feat: physics based car

This commit is contained in:
Asger Juul Brunshøj 2025-05-27 21:46:14 +02:00
parent 5b370c0679
commit 6c98c254b6
60 changed files with 7692 additions and 62 deletions

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/.direnv/
/target/
/docs/book/

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This file makes sure that Github Pages doesn't process mdBook's output.

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Original by Dempfi (https://github.com/dempfi/ayu)
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'use strict';
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// Fix back button cache problem
window.onunload = function() { };
// Global variable, shared between modules
function playground_text(playground, hidden = true) {
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win: 'Ctrl-Enter',
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let item;
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while (item = re.exec(txt)) {
snippet_crates.push(item[1]);
}
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}
}
function run_rust_code(code_block) {
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});
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code: text,
edition: edition,
};
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result_block.innerText = 'Running...';
fetch_with_timeout('https://play.rust-lang.org/evaluate.json', {
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localStorage.setItem('mdbook-sidebar', 'visible');
} catch (e) {
// Ignore error.
}
}
function hideSidebar() {
body.classList.remove('sidebar-visible');
body.classList.add('sidebar-hidden');
Array.from(sidebarLinks).forEach(function(link) {
link.setAttribute('tabIndex', -1);
});
sidebarToggleButton.setAttribute('aria-expanded', false);
sidebar.setAttribute('aria-hidden', true);
try {
localStorage.setItem('mdbook-sidebar', 'hidden');
} catch (e) {
// Ignore error.
}
}
// Toggle sidebar
sidebarToggleAnchor.addEventListener('change', function sidebarToggle() {
if (sidebarToggleAnchor.checked) {
const current_width = parseInt(
document.documentElement.style.getPropertyValue('--sidebar-target-width'), 10);
if (current_width < 150) {
document.documentElement.style.setProperty('--sidebar-target-width', '150px');
}
showSidebar();
} else {
hideSidebar();
}
});
sidebarResizeHandle.addEventListener('mousedown', initResize, false);
function initResize() {
window.addEventListener('mousemove', resize, false);
window.addEventListener('mouseup', stopResize, false);
body.classList.add('sidebar-resizing');
}
function resize(e) {
let pos = e.clientX - sidebar.offsetLeft;
if (pos < 20) {
hideSidebar();
} else {
if (body.classList.contains('sidebar-hidden')) {
showSidebar();
}
pos = Math.min(pos, window.innerWidth - 100);
document.documentElement.style.setProperty('--sidebar-target-width', pos + 'px');
}
}
//on mouseup remove windows functions mousemove & mouseup
function stopResize() {
body.classList.remove('sidebar-resizing');
window.removeEventListener('mousemove', resize, false);
window.removeEventListener('mouseup', stopResize, false);
}
document.addEventListener('touchstart', function(e) {
firstContact = {
x: e.touches[0].clientX,
time: Date.now(),
};
}, { passive: true });
document.addEventListener('touchmove', function(e) {
if (!firstContact) {
return;
}
const curX = e.touches[0].clientX;
const xDiff = curX - firstContact.x,
tDiff = Date.now() - firstContact.time;
if (tDiff < 250 && Math.abs(xDiff) >= 150) {
if (xDiff >= 0 && firstContact.x < Math.min(document.body.clientWidth * 0.25, 300)) {
showSidebar();
} else if (xDiff < 0 && curX < 300) {
hideSidebar();
}
firstContact = null;
}
}, { passive: true });
})();
(function chapterNavigation() {
document.addEventListener('keydown', function(e) {
if (e.altKey || e.ctrlKey || e.metaKey) {
return;
}
if (window.search && window.search.hasFocus()) {
return;
}
const html = document.querySelector('html');
function next() {
const nextButton = document.querySelector('.nav-chapters.next');
if (nextButton) {
window.location.href = nextButton.href;
}
}
function prev() {
const previousButton = document.querySelector('.nav-chapters.previous');
if (previousButton) {
window.location.href = previousButton.href;
}
}
function showHelp() {
const container = document.getElementById('mdbook-help-container');
const overlay = document.getElementById('mdbook-help-popup');
container.style.display = 'flex';
// Clicking outside the popup will dismiss it.
const mouseHandler = event => {
if (overlay.contains(event.target)) {
return;
}
if (event.button !== 0) {
return;
}
event.preventDefault();
event.stopPropagation();
document.removeEventListener('mousedown', mouseHandler);
hideHelp();
};
// Pressing esc will dismiss the popup.
const escapeKeyHandler = event => {
if (event.key === 'Escape') {
event.preventDefault();
event.stopPropagation();
document.removeEventListener('keydown', escapeKeyHandler, true);
hideHelp();
}
};
document.addEventListener('keydown', escapeKeyHandler, true);
document.getElementById('mdbook-help-container')
.addEventListener('mousedown', mouseHandler);
}
function hideHelp() {
document.getElementById('mdbook-help-container').style.display = 'none';
}
// Usually needs the Shift key to be pressed
switch (e.key) {
case '?':
e.preventDefault();
showHelp();
break;
}
// Rest of the keys are only active when the Shift key is not pressed
if (e.shiftKey) {
return;
}
switch (e.key) {
case 'ArrowRight':
e.preventDefault();
if (html.dir === 'rtl') {
prev();
} else {
next();
}
break;
case 'ArrowLeft':
e.preventDefault();
if (html.dir === 'rtl') {
next();
} else {
prev();
}
break;
}
});
})();
(function clipboard() {
const clipButtons = document.querySelectorAll('.clip-button');
function hideTooltip(elem) {
elem.firstChild.innerText = '';
elem.className = 'clip-button';
}
function showTooltip(elem, msg) {
elem.firstChild.innerText = msg;
elem.className = 'clip-button tooltipped';
}
const clipboardSnippets = new ClipboardJS('.clip-button', {
text: function(trigger) {
hideTooltip(trigger);
const playground = trigger.closest('pre');
return playground_text(playground, false);
},
});
Array.from(clipButtons).forEach(function(clipButton) {
clipButton.addEventListener('mouseout', function(e) {
hideTooltip(e.currentTarget);
});
});
clipboardSnippets.on('success', function(e) {
e.clearSelection();
showTooltip(e.trigger, 'Copied!');
});
clipboardSnippets.on('error', function(e) {
showTooltip(e.trigger, 'Clipboard error!');
});
})();
(function scrollToTop() {
const menuTitle = document.querySelector('.menu-title');
menuTitle.addEventListener('click', function() {
document.scrollingElement.scrollTo({ top: 0, behavior: 'smooth' });
});
})();
(function controllMenu() {
const menu = document.getElementById('menu-bar');
(function controllPosition() {
let scrollTop = document.scrollingElement.scrollTop;
let prevScrollTop = scrollTop;
const minMenuY = -menu.clientHeight - 50;
// When the script loads, the page can be at any scroll (e.g. if you reforesh it).
menu.style.top = scrollTop + 'px';
// Same as parseInt(menu.style.top.slice(0, -2), but faster
let topCache = menu.style.top.slice(0, -2);
menu.classList.remove('sticky');
let stickyCache = false; // Same as menu.classList.contains('sticky'), but faster
document.addEventListener('scroll', function() {
scrollTop = Math.max(document.scrollingElement.scrollTop, 0);
// `null` means that it doesn't need to be updated
let nextSticky = null;
let nextTop = null;
const scrollDown = scrollTop > prevScrollTop;
const menuPosAbsoluteY = topCache - scrollTop;
if (scrollDown) {
nextSticky = false;
if (menuPosAbsoluteY > 0) {
nextTop = prevScrollTop;
}
} else {
if (menuPosAbsoluteY > 0) {
nextSticky = true;
} else if (menuPosAbsoluteY < minMenuY) {
nextTop = prevScrollTop + minMenuY;
}
}
if (nextSticky === true && stickyCache === false) {
menu.classList.add('sticky');
stickyCache = true;
} else if (nextSticky === false && stickyCache === true) {
menu.classList.remove('sticky');
stickyCache = false;
}
if (nextTop !== null) {
menu.style.top = nextTop + 'px';
topCache = nextTop;
}
prevScrollTop = scrollTop;
}, { passive: true });
})();
(function controllBorder() {
function updateBorder() {
if (menu.offsetTop === 0) {
menu.classList.remove('bordered');
} else {
menu.classList.add('bordered');
}
}
updateBorder();
document.addEventListener('scroll', updateBorder, { passive: true });
})();
})();

