 | v 0.5 -0.5 -0.5 19 | v 0.5 -0.5 0.5 20 | v 0 -0.5 0 21 | v -0.5 0.5 0.5 22 | v -0.5 -0.5 0.5 23 | v 0.5 -0.5 0.5 24 | v 0.5 0.5 0.5 25 | v 0 0 0.5 26 | v 0.5 0.5 -0.5 27 | v 0.5 -0.5 -0.5 28 | v -0.5 -0.5 -0.5 29 | v -0.5 0.5 -0.5 30 | v 0 0 -0.5 31 | vn 0.57735026 -0.57735026 0.57735026 32 | vn 0.57735026 -0.57735026 -0.57735026 33 | vn 0.57735026 0.57735026 -0.57735026 34 | vn 0.57735026 0.57735026 0.57735026 35 | vn 1 0 0 36 | vn -0.57735026 0.57735026 0.57735026 37 | vn -0.57735026 0.57735026 -0.57735026 38 | vn -0.57735026 -0.57735026 -0.57735026 39 | vn -0.57735026 -0.57735026 0.57735026 40 | vn -1 0 0 41 | vn 0.57735026 0.57735026 0.57735026 42 | vn 0.57735026 0.57735026 -0.57735026 43 | vn -0.57735026 0.57735026 -0.57735026 44 | vn -0.57735026 0.57735026 0.57735026 45 | vn 0 1 0 46 | vn -0.57735026 -0.57735026 0.57735026 47 | vn -0.57735026 -0.57735026 -0.57735026 48 | vn 0.57735026 -0.57735026 -0.57735026 49 | vn 0.57735026 -0.57735026 0.57735026 50 | vn 0 -1 0 51 | vn -0.57735026 0.57735026 0.57735026 52 | vn -0.57735026 -0.57735026 0.57735026 53 | vn 0.57735026 -0.57735026 0.57735026 54 | vn 0.57735026 0.57735026 0.57735026 55 | vn 0 0 1 56 | vn 0.57735026 0.57735026 -0.57735026 57 | vn 0.57735026 -0.57735026 -0.57735026 58 | vn -0.57735026 -0.57735026 -0.57735026 59 | vn -0.57735026 0.57735026 -0.57735026 60 | vn 0 0 -1 61 | vt 0 0 62 | vt 0 1 63 | vt 1 1 64 | vt 1 0 65 | vt 0.5 0.5 66 | vt 1 0 67 | vt 1 1 68 | vt 0 1 69 | vt 0 0 70 | vt 0.5 0.5 71 | vt 0 0 72 | vt 0 1 73 | vt 0 1 74 | vt 0 0 75 | vt 0 0.5 76 | vt 0 0 77 | vt 0 1 78 | vt 0 1 79 | vt 0 0 80 | vt 0 0.5 81 | vt 0 0 82 | vt 0 1 83 | vt 1 1 84 | vt 1 0 85 | vt 0.5 0.5 86 | vt 1 0 87 | vt 1 1 88 | vt 0 1 89 | vt 0 0 90 | vt 0.5 0.5 91 | f 1/1/1 2/2/2 5/5/5 92 | f 2/2/2 3/3/3 5/5/5 93 | f 3/3/3 4/4/4 5/5/5 94 | f 4/4/4 1/1/1 5/5/5 95 | f 6/6/6 7/7/7 10/10/10 96 | f 7/7/7 8/8/8 10/10/10 97 | f 8/8/8 9/9/9 10/10/10 98 | f 9/9/9 6/6/6 10/10/10 99 | f 11/11/11 12/12/12 15/15/15 100 | f 12/12/12 13/13/13 15/15/15 101 | f 13/13/13 14/14/14 15/15/15 102 | f 14/14/14 11/11/11 15/15/15 103 | f 16/16/16 17/17/17 20/20/20 104 | f 17/17/17 18/18/18 20/20/20 105 | f 18/18/18 19/19/19 20/20/20 106 | f 19/19/19 16/16/16 20/20/20 107 | f 21/21/21 22/22/22 25/25/25 108 | f 22/22/22 23/23/23 25/25/25 109 | f 23/23/23 24/24/24 25/25/25 110 | f 24/24/24 21/21/21 25/25/25 111 | f 26/26/26 27/27/27 30/30/30 112 | f 27/27/27 28/28/28 30/30/30 113 | f 28/28/28 29/29/29 30/30/30 114 | f 29/29/29 26/26/26 30/30/30 -------------------------------------------------------------------------------- /src/lib.rs: -------------------------------------------------------------------------------- 1 | use wasm_bindgen::prelude::*; 2 | use mikktspace::{Geometry}; 3 | 4 | #[cfg(debug_assertions)] 5 | extern crate console_error_panic_hook; 6 | 7 | #[cfg(debug_assertions)] 8 | use std::panic; 9 | 10 | /****************************************************************************** 11 | * JavaScript interface. 12 | */ 13 | 14 | /// Generates vertex tangents for the given position/normal/texcoord attributes. 15 | #[wasm_bindgen] 16 | #[allow(non_snake_case)] 17 | pub fn generateTangents(position: Vec, normal: Vec, texcoord: Vec) -> Result, JsValue> { 18 | #[cfg(debug_assertions)] 19 | panic::set_hook(Box::new(console_error_panic_hook::hook)); 20 | 21 | let mut mesh = Mesh { position, normal, texcoord, tangent: Vec::new() }; 22 | if mikktspace::generate_tangents(&mut mesh) { 23 | Ok(mesh.tangent) 24 | } else { 25 | Err(JsValue::from_str("Failed to generate tangents.")) 26 | } 27 | } 28 | 29 | /****************************************************************************** 30 | * MikkTSpace library interface. 