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Schmidt","url":"https://thi.ng"},"license":"Apache-2.0","homepage":"https://thi.ng/timestep","keywords":["deterministic","fractional","interpolation","physics","simulation","time","typescript","vector"],"repository":{"type":"git","url":"git+https://codeberg.org/thi.ng/umbrella.git","directory":"packages/timestep"},"description":"Deterministic fixed timestep simulation updates with state interpolation","maintainers":[{"name":"thi.ng","email":"k+npm@thi.ng"}],"readme":"<!-- This file is generated - DO NOT EDIT! -->\n<!-- Please see: https://codeberg.org/thi.ng/umbrella/src/branch/develop/CONTRIBUTING.md#changes-to-readme-files -->\n# ![@thi.ng/timestep](https://codeberg.org/thi.ng/umbrella/media/branch/develop/assets/banners/thing-timestep.svg?5087f691)\n\n[![npm version](https://img.shields.io/npm/v/@thi.ng/timestep.svg)](https://www.npmjs.com/package/@thi.ng/timestep)\n![npm downloads](https://img.shields.io/npm/dm/@thi.ng/timestep.svg)\n[![Mastodon Follow](https://img.shields.io/mastodon/follow/109331703950160316?domain=https%3A%2F%2Fmastodon.thi.ng&style=social)](https://mastodon.thi.ng/@toxi)\n\n> [!NOTE]\n\n> This is one of 217 standalone projects. LLM-free, human-made and\n> cared for software, maintained as part of the\n> [@thi.ng/umbrella](https://codeberg.org/thi.ng/umbrella/) ecosystem and\n> anti-framework.\n>\n> 🚀 Please help me to work full-time on these projects by [sponsoring\n> me](https://codeberg.org/thi.ng/umbrella/src/branch/develop/CONTRIBUTING.md#donations).\n> Thank you! ❤️\n\n- [About](#about)\n  - [Managing fixed timestep updates](#managing-fixed-timestep-updates)\n- [Status](#status)\n- [Related packages](#related-packages)\n- [Installation](#installation)\n- [Dependencies](#dependencies)\n- [Usage examples](#usage-examples)\n- [API](#api)\n- [Authors](#authors)\n- [License](#license)\n\n## About\n\nDeterministic fixed timestep simulation updates with state interpolation.\n\nFor a more thorough description of both the problem and solution(s), please see\n[Glenn Fiedler's article](https://www.gafferongames.com/post/fix_your_timestep/)\nupon which this implementation is principally based on.\n\n### Managing fixed timestep updates\n\nThe package provides a configurable [`TimeStep`\nclass](https://docs.thi.ng/umbrella/timestep/classes/TimeStep.html) to manage\nthe update logic. To participate in these managed updates, the user must provide\nstate values/wrappers implementing the [`ITimeStep`\ninterface](https://docs.thi.ng/umbrella/timestep/interfaces/ITimeStep.html) for\nthe two main phases of the frame update:\n\n- `integrate(dt: number, ctx: ReadonlyTimeStep): void`: Depending on actual\n    elapsed time and the configured timestep, this function might be called\n    several times per update cycle to update the sim to its next desired state\n    to:\n    1. Backup the current state of the sim (at the beginning of that function\n    call). This backup is required for the second phase of the update.\n    2. Update the state to the desired next state using the provided timestep\n    `dt` (`ctx` is only given for information).\n- `interpolate(alpha: number, ctx: ReadonlyTimeStep): void`: In this phase a\n  previously backed up state should be linearly interpolated to the current\n  state using the provided `alpha` tween factor and the result stored separately\n  such that it can be used for subsequent rendering/display purposes.\n\nIn other words, this means any updatable state value will require 3 versions:\nprevious, current (next), interpolated. **Only the interpolated version is to be\nused for rendering (or other userland purposes).** For that reason, the package\nalso provides wrappers for\n[numeric](https://docs.thi.ng/umbrella/timestep/functions/defNumeric.html) and\n[vector-based](https://docs.thi.ng/umbrella/timestep/functions/defVector.html)\n(arbitrary length and optimized 2D/3D/4D versions) state variables, illustrated\nin the following short example:\n\n```ts tangle:export/readme.ts\nimport { defTimeStep, defNumeric, defVector2 } from \"@thi.ng/timestep\";\nimport { maddN2 } from \"@thi.ng/vectors\";\n\n// initialize with default options (i.e. dt = 1/60 = 60 fps)\n// start time is given in milliseconds but will be converted to seconds\n// see: https://docs.thi.ng/umbrella/timestep/interfaces/TimestepOpts.html\nconst sim = defTimeStep({ dt: 1 / 60, startTime: Date.now() });\n\n// define numeric state variable, increase using @ 10 units per second\nconst a = defNumeric(0, (x, dt) => x + dt * 10);\n\n// define vector state variable, update by applying velocity of [-10, 20] (per second)\n// also see thi.ng/vectors for hundreds of other useful vector operations...\n// the update function MUST write its result in given vector (1st arg)\nconst b = defVector2([0, 0], (v, dt) => maddN2(v, [-10, 20], dt, v));\n\n// even though the sim will update at a fixed (theoretical) 60 fps,\n// the simulated render frame rate here is only 25 fps...