9
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@ -0,0 +1,9 @@
[book]
authors = ["Asger Juul Brunshøj"]
language = "en"
src = "src"
title = "docs"
[preprocessor.katex]
after = ["links"]
pre-render = true

209
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@ -0,0 +1,209 @@
<!DOCTYPE HTML>
<html lang="en" class="light sidebar-visible" dir="ltr">
<head>
<!-- Book generated using mdBook -->
<meta charset="UTF-8">
<title>Chapter 1 - docs</title>
<!-- Custom HTML head -->
<meta name="description" content="">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="theme-color" content="#ffffff">
<link rel="icon" href="favicon.svg">
<link rel="shortcut icon" href="favicon.png">
<link rel="stylesheet" href="css/variables.css">
<link rel="stylesheet" href="css/general.css">
<link rel="stylesheet" href="css/chrome.css">
<link rel="stylesheet" href="css/print.css" media="print">
<!-- Fonts -->
<link rel="stylesheet" href="FontAwesome/css/font-awesome.css">
<link rel="stylesheet" href="fonts/fonts.css">
<!-- Highlight.js Stylesheets -->
<link rel="stylesheet" id="highlight-css" href="highlight.css">
<link rel="stylesheet" id="tomorrow-night-css" href="tomorrow-night.css">
<link rel="stylesheet" id="ayu-highlight-css" href="ayu-highlight.css">
<!-- Custom theme stylesheets -->
<!-- Provide site root and default themes to javascript -->
<script>
const path_to_root = "";
const default_light_theme = "light";
const default_dark_theme = "navy";
</script>
<!-- Start loading toc.js asap -->
<script src="toc.js"></script>
</head>
<body>
<div id="mdbook-help-container">
<div id="mdbook-help-popup">
<h2 class="mdbook-help-title">Keyboard shortcuts</h2>
<div>
<p>Press <kbd></kbd> or <kbd></kbd> to navigate between chapters</p>
<p>Press <kbd>S</kbd> or <kbd>/</kbd> to search in the book</p>
<p>Press <kbd>?</kbd> to show this help</p>
<p>Press <kbd>Esc</kbd> to hide this help</p>
</div>
</div>
</div>
<div id="body-container">
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<script>
try {
let theme = localStorage.getItem('mdbook-theme');
let sidebar = localStorage.getItem('mdbook-sidebar');
if (theme.startsWith('"') && theme.endsWith('"')) {
localStorage.setItem('mdbook-theme', theme.slice(1, theme.length - 1));
}
if (sidebar.startsWith('"') && sidebar.endsWith('"')) {
localStorage.setItem('mdbook-sidebar', sidebar.slice(1, sidebar.length - 1));
}
} catch (e) { }
</script>
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<script>
const default_theme = window.matchMedia("(prefers-color-scheme: dark)").matches ? default_dark_theme : default_light_theme;
let theme;
try { theme = localStorage.getItem('mdbook-theme'); } catch(e) { }
if (theme === null || theme === undefined) { theme = default_theme; }
const html = document.documentElement;
html.classList.remove('light')
html.classList.add(theme);
html.classList.add("js");
</script>
<input type="checkbox" id="sidebar-toggle-anchor" class="hidden">
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<script>
let sidebar = null;
const sidebar_toggle = document.getElementById("sidebar-toggle-anchor");
if (document.body.clientWidth >= 1080) {
try { sidebar = localStorage.getItem('mdbook-sidebar'); } catch(e) { }
sidebar = sidebar || 'visible';
} else {
sidebar = 'hidden';
}
sidebar_toggle.checked = sidebar === 'visible';
html.classList.remove('sidebar-visible');
html.classList.add("sidebar-" + sidebar);
</script>
<nav id="sidebar" class="sidebar" aria-label="Table of contents">
<!-- populated by js -->
<mdbook-sidebar-scrollbox class="sidebar-scrollbox"></mdbook-sidebar-scrollbox>
<noscript>
<iframe class="sidebar-iframe-outer" src="toc.html"></iframe>
</noscript>
<div id="sidebar-resize-handle" class="sidebar-resize-handle">
<div class="sidebar-resize-indicator"></div>
</div>
</nav>
<div id="page-wrapper" class="page-wrapper">
<div class="page">
<div id="menu-bar-hover-placeholder"></div>
<div id="menu-bar" class="menu-bar sticky">
<div class="left-buttons">
<label id="sidebar-toggle" class="icon-button" for="sidebar-toggle-anchor" title="Toggle Table of Contents" aria-label="Toggle Table of Contents" aria-controls="sidebar">
<i class="fa fa-bars"></i>
</label>
<button id="theme-toggle" class="icon-button" type="button" title="Change theme" aria-label="Change theme" aria-haspopup="true" aria-expanded="false" aria-controls="theme-list">
<i class="fa fa-paint-brush"></i>
</button>
<ul id="theme-list" class="theme-popup" aria-label="Themes" role="menu">
<li role="none"><button role="menuitem" class="theme" id="default_theme">Auto</button></li>
<li role="none"><button role="menuitem" class="theme" id="light">Light</button></li>
<li role="none"><button role="menuitem" class="theme" id="rust">Rust</button></li>
<li role="none"><button role="menuitem" class="theme" id="coal">Coal</button></li>
<li role="none"><button role="menuitem" class="theme" id="navy">Navy</button></li>
<li role="none"><button role="menuitem" class="theme" id="ayu">Ayu</button></li>
</ul>
<button id="search-toggle" class="icon-button" type="button" title="Search (`/`)" aria-label="Toggle Searchbar" aria-expanded="false" aria-keyshortcuts="/ s" aria-controls="searchbar">
<i class="fa fa-search"></i>
</button>
</div>
<h1 class="menu-title">docs</h1>
<div class="right-buttons">
<a href="print.html" title="Print this book" aria-label="Print this book">
<i id="print-button" class="fa fa-print"></i>
</a>
</div>
</div>
<div id="search-wrapper" class="hidden">
<form id="searchbar-outer" class="searchbar-outer">
<input type="search" id="searchbar" name="searchbar" placeholder="Search this book ..." aria-controls="searchresults-outer" aria-describedby="searchresults-header">
</form>
<div id="searchresults-outer" class="searchresults-outer hidden">
<div id="searchresults-header" class="searchresults-header"></div>
<ul id="searchresults">
</ul>
</div>
</div>
<!-- Apply ARIA attributes after the sidebar and the sidebar toggle button are added to the DOM -->
<script>
document.getElementById('sidebar-toggle').setAttribute('aria-expanded', sidebar === 'visible');
document.getElementById('sidebar').setAttribute('aria-hidden', sidebar !== 'visible');
Array.from(document.querySelectorAll('#sidebar a')).forEach(function(link) {
link.setAttribute('tabIndex', sidebar === 'visible' ? 0 : -1);
});
</script>
<div id="content" class="content">
<main>
<h1 id="chapter-1"><a class="header" href="#chapter-1">Chapter 1</a></h1>
</main>
<nav class="nav-wrapper" aria-label="Page navigation">
<!-- Mobile navigation buttons -->
<div style="clear: both"></div>
</nav>
</div>
</div>
<nav class="nav-wide-wrapper" aria-label="Page navigation">
</nav>
</div>
<script>
window.playground_copyable = true;
</script>
<script src="elasticlunr.min.js"></script>
<script src="mark.min.js"></script>
<script src="searcher.js"></script>
<script src="clipboard.min.js"></script>
<script src="highlight.js"></script>
<script src="book.js"></script>
<!-- Custom JS scripts -->
</div>
</body>
</html>