31 | */ 32 | 33 | pub struct Mesh { 34 | position: Vec, 35 | normal: Vec, 36 | texcoord: Vec, 37 | tangent: Vec, 38 | } 39 | 40 | impl Geometry for Mesh { 41 | fn num_faces(&self) -> usize { 42 | self.position.len() / 9 43 | } 44 | 45 | fn num_vertices_of_face(&self, _face: usize) -> usize { 46 | 3 47 | } 48 | 49 | fn position(&self, face: usize, vert: usize) -> [f32; 3] { 50 | [ 51 | self.position[face * 9 + vert * 3 + 0], 52 | self.position[face * 9 + vert * 3 + 1], 53 | self.position[face * 9 + vert * 3 + 2], 54 | ] 55 | } 56 | 57 | fn normal(&self, face: usize, vert: usize) -> [f32; 3] { 58 | [ 59 | self.normal[face * 9 + vert * 3 + 0], 60 | self.normal[face * 9 + vert * 3 + 1], 61 | self.normal[face * 9 + vert * 3 + 2], 62 | ] 63 | } 64 | 65 | fn tex_coord(&self, face: usize, vert: usize) -> [f32; 2] { 66 | [ 67 | self.texcoord[face * 6 + vert * 2 + 0], 68 | self.texcoord[face * 6 + vert * 2 + 1], 69 | ] 70 | } 71 | 72 | fn set_tangent_encoded(&mut self, tangent: [f32; 4], _face: usize, _vert: usize) { 73 | self.tangent.push(tangent[0]); 74 | self.tangent.push(tangent[1]); 75 | self.tangent.push(tangent[2]); 76 | self.tangent.push(tangent[3]); 77 | } 78 | } 79 | 80 | /****************************************************************************** 81 | * Debugging. 82 | */ 83 | 84 | #[cfg(debug_assertions)] 85 | #[wasm_bindgen] 86 | extern "C" { 87 | #[wasm_bindgen(js_namespace = console)] 88 | fn log(s: &str); 89 | } 90 | 91 | #[cfg(debug_assertions)] 92 | #[allow(unused_macros)] 93 | macro_rules! console_log { 94 | ($($t:tt)*) => (log(&format_args!($($t)*).to_string())) 95 | } 96 | 97 | #[cfg(debug_assertions)] 98 | #[wasm_bindgen] 99 | pub fn init_panic_hook() { 100 | console_error_panic_hook::set_once(); 101 | } 102 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # mikktspace-wasm 2 | 3 | [![Latest NPM release](https://img.shields.io/npm/v/mikktspace.svg)](https://www.npmjs.com/package/mikktspace) 4 | [![Build Status](https://github.com/donmccurdy/mikktspace-wasm/workflows/build/badge.svg?branch=main&event=push)](https://github.com/donmccurdy/mikktspace-wasm/actions?query=workflow%3Abuild) 5 | 6 | [MikkTSpace](http://www.mikktspace.com/) vertex tangent calculation, in Web Assembly. 7 | 8 | > A common misunderstanding about tangent space normal maps is that this representation is somehow asset independent. However, normals sampled/captured from a high resolution surface and then transformed into tangent space is more like an encoding. Thus to reverse the original captured field of normals the transformation used to decode would have to be the exact inverse of that which was used to encode. 9 | > 10 | > — Morten S. Mikkelsen 11 | 12 | When normal maps render incorrectly, with distortion or unexpectedly inverted insets and extrusions, this misconception may be the cause. Most normal map bakers use the MikkTSpace standard to generate vertex tangents while creating a normal map, and the technique is recommended by the glTF 2.0 specification. Engines reconstructing the tangent space at runtime often use other methods — e.g. derivatives in the pixel shader — for efficiency, when original tangents are not provided. This works well for _most_ assets, but may not work as well for others. 