\nsetInterval(() => {\n    // provide current time and an array of state values to update\n    // (any ITimeStep impl can be given here, incl. custom types)\n    sim.update(Date.now(), [a, b]);\n    // show current frame, num updates, time (relative to start) and interpolated state values\n    console.log(sim.frame, sim.updates, sim.current, a.value, b.value);\n}, 1000 / 25);\n\n// 1   2   0.042 0.253  [ -0.253, 0.506 ]\n// 2   4   0.082 0.663  [ -0.663, 1.326 ]\n// 3   7   0.124 1.073  [ -1.073, 2.146 ]\n// 4   9   0.164 1.483  [ -1.483, 2.966 ]\n// 5   12  0.206 1.893  [ -1.893, 3.786 ]\n// 6   14  0.246 2.293  [ -2.293, 4.586 ]\n// 7   17  0.288 2.713  [ -2.713, 5.426 ]\n// 8   19  0.328 3.123  [ -3.123, 6.246 ]\n// 9   22  0.371 3.543  [ -3.543, 7.086 ]\n// 10  24  0.411 3.953  [ -3.953, 7.906 ]\n// 11  27  0.452 4.353  [ -4.353, 8.706 ]\n// 12  29  0.493 4.773  [ -4.773, 9.546 ]\n// 13  32  0.534 5.173  [ -5.173, 10.346 ]\n// 14  34  0.575 5.593  [ -5.593, 11.186 ]\n// 15  37  0.617 6.003  [ -6.003, 12.006 ]\n// 16  39  0.659 6.423  [ -6.423, 12.846 ]\n// 17  42  0.700 6.833  [ -6.833, 13.666 ]\n// 18  44  0.740 7.233  [ -7.233, 14.466 ]\n// 19  46  0.781 7.643  [ -7.643, 15.286 ]\n// 20  49  0.822 8.053  [ -8.053, 16.106 ]\n// 21  51  0.861 8.453  [ -8.453, 16.906 ]\n// 22  54  0.904 8.873  [ -8.873, 17.746 ]\n// 23  56  0.944 9.283  [ -9.283, 18.566 ]\n// 24  59  0.986 9.703  [ -9.703, 19.406 ]\n// 25  61  1.028 10.113 [ -10.113, 20.226 ]\n// ...\n```\n\nSince the 25 fps render framerate is not a multiple of the 60 fps used by the\nsim, the output shows that for each render frame (1st column), there're either 2\nor 3 sim updates performed (2nd column) to accommodate the 60 fps.\n\nThis should then also clarify _why_ state interpolation is the final step of\neach update cycle: When multiple updates are performed in a single frame, the\nsim's state is technically _ahead_ of the render time line and therefore we need\nto compute (interpolate) the correct state between previous and current, then\nuse these interpolated values for rendering (in the abstract sense)...\n\nThe last row also shows that both `a` and `b` arrive at their expected values\nafter 1 second (25 frames)...\n\n## Status\n\n**ALPHA** - bleeding edge / work-in-progress\n\n[Search or submit any issues for this package](https://codeberg.org/thi.ng/umbrella/issues?q=%5Btimestep%5D)\n\n## Related packages\n\n- [@thi.ng/boids](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/boids) - n-dimensional boids simulation with modular behavior system\n\n## Installation\n\n```bash\nyarn add @thi.ng/timestep\n```\n\nESM import:\n\n```ts\nimport * as ts from \"@thi.ng/timestep\";\n```\n\nBrowser ESM import:\n\n```html\n<script type=\"module\" src=\"https://esm.run/@thi.ng/timestep\"></script>\n```\n\n[JSDelivr documentation](https://www.jsdelivr.com/)\n\nFor Node.js REPL:\n\n```js\nconst ts = await import(\"@thi.ng/timestep\");\n```\n\nPackage sizes (brotli'd, pre-treeshake): ESM: 1.03 KB\n\n## Dependencies\n\n- [@thi.ng/api](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/api)\n- [@thi.ng/math](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/math)\n- [@thi.ng/vectors](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/vectors)\n\nNote: @thi.ng/api is in _most_ cases a type-only import (not used at runtime)\n\n## Usage examples\n\nOne project in this repo's\n[/examples](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples)\ndirectory is using this package:\n\n| Screenshot                                                                                                         | Description                                                    | Live demo                                         | Source                                                                                 |\n|:-------------------------------------------------------------------------------------------------------------------|:---------------------------------------------------------------|:--------------------------------------------------|:---------------------------------------------------------------------------------------|\n| <img src=\"https://codeberg.org/thi.ng/umbrella/media/branch/develop/assets/examples/boid-basics.png\" width=\"240\"/> | Basic 2D boid simulation and spatial indexing neighbor lookups | [Demo](https://demo.thi.ng/umbrella/boid-basics/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/boid-basics) |\n\n## API\n\n[Generated API docs](https://docs.thi.ng/umbrella/timestep/)\n\nTODO\n\n## Authors\n\n- [Karsten Schmidt](https://thi.ng)\n\nIf this project contributes to an academic publication, please cite it as:\n\n```bibtex\n@misc{thing-timestep,\n  title = \"@thi.ng/timestep\",\n  author = \"Karsten Schmidt\",\n  note = \"https://thi.ng/timestep\",\n  year = 2023\n}\n```\n\n## License\n\n&copy; 2023 - 2026 Karsten Schmidt // Apache License 2.0\n","readmeFilename":"README.md"}