7
docs/clipboard.min.js vendored Normal file

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701
docs/css/chrome.css Normal file
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@ -0,0 +1,701 @@
/* CSS for UI elements (a.k.a. chrome) */
html {
scrollbar-color: var(--scrollbar) var(--bg);
}
#searchresults a,
.content a:link,
a:visited,
a > .hljs {
color: var(--links);
}
/*
body-container is necessary because mobile browsers don't seem to like
overflow-x on the body tag when there is a <meta name="viewport"> tag.
*/
#body-container {
/*
This is used when the sidebar pushes the body content off the side of
the screen on small screens. Without it, dragging on mobile Safari
will want to reposition the viewport in a weird way.
*/
overflow-x: clip;
}
/* Menu Bar */
#menu-bar,
#menu-bar-hover-placeholder {
z-index: 101;
margin: auto calc(0px - var(--page-padding));
}
#menu-bar {
position: relative;
display: flex;
flex-wrap: wrap;
background-color: var(--bg);
border-block-end-color: var(--bg);
border-block-end-width: 1px;
border-block-end-style: solid;
}
#menu-bar.sticky,
#menu-bar-hover-placeholder:hover + #menu-bar,
#menu-bar:hover,
html.sidebar-visible #menu-bar {
position: -webkit-sticky;
position: sticky;
top: 0 !important;
}
#menu-bar-hover-placeholder {
position: sticky;
position: -webkit-sticky;
top: 0;
height: var(--menu-bar-height);
}
#menu-bar.bordered {
border-block-end-color: var(--table-border-color);
}
#menu-bar i, #menu-bar .icon-button {
position: relative;
padding: 0 8px;
z-index: 10;
line-height: var(--menu-bar-height);
cursor: pointer;
transition: color 0.5s;
}
@media only screen and (max-width: 420px) {
#menu-bar i, #menu-bar .icon-button {
padding: 0 5px;
}
}
.icon-button {
border: none;
background: none;
padding: 0;
color: inherit;
}
.icon-button i {
margin: 0;
}
.right-buttons {
margin: 0 15px;
}
.right-buttons a {
text-decoration: none;
}
.left-buttons {
display: flex;
margin: 0 5px;
}
html:not(.js) .left-buttons button {
display: none;
}
.menu-title {
display: inline-block;
font-weight: 200;
font-size: 2.4rem;
line-height: var(--menu-bar-height);
text-align: center;
margin: 0;
flex: 1;
white-space: nowrap;
overflow: hidden;
text-overflow: ellipsis;
}
.menu-title {
cursor: pointer;
}
.menu-bar,
.menu-bar:visited,
.nav-chapters,
.nav-chapters:visited,
.mobile-nav-chapters,
.mobile-nav-chapters:visited,
.menu-bar .icon-button,
.menu-bar a i {
color: var(--icons);
}
.menu-bar i:hover,
.menu-bar .icon-button:hover,
.nav-chapters:hover,
.mobile-nav-chapters i:hover {
color: var(--icons-hover);
}
/* Nav Icons */
.nav-chapters {
font-size: 2.5em;
text-align: center;
text-decoration: none;
position: fixed;
top: 0;
bottom: 0;
margin: 0;
max-width: 150px;
min-width: 90px;
display: flex;
justify-content: center;
align-content: center;
flex-direction: column;
transition: color 0.5s, background-color 0.5s;
}
.nav-chapters:hover {
text-decoration: none;
background-color: var(--theme-hover);
transition: background-color 0.15s, color 0.15s;
}
.nav-wrapper {
margin-block-start: 50px;
display: none;
}
.mobile-nav-chapters {
font-size: 2.5em;
text-align: center;
text-decoration: none;
width: 90px;
border-radius: 5px;
background-color: var(--sidebar-bg);
}
/* Only Firefox supports flow-relative values */
.previous { float: left; }
[dir=rtl] .previous { float: right; }
/* Only Firefox supports flow-relative values */
.next {
float: right;
right: var(--page-padding);
}
[dir=rtl] .next {
float: left;
right: unset;
left: var(--page-padding);
}
/* Use the correct buttons for RTL layouts*/
[dir=rtl] .previous i.fa-angle-left:before {content:"\f105";}
[dir=rtl] .next i.fa-angle-right:before { content:"\f104"; }
@media only screen and (max-width: 1080px) {
.nav-wide-wrapper { display: none; }
.nav-wrapper { display: block; }
}
/* sidebar-visible */
@media only screen and (max-width: 1380px) {
#sidebar-toggle-anchor:checked ~ .page-wrapper .nav-wide-wrapper { display: none; }
#sidebar-toggle-anchor:checked ~ .page-wrapper .nav-wrapper { display: block; }
}
/* Inline code */
:not(pre) > .hljs {
display: inline;
padding: 0.1em 0.3em;
border-radius: 3px;
}
:not(pre):not(a) > .hljs {
color: var(--inline-code-color);
overflow-x: initial;
}
a:hover > .hljs {
text-decoration: underline;
}
pre {
position: relative;
}
pre > .buttons {
position: absolute;
z-index: 100;
right: 0px;
top: 2px;
margin: 0px;
padding: 2px 0px;
color: var(--sidebar-fg);
cursor: pointer;
visibility: hidden;
opacity: 0;
transition: visibility 0.1s linear, opacity 0.1s linear;
}
pre:hover > .buttons {
visibility: visible;
opacity: 1
}
pre > .buttons :hover {
color: var(--sidebar-active);
border-color: var(--icons-hover);
background-color: var(--theme-hover);
}
pre > .buttons i {
margin-inline-start: 8px;
}
pre > .buttons button {
cursor: inherit;
margin: 0px 5px;
padding: 4px 4px 3px 5px;
font-size: 23px;
border-style: solid;
border-width: 1px;
border-radius: 4px;
border-color: var(--icons);
background-color: var(--theme-popup-bg);
transition: 100ms;
transition-property: color,border-color,background-color;
color: var(--icons);
}
pre > .buttons button.clip-button {
padding: 2px 4px 0px 6px;
}
pre > .buttons button.clip-button::before {
/* clipboard image from octicons (https://github.com/primer/octicons/tree/v2.0.0) MIT license
*/
content: url('data:image/svg+xml,<svg width="21" height="20" viewBox="0 0 24 25" \
xmlns="http://www.w3.org/2000/svg" aria-label="Copy to clipboard">\
<path d="M18 20h2v3c0 1-1 2-2 2H2c-.998 0-2-1-2-2V5c0-.911.755-1.667 1.667-1.667h5A3.323 3.323 0 \
0110 0a3.323 3.323 0 013.333 3.333h5C19.245 3.333 20 4.09 20 5v8.333h-2V9H2v14h16v-3zM3 \
7h14c0-.911-.793-1.667-1.75-1.667H13.5c-.957 0-1.75-.755-1.75-1.666C11.75 2.755 10.957 2 10 \
2s-1.75.755-1.75 1.667c0 .911-.793 1.666-1.75 1.666H4.75C3.793 5.333 3 6.09 3 7z"/>\
<path d="M4 19h6v2H4zM12 11H4v2h8zM4 17h4v-2H4zM15 15v-3l-4.5 4.5L15 21v-3l8.027-.032L23 15z"/>\
</svg>');
filter: var(--copy-button-filter);
}
pre > .buttons button.clip-button:hover::before {
filter: var(--copy-button-filter-hover);
}
@media (pointer: coarse) {
pre > .buttons button {
/* On mobile, make it easier to tap buttons. */
padding: 0.3rem 1rem;
}
.sidebar-resize-indicator {
/* Hide resize indicator on devices with limited accuracy */
display: none;
}
}
pre > code {
display: block;
padding: 1rem;
}
/* FIXME: ACE editors overlap their buttons because ACE does absolute
positioning within the code block which breaks padding. The only solution I
can think of is to move the padding to the outer pre tag (or insert a div
wrapper), but that would require fixing a whole bunch of CSS rules.
*/
.hljs.ace_editor {
padding: 0rem 0rem;
}
pre > .result {
margin-block-start: 10px;
}
/* Search */
#searchresults a {
text-decoration: none;
}
mark {
border-radius: 2px;
padding-block-start: 0;
padding-block-end: 1px;
padding-inline-start: 3px;
padding-inline-end: 3px;
margin-block-start: 0;
margin-block-end: -1px;
margin-inline-start: -3px;
margin-inline-end: -3px;
background-color: var(--search-mark-bg);
transition: background-color 300ms linear;
cursor: pointer;
}
mark.fade-out {
background-color: rgba(0,0,0,0) !important;
cursor: auto;
}
.searchbar-outer {
margin-inline-start: auto;
margin-inline-end: auto;
max-width: var(--content-max-width);
}