13 | 14 | If you have an... 15 | 16 | - **Asset** that needs to render predictably in many engines 17 | - **Asset Pipeline** that needs to produce assets with predictable normal map behavior 18 | - **Engine** that needs to support arbitrary assets perfectly (and can afford the per-vertex pre-processing) 19 | 20 | ...then MikkTSpace vertex tangents may resolve or prevent rendering issues with normal maps. 21 | 22 | | correct | incorrect | 23 | |---------|-----------| 24 | | ![correct rendering](./assets/correct.png) | ![incorrect rendering](./assets/incorrect.png) | 25 | 26 | > **Figure:** *[Flight Helmet](https://github.com/KhronosGroup/glTF-Sample-Models/tree/master/2.0/FlightHelmet) glTF 2.0 sample, shown with correct (left) and incorrect (right) vertex tangents.* 27 | 28 | ## Other considerations 29 | 30 | The MikkTSpace algorithm requires unindexed (unwelded) triangles as input. It is safe to create an index (welding vertices whose tangents and other attributes are identical) after generating tangents, but you _cannot_ reuse prior indices after generating tangents. This additional cost is, perhaps, why some realtime engines choose to generate tangents with cheaper alternative algorithms, when pre-computed tangents are not provided with the asset. 31 | 32 | When generating vertex tangents for [glTF 2.0](https://github.com/KhronosGroup/glTF) assets, you will want to flip the sign of the tangents (`tangent.w *= -1`) before storing them in the glTF file. While MikkTSpace does not document a particular UV convention that I could find, this [appears to be a necessary conversion](https://github.com/KhronosGroup/glTF-Sample-Models/issues/174) to the [texture coordinate convention used in glTF](https://github.com/KhronosGroup/glTF/blob/master/specification/2.0/README.md#images). 33 | 34 | ## Quickstart 35 | 36 | Installation: 37 | 38 | ``` 39 | npm install --save mikktspace 40 | ``` 41 | 42 | The `mikktspace` package includes two entrypoints. For modern projects, the default entrypoint uses 43 | [ES Modules](https://eloquentjavascript.net/10_modules.html#h_hF2FmOVxw7): 44 | 45 | ```js 46 | import { generateTangents } from 'mikktspace'; 47 | 48 | const tangents = generateTangents(positions, normals, uvs); // → Float32Array 49 | ``` 50 | 51 | Node.js does not yet support ES Modules with WebAssembly particularly well (as of Node.js v14), so the `mikktspace` 52 | package also provides a CommonJS entrypoint. The CommonJS entrypoint works only in Node.js. 53 | 54 | ```js 55 | const { generateTangents } = require('mikktspace'); 56 | 57 | const tangents = generateTangents(positions, normals, uvs); // → Float32Array 58 | ``` 59 | 60 | ## API 61 | 62 | ### generateTangents 63 | 64 | Generates vertex tangents for the given position/normal/texcoord attributes. Triangles of the 65 | input geometry must be unindexed/unwelded. 66 | 67 | **Parameters** 68 | 69 | - `positions`: [`Float32Array`][1] 70 | - `normals`: [`Float32Array`][1] 71 | - `uvs`: [`Float32Array`][1] 72 | 73 | **Returns** 74 | 75 | [`Float32Array`][1] 76 | 77 | [1]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float32Array 78 | 79 | ## Contributing 80 | 81 | 1. Install [Rust](https://www.rust-lang.org/tools/install) and [wasm-pack](https://rustwasm.github.io/wasm-pack/installer/) 82 | 2. Install local dependencies: `yarn install` 83 | 3. Build: `yarn dist` 84 | 4. Test: `yarn test` 85 | 86 | ## Credits 87 | 88 | This WebAssembly library is made possible by the [gltf-rs/mikktspace](https://github.com/gltf-rs/mikktspace) 89 | project, and by the [MikkTSpace standard](http://www.mikktspace.com/) created by Morten S. Mikkelsen. 