#searchbar {
width: 100%;
margin-block-start: 5px;
margin-block-end: 0;
margin-inline-start: auto;
margin-inline-end: auto;
padding: 10px 16px;
transition: box-shadow 300ms ease-in-out;
border: 1px solid var(--searchbar-border-color);
border-radius: 3px;
background-color: var(--searchbar-bg);
color: var(--searchbar-fg);
}
#searchbar:focus,
#searchbar.active {
box-shadow: 0 0 3px var(--searchbar-shadow-color);
}
.searchresults-header {
font-weight: bold;
font-size: 1em;
padding-block-start: 18px;
padding-block-end: 0;
padding-inline-start: 5px;
padding-inline-end: 0;
color: var(--searchresults-header-fg);
}
.searchresults-outer {
margin-inline-start: auto;
margin-inline-end: auto;
max-width: var(--content-max-width);
border-block-end: 1px dashed var(--searchresults-border-color);
}
ul#searchresults {
list-style: none;
padding-inline-start: 20px;
}
ul#searchresults li {
margin: 10px 0px;
padding: 2px;
border-radius: 2px;
}
ul#searchresults li.focus {
background-color: var(--searchresults-li-bg);
}
ul#searchresults span.teaser {
display: block;
clear: both;
margin-block-start: 5px;
margin-block-end: 0;
margin-inline-start: 20px;
margin-inline-end: 0;
font-size: 0.8em;
}
ul#searchresults span.teaser em {
font-weight: bold;
font-style: normal;
}
/* Sidebar */
.sidebar {
position: fixed;
left: 0;
top: 0;
bottom: 0;
width: var(--sidebar-width);
font-size: 0.875em;
box-sizing: border-box;
-webkit-overflow-scrolling: touch;
overscroll-behavior-y: contain;
background-color: var(--sidebar-bg);
color: var(--sidebar-fg);
}
.sidebar-iframe-inner {
--padding: 10px;
background-color: var(--sidebar-bg);
padding: var(--padding);
margin: 0;
font-size: 1.4rem;
color: var(--sidebar-fg);
min-height: calc(100vh - var(--padding) * 2);
}
.sidebar-iframe-outer {
border: none;
height: 100%;
position: absolute;
top: 0;
bottom: 0;
left: 0;
right: 0;
}
[dir=rtl] .sidebar { left: unset; right: 0; }
.sidebar-resizing {
-moz-user-select: none;
-webkit-user-select: none;
-ms-user-select: none;
user-select: none;
}
html:not(.sidebar-resizing) .sidebar {
transition: transform 0.3s; /* Animation: slide away */
}
.sidebar code {
line-height: 2em;
}
.sidebar .sidebar-scrollbox {
overflow-y: auto;
position: absolute;
top: 0;
bottom: 0;
left: 0;
right: 0;
padding: 10px 10px;
}
.sidebar .sidebar-resize-handle {
position: absolute;
cursor: col-resize;
width: 0;
right: calc(var(--sidebar-resize-indicator-width) * -1);
top: 0;
bottom: 0;
display: flex;
align-items: center;
}
.sidebar-resize-handle .sidebar-resize-indicator {
width: 100%;
height: 16px;
color: var(--icons);
margin-inline-start: var(--sidebar-resize-indicator-space);
display: flex;
align-items: center;
justify-content: flex-start;
}
.sidebar-resize-handle .sidebar-resize-indicator::before {
content: "";
width: 2px;
height: 12px;
border-left: dotted 2px currentColor;
}
.sidebar-resize-handle .sidebar-resize-indicator::after {
content: "";
width: 2px;
height: 16px;
border-left: dotted 2px currentColor;
}
[dir=rtl] .sidebar .sidebar-resize-handle {
left: calc(var(--sidebar-resize-indicator-width) * -1);
right: unset;
}
.js .sidebar .sidebar-resize-handle {
cursor: col-resize;
width: calc(var(--sidebar-resize-indicator-width) - var(--sidebar-resize-indicator-space));
}
/* sidebar-hidden */
#sidebar-toggle-anchor:not(:checked) ~ .sidebar {
transform: translateX(calc(0px - var(--sidebar-width) - var(--sidebar-resize-indicator-width)));
z-index: -1;
}
[dir=rtl] #sidebar-toggle-anchor:not(:checked) ~ .sidebar {
transform: translateX(calc(var(--sidebar-width) + var(--sidebar-resize-indicator-width)));
}
.sidebar::-webkit-scrollbar {
background: var(--sidebar-bg);
}
.sidebar::-webkit-scrollbar-thumb {
background: var(--scrollbar);
}
/* sidebar-visible */
#sidebar-toggle-anchor:checked ~ .page-wrapper {
transform: translateX(calc(var(--sidebar-width) + var(--sidebar-resize-indicator-width)));
}
[dir=rtl] #sidebar-toggle-anchor:checked ~ .page-wrapper {
transform: translateX(calc(0px - var(--sidebar-width) - var(--sidebar-resize-indicator-width)));
}
@media only screen and (min-width: 620px) {
#sidebar-toggle-anchor:checked ~ .page-wrapper {
transform: none;
margin-inline-start: calc(var(--sidebar-width) + var(--sidebar-resize-indicator-width));
}
[dir=rtl] #sidebar-toggle-anchor:checked ~ .page-wrapper {
transform: none;
}
}
.chapter {
list-style: none outside none;
padding-inline-start: 0;
line-height: 2.2em;
}
.chapter ol {
width: 100%;
}
.chapter li {
display: flex;
color: var(--sidebar-non-existant);
}
.chapter li a {
display: block;
padding: 0;
text-decoration: none;
color: var(--sidebar-fg);
}
.chapter li a:hover {
color: var(--sidebar-active);
}
.chapter li a.active {
color: var(--sidebar-active);
}
.chapter li > a.toggle {
cursor: pointer;
display: block;
margin-inline-start: auto;
padding: 0 10px;
user-select: none;
opacity: 0.68;
}
.chapter li > a.toggle div {
transition: transform 0.5s;
}
/* collapse the section */
.chapter li:not(.expanded) + li > ol {
display: none;
}
.chapter li.chapter-item {
line-height: 1.5em;
margin-block-start: 0.6em;
}
.chapter li.expanded > a.toggle div {
transform: rotate(90deg);
}
.spacer {
width: 100%;
height: 3px;
margin: 5px 0px;
}
.chapter .spacer {
background-color: var(--sidebar-spacer);
}
@media (-moz-touch-enabled: 1), (pointer: coarse) {
.chapter li a { padding: 5px 0; }
.spacer { margin: 10px 0; }
}
.section {
list-style: none outside none;
padding-inline-start: 20px;
line-height: 1.9em;
}
/* Theme Menu Popup */
.theme-popup {
position: absolute;
left: 10px;
top: var(--menu-bar-height);
z-index: 1000;
border-radius: 4px;
font-size: 0.7em;
color: var(--fg);
background: var(--theme-popup-bg);
border: 1px solid var(--theme-popup-border);
margin: 0;
padding: 0;
list-style: none;
display: none;
/* Don't let the children's background extend past the rounded corners. */
overflow: hidden;
}
[dir=rtl] .theme-popup { left: unset; right: 10px; }
.theme-popup .default {
color: var(--icons);
}
.theme-popup .theme {
width: 100%;
border: 0;
margin: 0;
padding: 2px 20px;
line-height: 25px;
white-space: nowrap;
text-align: start;
cursor: pointer;
color: inherit;
background: inherit;
font-size: inherit;
}
.theme-popup .theme:hover {
background-color: var(--theme-hover);
}
.theme-selected::before {
display: inline-block;
content: "✓";
margin-inline-start: -14px;
width: 14px;
}
/* The container for the help popup that covers the whole window. */
#mdbook-help-container {
/* Position and size for the whole window. */
position: fixed;
top: 0;
left: 0;
right: 0;
bottom: 0;
/* This uses flex layout (which is set in book.js), and centers the popup
in the window.*/
display: none;
align-items: center;
justify-content: center;
z-index: 1000;
/* Dim out the book while the popup is visible. */
background: var(--overlay-bg);
}
/* The popup help box. */
#mdbook-help-popup {
box-shadow: 0 4px 24px rgba(0,0,0,0.15);
min-width: 300px;
max-width: 500px;
width: 100%;
box-sizing: border-box;
display: flex;
flex-direction: column;
align-items: center;
background-color: var(--bg);
color: var(--fg);
border-width: 1px;
border-color: var(--theme-popup-border);
border-style: solid;
border-radius: 8px;
padding: 10px;
}
.mdbook-help-title {
text-align: center;
/* mdbook's margin for h2 is way too large. */
margin: 10px;
}

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/* Base styles and content styles */
:root {
/* Browser default font-size is 16px, this way 1 rem = 10px */
font-size: 62.5%;
color-scheme: var(--color-scheme);
}
html {
font-family: "Open Sans", sans-serif;
color: var(--fg);
background-color: var(--bg);
text-size-adjust: none;
-webkit-text-size-adjust: none;
}
body {
margin: 0;
font-size: 1.6rem;
overflow-x: hidden;
}
code {
font-family: var(--mono-font) !important;
font-size: var(--code-font-size);
direction: ltr !important;
}
/* make long words/inline code not x overflow */
main {
overflow-wrap: break-word;
}
/* make wide tables scroll if they overflow */
.table-wrapper {
overflow-x: auto;
}
/* Don't change font size in headers. */
h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
font-size: unset;
}
.left { float: left; }
.right { float: right; }
.boring { opacity: 0.6; }
.hide-boring .boring { display: none; }
.hidden { display: none !important; }
h2, h3 { margin-block-start: 2.5em; }
h4, h5 { margin-block-start: 2em; }
.header + .header h3,
.header + .header h4,
.header + .header h5 {
margin-block-start: 1em;
}
h1:target::before,
h2:target::before,
h3:target::before,
h4:target::before,
h5:target::before,
h6:target::before {
display: inline-block;
content: "»";
margin-inline-start: -30px;
width: 30px;
}
/* This is broken on Safari as of version 14, but is fixed
in Safari Technology Preview 117 which I think will be Safari 14.2.
https://bugs.webkit.org/show_bug.cgi?id=218076
*/
:target {
/* Safari does not support logical properties */
scroll-margin-top: calc(var(--menu-bar-height) + 0.5em);
}
.page {
outline: 0;
padding: 0 var(--page-padding);
margin-block-start: calc(0px - var(--menu-bar-height)); /* Compensate for the #menu-bar-hover-placeholder */
}
.page-wrapper {
box-sizing: border-box;
background-color: var(--bg);
}
.no-js .page-wrapper,
.js:not(.sidebar-resizing) .page-wrapper {
transition: margin-left 0.3s ease, transform 0.3s ease; /* Animation: slide away */
}
[dir=rtl] .js:not(.sidebar-resizing) .page-wrapper {
transition: margin-right 0.3s ease, transform 0.3s ease; /* Animation: slide away */
}
.content {
overflow-y: auto;
padding: 0 5px 50px 5px;
}
.content main {
margin-inline-start: auto;
margin-inline-end: auto;
max-width: var(--content-max-width);
}
.content p { line-height: 1.45em; }
.content ol { line-height: 1.45em; }
.content ul { line-height: 1.45em; }
.content a { text-decoration: none; }
.content a:hover { text-decoration: underline; }
.content img, .content video { max-width: 100%; }
.content .header:link,
.content .header:visited {
color: var(--fg);
}
.content .header:link,
.content .header:visited:hover {
text-decoration: none;
}
table {
margin: 0 auto;
border-collapse: collapse;
}
table td {
padding: 3px 20px;
border: 1px var(--table-border-color) solid;
}
table thead {
background: var(--table-header-bg);
}
table thead td {
font-weight: 700;
border: none;
}
table thead th {
padding: 3px 20px;
}
table thead tr {
border: 1px var(--table-header-bg) solid;
}
/* Alternate background colors for rows */
table tbody tr:nth-child(2n) {
background: var(--table-alternate-bg);
}
blockquote {
margin: 20px 0;
padding: 0 20px;
color: var(--fg);
background-color: var(--quote-bg);
border-block-start: .1em solid var(--quote-border);
border-block-end: .1em solid var(--quote-border);
}
.warning {
margin: 20px;
padding: 0 20px;
border-inline-start: 2px solid var(--warning-border);
}
.warning:before {
position: absolute;
width: 3rem;
height: 3rem;
margin-inline-start: calc(-1.5rem - 21px);
content: "ⓘ";
text-align: center;
background-color: var(--bg);
color: var(--warning-border);
font-weight: bold;
font-size: 2rem;
}
blockquote .warning:before {
background-color: var(--quote-bg);
}
kbd {
background-color: var(--table-border-color);
border-radius: 4px;
border: solid 1px var(--theme-popup-border);
box-shadow: inset 0 -1px 0 var(--theme-hover);
display: inline-block;
font-size: var(--code-font-size);
font-family: var(--mono-font);
line-height: 10px;
padding: 4px 5px;
vertical-align: middle;
}
sup {
/* Set the line-height for superscript and footnote references so that there
isn't an awkward space appearing above lines that contain the footnote.
See https://github.com/rust-lang/mdBook/pull/2443#discussion_r1813773583
for an explanation.
*/
line-height: 0;
}
.footnote-definition {
font-size: 0.9em;
}
/* The default spacing for a list is a little too large. */
.footnote-definition ul,
.footnote-definition ol {
padding-left: 20px;
}
.footnote-definition > li {
/* Required to position the ::before target */
position: relative;
}
.footnote-definition > li:target {
scroll-margin-top: 50vh;
}
.footnote-reference:target {
scroll-margin-top: 50vh;
}
/* Draws a border around the footnote (including the marker) when it is selected.
TODO: If there are multiple linkbacks, highlight which one you just came
from so you know which one to click.
*/
.footnote-definition > li:target::before {
border: 2px solid var(--footnote-highlight);
border-radius: 6px;
position: absolute;
top: -8px;
right: -8px;
bottom: -8px;
left: -32px;
pointer-events: none;
content: "";
}
/* Pulses the footnote reference so you can quickly see where you left off reading.
This could use some improvement.
*/
@media not (prefers-reduced-motion) {
.footnote-reference:target {
animation: fn-highlight 0.8s;
border-radius: 2px;
}
@keyframes fn-highlight {
from {
background-color: var(--footnote-highlight);
}
}
}
.tooltiptext {
position: absolute;
visibility: hidden;
color: #fff;
background-color: #333;
transform: translateX(-50%); /* Center by moving tooltip 50% of its width left */
left: -8px; /* Half of the width of the icon */
top: -35px;
font-size: 0.8em;
text-align: center;
border-radius: 6px;
padding: 5px 8px;
margin: 5px;
z-index: 1000;
}
.tooltipped .tooltiptext {
visibility: visible;
}
.chapter li.part-title {
color: var(--sidebar-fg);
margin: 5px 0px;
font-weight: bold;
}
.result-no-output {
font-style: italic;
}