90 | -------------------------------------------------------------------------------- /test/test.js: -------------------------------------------------------------------------------- 1 | const mikktspace = require('../'); 2 | const tape = require('tape'); 3 | const path = require('path'); 4 | const { NodeIO } = require('@gltf-transform/core'); 5 | const { unweld } = require('@gltf-transform/functions'); 6 | 7 | tape('generateTangents', async (t) => { 8 | const io = new NodeIO(); 9 | const document = await io.read(path.resolve(__dirname, './cube.glb')); 10 | await document.transform(unweld()); 11 | const cube = document.getRoot().listMeshes()[0].listPrimitives()[0]; 12 | 13 | const tangentArray = mikktspace.generateTangents( 14 | cube.getAttribute('POSITION').getArray(), 15 | cube.getAttribute('NORMAL').getArray(), 16 | cube.getAttribute('TEXCOORD_0').getArray(), 17 | ); 18 | 19 | t.ok(tangentArray instanceof Float32Array, 'returns float32array'); 20 | t.equals(tangentArray.length, TANGENTS_EXPECTED.length, 'length matches inputs'); 21 | 22 | const invalid = []; 23 | for (let i = 0; i < tangentArray.length; i++) { 24 | if (tangentArray[i] !== TANGENTS_EXPECTED[i]) { 25 | invalid.push({actual: tangentArray[i], expected: TANGENTS_EXPECTED[i], index: i}); 26 | } 27 | } 28 | 29 | t.deepEquals(invalid, [], 'tangents match expected values'); 30 | t.end(); 31 | }); 32 | 33 | tape('generateTangents | memory', async (t) => { 34 | const io = new NodeIO(); 35 | const document = await io.read(path.resolve(__dirname, './cube.glb')); 36 | await document.transform(unweld()); 37 | const cube = document.getRoot().listMeshes()[0].listPrimitives()[0]; 38 | 39 | let initialMemory = -1; 40 | 41 | for (let i = 0; i < 1000; i++) { 42 | const tangentArray = mikktspace.generateTangents( 43 | cube.getAttribute('POSITION').getArray(), 44 | cube.getAttribute('NORMAL').getArray(), 45 | cube.getAttribute('TEXCOORD_0').getArray(), 46 | ); 47 | 48 | const currentMemory = mikktspace.__wasm.memory.buffer.byteLength / 1024 / 1024; 49 | if (i === 0) { 50 | initialMemory = currentMemory; 51 | } else if ((i % 100) === 0) { 52 | t.equals(currentMemory, initialMemory, `memory = ${initialMemory} MB @ ${i}/1000`); 53 | } 54 | } 55 | t.end(); 56 | }); 57 | 58 | tape('generateTangents | error handling', (t) => { 59 | const positions = new Float32Array(); 60 | const normals = new Float32Array(); 61 | const uvs = new Float32Array([1, 1]); 62 | t.throws(() => mikktspace.generateTangents(positions, normals, uvs), /Failed/, 'error handling'); 63 | t.end(); 64 | }); 65 | 66 | const TANGENTS_EXPECTED = new Float32Array([ 67 | 0.40824824,0.81649655,0.40824824,1, 68 | 0.40824824,0.81649655,-0.40824824,1, 69 | 0,1,0,1, 70 | 0.40824824,0.81649655,-0.40824824,1, 71 | -0.40824824,0.81649655,0.40824824,1, 72 | 0,1,0,1, 73 | -0.40824824,0.81649655,0.40824824,1, 74 | -0.40824824,0.81649655,-0.40824824,1, 75 | 0,1,0,1, 76 | -0.40824824,0.81649655,-0.40824824,1, 77 | 0.40824824,0.81649655,0.40824824,1, 78 | 0,1,0,1, 79 | 0.40824824,0.81649655,-0.40824824,-1, 80 | 0.40824824,0.81649655,0.40824824,-1, 81 | 0,1,0,-1, 82 | 0.40824824,0.81649655,0.40824824,-1, 83 | -0.40824824,0.81649655,-0.40824824,-1, 84 | 0,1,0,-1, 85 | -0.40824824,0.81649655,-0.40824824,-1, 86 | -0.40824824,0.81649655,0.40824824,-1, 87 | 0,1,0,-1, 88 | -0.40824824,0.81649655,0.40824824,-1, 89 | 0.40824824,0.81649655,-0.40824824,-1, 90 | 0,1,0,-1, 91 | 1,0,0,-1, 92 | 1,0,0,-1, 93 | 1,0,0,-1, 94 | 1,0,0,-1, 95 | 1,0,0,-1, 96 | 1,0,0,-1, 97 | 1,0,0,-1, 98 | 1,0,0,-1, 99 | 1,0,0,-1, 100 | 1,0,0,-1, 101 | 1,0,0,-1, 102 | 1,0,0,-1, 103 | -0.40824824,0.81649655,0.40824824,-1, 104 | -0.40824824,0.81649655,-0.40824824,-1, 105 | 1,0,0,-1, 106 | 1,0,0,-1, 107 | 0.40824824,0.81649655,-0.40824824,1, 108 | 1,0,0,-1, 109 | 0.40824824,0.81649655,-0.40824824,1, 110 | 0.40824824,0.81649655,0.40824824,1, 111 | 1,0,0,-1, 112 | 0.40824824,0.81649655,0.40824824,1, 113 | 1,0,0,-1, 114 | 1,0,0,-1, 115 | 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