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#sidebar,
#menu-bar,
.nav-chapters,
.mobile-nav-chapters {
display: none;
}
#page-wrapper.page-wrapper {
transform: none !important;
margin-inline-start: 0px;
overflow-y: initial;
}
#content {
max-width: none;
margin: 0;
padding: 0;
}
.page {
overflow-y: initial;
}
code {
direction: ltr !important;
}
pre > .buttons {
z-index: 2;
}
a, a:visited, a:active, a:hover {
color: #4183c4;
text-decoration: none;
}
h1, h2, h3, h4, h5, h6 {
page-break-inside: avoid;
page-break-after: avoid;
}
pre, code {
page-break-inside: avoid;
white-space: pre-wrap;
}
.fa {
display: none !important;
}

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/* Globals */
:root {
--sidebar-target-width: 300px;
--sidebar-width: min(var(--sidebar-target-width), 80vw);
--sidebar-resize-indicator-width: 8px;
--sidebar-resize-indicator-space: 2px;
--page-padding: 15px;
--content-max-width: 750px;
--menu-bar-height: 50px;
--mono-font: "Source Code Pro", Consolas, "Ubuntu Mono", Menlo, "DejaVu Sans Mono", monospace, monospace;
--code-font-size: 0.875em; /* please adjust the ace font size accordingly in editor.js */
}
/* Themes */
.ayu {
--bg: hsl(210, 25%, 8%);
--fg: #c5c5c5;
--sidebar-bg: #14191f;
--sidebar-fg: #c8c9db;
--sidebar-non-existant: #5c6773;
--sidebar-active: #ffb454;
--sidebar-spacer: #2d334f;
--scrollbar: var(--sidebar-fg);
--icons: #737480;
--icons-hover: #b7b9cc;
--links: #0096cf;
--inline-code-color: #ffb454;
--theme-popup-bg: #14191f;
--theme-popup-border: #5c6773;
--theme-hover: #191f26;
--quote-bg: hsl(226, 15%, 17%);
--quote-border: hsl(226, 15%, 22%);
--warning-border: #ff8e00;
--table-border-color: hsl(210, 25%, 13%);
--table-header-bg: hsl(210, 25%, 28%);
--table-alternate-bg: hsl(210, 25%, 11%);
--searchbar-border-color: #848484;
--searchbar-bg: #424242;
--searchbar-fg: #fff;
--searchbar-shadow-color: #d4c89f;
--searchresults-header-fg: #666;
--searchresults-border-color: #888;
--searchresults-li-bg: #252932;
--search-mark-bg: #e3b171;
--color-scheme: dark;
/* Same as `--icons` */
--copy-button-filter: invert(45%) sepia(6%) saturate(621%) hue-rotate(198deg) brightness(99%) contrast(85%);
/* Same as `--sidebar-active` */
--copy-button-filter-hover: invert(68%) sepia(55%) saturate(531%) hue-rotate(341deg) brightness(104%) contrast(101%);
--footnote-highlight: #2668a6;
--overlay-bg: rgba(33, 40, 48, 0.4);
}
.coal {
--bg: hsl(200, 7%, 8%);
--fg: #98a3ad;
--sidebar-bg: #292c2f;
--sidebar-fg: #a1adb8;
--sidebar-non-existant: #505254;
--sidebar-active: #3473ad;
--sidebar-spacer: #393939;
--scrollbar: var(--sidebar-fg);
--icons: #43484d;
--icons-hover: #b3c0cc;
--links: #2b79a2;
--inline-code-color: #c5c8c6;
--theme-popup-bg: #141617;
--theme-popup-border: #43484d;
--theme-hover: #1f2124;
--quote-bg: hsl(234, 21%, 18%);
--quote-border: hsl(234, 21%, 23%);
--warning-border: #ff8e00;
--table-border-color: hsl(200, 7%, 13%);
--table-header-bg: hsl(200, 7%, 28%);
--table-alternate-bg: hsl(200, 7%, 11%);
--searchbar-border-color: #aaa;
--searchbar-bg: #b7b7b7;
--searchbar-fg: #000;
--searchbar-shadow-color: #aaa;
--searchresults-header-fg: #666;
--searchresults-border-color: #98a3ad;
--searchresults-li-bg: #2b2b2f;
--search-mark-bg: #355c7d;
--color-scheme: dark;
/* Same as `--icons` */
--copy-button-filter: invert(26%) sepia(8%) saturate(575%) hue-rotate(169deg) brightness(87%) contrast(82%);
/* Same as `--sidebar-active` */
--copy-button-filter-hover: invert(36%) sepia(70%) saturate(503%) hue-rotate(167deg) brightness(98%) contrast(89%);
--footnote-highlight: #4079ae;
--overlay-bg: rgba(33, 40, 48, 0.4);
}
.light, html:not(.js) {
--bg: hsl(0, 0%, 100%);
--fg: hsl(0, 0%, 0%);
--sidebar-bg: #fafafa;
--sidebar-fg: hsl(0, 0%, 0%);
--sidebar-non-existant: #aaaaaa;
--sidebar-active: #1f1fff;
--sidebar-spacer: #f4f4f4;
--scrollbar: #8F8F8F;
--icons: #747474;
--icons-hover: #000000;
--links: #20609f;
--inline-code-color: #301900;
--theme-popup-bg: #fafafa;
--theme-popup-border: #cccccc;
--theme-hover: #e6e6e6;
--quote-bg: hsl(197, 37%, 96%);
--quote-border: hsl(197, 37%, 91%);
--warning-border: #ff8e00;
--table-border-color: hsl(0, 0%, 95%);
--table-header-bg: hsl(0, 0%, 80%);
--table-alternate-bg: hsl(0, 0%, 97%);
--searchbar-border-color: #aaa;
--searchbar-bg: #fafafa;
--searchbar-fg: #000;
--searchbar-shadow-color: #aaa;
--searchresults-header-fg: #666;
--searchresults-border-color: #888;
--searchresults-li-bg: #e4f2fe;
--search-mark-bg: #a2cff5;
--color-scheme: light;
/* Same as `--icons` */
--copy-button-filter: invert(45.49%);
/* Same as `--sidebar-active` */
--copy-button-filter-hover: invert(14%) sepia(93%) saturate(4250%) hue-rotate(243deg) brightness(99%) contrast(130%);
--footnote-highlight: #7e7eff;
--overlay-bg: rgba(200, 200, 205, 0.4);
}
.navy {
--bg: hsl(226, 23%, 11%);
--fg: #bcbdd0;
--sidebar-bg: #282d3f;
--sidebar-fg: #c8c9db;
--sidebar-non-existant: #505274;
--sidebar-active: #2b79a2;
--sidebar-spacer: #2d334f;
--scrollbar: var(--sidebar-fg);
--icons: #737480;
--icons-hover: #b7b9cc;
--links: #2b79a2;
--inline-code-color: #c5c8c6;
--theme-popup-bg: #161923;
--theme-popup-border: #737480;
--theme-hover: #282e40;
--quote-bg: hsl(226, 15%, 17%);
--quote-border: hsl(226, 15%, 22%);
--warning-border: #ff8e00;
--table-border-color: hsl(226, 23%, 16%);
--table-header-bg: hsl(226, 23%, 31%);
--table-alternate-bg: hsl(226, 23%, 14%);
--searchbar-border-color: #aaa;
--searchbar-bg: #aeaec6;
--searchbar-fg: #000;
--searchbar-shadow-color: #aaa;
--searchresults-header-fg: #5f5f71;
--searchresults-border-color: #5c5c68;
--searchresults-li-bg: #242430;
--search-mark-bg: #a2cff5;
--color-scheme: dark;
/* Same as `--icons` */
--copy-button-filter: invert(51%) sepia(10%) saturate(393%) hue-rotate(198deg) brightness(86%) contrast(87%);
/* Same as `--sidebar-active` */
--copy-button-filter-hover: invert(46%) sepia(20%) saturate(1537%) hue-rotate(156deg) brightness(85%) contrast(90%);
--footnote-highlight: #4079ae;
--overlay-bg: rgba(33, 40, 48, 0.4);
}
.rust {
--bg: hsl(60, 9%, 87%);
--fg: #262625;
--sidebar-bg: #3b2e2a;
--sidebar-fg: #c8c9db;
--sidebar-non-existant: #505254;
--sidebar-active: #e69f67;
--sidebar-spacer: #45373a;
--scrollbar: var(--sidebar-fg);
--icons: #737480;
--icons-hover: #262625;
--links: #2b79a2;
--inline-code-color: #6e6b5e;
--theme-popup-bg: #e1e1db;
--theme-popup-border: #b38f6b;
--theme-hover: #99908a;
--quote-bg: hsl(60, 5%, 75%);
--quote-border: hsl(60, 5%, 70%);
--warning-border: #ff8e00;
--table-border-color: hsl(60, 9%, 82%);
--table-header-bg: #b3a497;
--table-alternate-bg: hsl(60, 9%, 84%);
--searchbar-border-color: #aaa;
--searchbar-bg: #fafafa;
--searchbar-fg: #000;
--searchbar-shadow-color: #aaa;
--searchresults-header-fg: #666;
--searchresults-border-color: #888;
--searchresults-li-bg: #dec2a2;
--search-mark-bg: #e69f67;
/* Same as `--icons` */
--copy-button-filter: invert(51%) sepia(10%) saturate(393%) hue-rotate(198deg) brightness(86%) contrast(87%);
/* Same as `--sidebar-active` */
--copy-button-filter-hover: invert(77%) sepia(16%) saturate(1798%) hue-rotate(328deg) brightness(98%) contrast(83%);
--footnote-highlight: #d3a17a;
--overlay-bg: rgba(150, 150, 150, 0.25);
}
@media (prefers-color-scheme: dark) {
html:not(.js) {
--bg: hsl(200, 7%, 8%);
--fg: #98a3ad;
--sidebar-bg: #292c2f;
--sidebar-fg: #a1adb8;
--sidebar-non-existant: #505254;
--sidebar-active: #3473ad;
--sidebar-spacer: #393939;
--scrollbar: var(--sidebar-fg);
--icons: #43484d;
--icons-hover: #b3c0cc;
--links: #2b79a2;
--inline-code-color: #c5c8c6;
--theme-popup-bg: #141617;
--theme-popup-border: #43484d;
--theme-hover: #1f2124;
--quote-bg: hsl(234, 21%, 18%);
--quote-border: hsl(234, 21%, 23%);
--warning-border: #ff8e00;
--table-border-color: hsl(200, 7%, 13%);
--table-header-bg: hsl(200, 7%, 28%);
--table-alternate-bg: hsl(200, 7%, 11%);
--searchbar-border-color: #aaa;
--searchbar-bg: #b7b7b7;
--searchbar-fg: #000;
--searchbar-shadow-color: #aaa;
--searchresults-header-fg: #666;
--searchresults-border-color: #98a3ad;
--searchresults-li-bg: #2b2b2f;
--search-mark-bg: #355c7d;
--color-scheme: dark;
/* Same as `--icons` */
--copy-button-filter: invert(26%) sepia(8%) saturate(575%) hue-rotate(169deg) brightness(87%) contrast(82%);
/* Same as `--sidebar-active` */
--copy-button-filter-hover: invert(36%) sepia(70%) saturate(503%) hue-rotate(167deg) brightness(98%) contrast(89%);
}
}

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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 199.7 184.2">
<style>
@media (prefers-color-scheme: dark) {
svg { fill: white; }
}
</style>
<path d="M189.5,36.8c0.2,2.8,0,5.1-0.6,6.8L153,162c-0.6,2.1-2,3.7-4.2,5c-2.2,1.2-4.4,1.9-6.7,1.9H31.4c-9.6,0-15.3-2.8-17.3-8.4
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import math
import drawsvg as draw
import os
from pathlib import Path
images_path = Path(os.path.realpath(__file__)).parent.joinpath('src').joinpath('images')
# Define arrowhead marker
arrow = draw.Marker(0,0,10,10, refX="10", refY="5", markerWidth="6", markerHeight="6", orient='auto-start-reverse')
arrow.append(draw.Path(d='M 0 0 L 10 5 L 0 10 z', fill='black'))
class Point:
def __init__(self, x, y):
self.x = x
self.y = y
def force_diagram():
d = draw.Drawing(600, 600, origin='center')
# Outline drawing area
d.append(draw.Rectangle(-300,-300,600,600, fill='white'))
# Coordinate system
c = translate(coordinate_system(), -230, -230)
d.append(c)
# Define group
g = draw.Group(fill='black', stroke='black', stroke_width=1.5)
A = Point(0, -200)
B = Point(0, 200)
steering_angle = 20
w = 300
g.append(draw.Rectangle(-w/2,-280, w, 560, fill='none', stroke_width=1))
wheel = draw.Rectangle(-15,-40, 30, 80, fill='none', stroke_width=1)
g.append(translate(rotate(wheel, steering_angle), -w/2, A.y))
g.append(translate(rotate(wheel, steering_angle), w/2, A.y))
g.append(translate(wheel, -w/2, B.y))
g.append(translate(wheel, w/2, B.y))
# Center of Mass
g.append(draw.Circle(0, 0, 3))
g.append(text("CM", 0, 0, angle=180))
# Velocity vector
g.append(draw.Line(0, 0, -50, -160, marker_end=arrow))
g.append(text("v", -50, -160, angle=-110))
# Point A
g.append(text("A", A.x, A.y, angle=180))
g.append(draw.Circle(A.x, A.y, 3))
g.append(draw.Line(A.x, A.y, 80, -170, marker_end=arrow))
g.append(text("F_A", 80, -170))
# Point B
g.append(text("B", B.x, B.y, angle=180))
g.append(draw.Circle(B.x, B.y, 3))
g.append(draw.Line(B.x, B.y, 70, 200, marker_end=arrow))
g.append(text("F_B", 70, 200))
d.append(translate(g, 100, 0))
d.save_svg(f'{images_path}/force_diagram.svg')
def coordinate_system():
g = draw.Group(stroke='black', stroke_width=1.5)
g.append(draw.Line(0, 0, 50, 0, marker_end=arrow))
g.append(text("x", 50, 0))
g.append(draw.Line(0, 0, 0, 50, marker_end=arrow))
g.append(text("y", 0, 50, angle=90))
# Arc
cx = 0
cy = 0
r = 50
start = 120
end = -30
start_angle = math.radians(start)
end_angle = math.radians(end)
x0 = cx + r * math.cos(start_angle)
y0 = cy + r * math.sin(start_angle)
x1 = cx + r * math.cos(end_angle)
y1 = cy + r * math.sin(end_angle)
# SVG arc path from (x0, y0) to (x1, y1) around center
path_d = f'M {x0} {y0} A {r} {r} 0 1 1 {x1} {y1}'
arc = draw.Path(d=path_d, fill='none', marker_end=arrow)
g.append(arc)
return g
# Wrap in translated group
def translate(t, x, y):
g = draw.Group(transform=f"translate({x},{y})")
g.append(t)
return g
# Wrap in rotated group
def rotate(t, a):
g = draw.Group(transform=f"rotate({a})")
g.append(t)
return g
def text(text, x, y, offset=20, angle=0):
angle = math.radians(angle)
x = x + offset * math.cos(angle)
y = y + offset * math.sin(angle)
return draw.Text(text, 18, x, y, stroke_width=1, center=True)
force_diagram()

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Apache License
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Copyright 2010, 2012 Adobe Systems Incorporated (http://www.adobe.com/), with Reserved Font Name 'Source'. All Rights Reserved. Source is a trademark of Adobe Systems Incorporated in the United States and/or other countries.
This Font Software is licensed under the SIL Open Font License, Version 1.1.
This license is copied below, and is also available with a FAQ at:
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-----------------------------------------------------------
SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
-----------------------------------------------------------
PREAMBLE
The goals of the Open Font License (OFL) are to stimulate worldwide
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distributed by the Copyright Holder(s).
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Original Version, by changing formats or by porting the Font Software to a
new environment.
"Author" refers to any designer, engineer, programmer, technical
writer or other person who contributed to the Font Software.
PERMISSION & CONDITIONS
Permission is hereby granted, free of charge, to any person obtaining
a copy of the Font Software, to use, study, copy, merge, embed, modify,
redistribute, and sell modified and unmodified copies of the Font
Software, subject to the following conditions:
1) Neither the Font Software nor any of its individual components,
in Original or Modified Versions, may be sold by itself.
2) Original or Modified Versions of the Font Software may be bundled,
redistributed and/or sold with any software, provided that each copy
contains the above copyright notice and this license. These can be
included either as stand-alone text files, human-readable headers or
in the appropriate machine-readable metadata fields within text or
binary files as long as those fields can be easily viewed by the user.
3) No Modified Version of the Font Software may use the Reserved Font
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100
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/* Open Sans is licensed under the Apache License, Version 2.0. See http://www.apache.org/licenses/LICENSE-2.0 */
/* Source Code Pro is under the Open Font License. See https://scripts.sil.org/cms/scripts/page.php?site_id=nrsi&id=OFL */
/* open-sans-300 - latin_vietnamese_latin-ext_greek-ext_greek_cyrillic-ext_cyrillic */
@font-face {
font-family: 'Open Sans';
font-style: normal;
font-weight: 300;
src: local('Open Sans Light'), local('OpenSans-Light'),
url('../fonts/open-sans-v17-all-charsets-300.woff2') format('woff2');
}
/* open-sans-300italic - latin_vietnamese_latin-ext_greek-ext_greek_cyrillic-ext_cyrillic */
@font-face {
font-family: 'Open Sans';
font-style: italic;
font-weight: 300;
src: local('Open Sans Light Italic'), local('OpenSans-LightItalic'),
url('../fonts/open-sans-v17-all-charsets-300italic.woff2') format('woff2');
}
/* open-sans-regular - latin_vietnamese_latin-ext_greek-ext_greek_cyrillic-ext_cyrillic */
@font-face {
font-family: 'Open Sans';
font-style: normal;
font-weight: 400;
src: local('Open Sans Regular'), local('OpenSans-Regular'),
url('../fonts/open-sans-v17-all-charsets-regular.woff2') format('woff2');
}
/* open-sans-italic - latin_vietnamese_latin-ext_greek-ext_greek_cyrillic-ext_cyrillic */
@font-face {
font-family: 'Open Sans';
font-style: italic;
font-weight: 400;
src: local('Open Sans Italic'), local('OpenSans-Italic'),
url('../fonts/open-sans-v17-all-charsets-italic.woff2') format('woff2');
}
/* open-sans-600 - latin_vietnamese_latin-ext_greek-ext_greek_cyrillic-ext_cyrillic */
@font-face {
font-family: 'Open Sans';
font-style: normal;
font-weight: 600;
src: local('Open Sans SemiBold'), local('OpenSans-SemiBold'),
url('../fonts/open-sans-v17-all-charsets-600.woff2') format('woff2');
}
/* open-sans-600italic - latin_vietnamese_latin-ext_greek-ext_greek_cyrillic-ext_cyrillic */
@font-face {
font-family: 'Open Sans';
font-style: italic;
font-weight: 600;
src: local('Open Sans SemiBold Italic'), local('OpenSans-SemiBoldItalic'),
url('../fonts/open-sans-v17-all-charsets-600italic.woff2') format('woff2');
}
/* open-sans-700 - latin_vietnamese_latin-ext_greek-ext_greek_cyrillic-ext_cyrillic */
@font-face {
font-family: 'Open Sans';
font-style: normal;
font-weight: 700;
src: local('Open Sans Bold'), local('OpenSans-Bold'),
url('../fonts/open-sans-v17-all-charsets-700.woff2') format('woff2');
}
/* open-sans-700italic - latin_vietnamese_latin-ext_greek-ext_greek_cyrillic-ext_cyrillic */
@font-face {
font-family: 'Open Sans';
font-style: italic;
font-weight: 700;
src: local('Open Sans Bold Italic'), local('OpenSans-BoldItalic'),
url('../fonts/open-sans-v17-all-charsets-700italic.woff2') format('woff2');
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@font-face {
font-family: 'Open Sans';
font-style: normal;
font-weight: 800;
src: local('Open Sans ExtraBold'), local('OpenSans-ExtraBold'),
url('../fonts/open-sans-v17-all-charsets-800.woff2') format('woff2');
}
/* open-sans-800italic - latin_vietnamese_latin-ext_greek-ext_greek_cyrillic-ext_cyrillic */
@font-face {
font-family: 'Open Sans';
font-style: italic;
font-weight: 800;
src: local('Open Sans ExtraBold Italic'), local('OpenSans-ExtraBoldItalic'),
url('../fonts/open-sans-v17-all-charsets-800italic.woff2') format('woff2');
}
/* source-code-pro-500 - latin_vietnamese_latin-ext_greek_cyrillic-ext_cyrillic */
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font-family: 'Source Code Pro';
font-style: normal;
font-weight: 500;
src: url('../fonts/source-code-pro-v11-all-charsets-500.woff2') format('woff2');
}

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/*
* An increased contrast highlighting scheme loosely based on the
* "Base16 Atelier Dune Light" theme by Bram de Haan
* (http://atelierbram.github.io/syntax-highlighting/atelier-schemes/dune)
* Original Base16 color scheme by Chris Kempson
* (https://github.com/chriskempson/base16)
*/
/* Comment */
.hljs-comment,
.hljs-quote {
color: #575757;
}
/* Red */
.hljs-variable,
.hljs-template-variable,
.hljs-attribute,
.hljs-attr,
.hljs-tag,
.hljs-name,
.hljs-regexp,
.hljs-link,
.hljs-name,
.hljs-selector-id,
.hljs-selector-class {
color: #d70025;
}
/* Orange */
.hljs-number,
.hljs-meta,
.hljs-built_in,
.hljs-builtin-name,
.hljs-literal,
.hljs-type,
.hljs-params {
color: #b21e00;
}
/* Green */
.hljs-string,
.hljs-symbol,
.hljs-bullet {
color: #008200;
}
/* Blue */
.hljs-title,
.hljs-section {
color: #0030f2;
}
/* Purple */
.hljs-keyword,
.hljs-selector-tag {
color: #9d00ec;
}
.hljs {
display: block;
overflow-x: auto;
background: #f6f7f6;
color: #000;
}
.hljs-emphasis {
font-style: italic;
}
.hljs-strong {
font-weight: bold;
}
.hljs-addition {
color: #22863a;
background-color: #f0fff4;
}
.hljs-deletion {
color: #b31d28;
background-color: #ffeef0;
}

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<!DOCTYPE HTML>
<html lang="en" class="light sidebar-visible" dir="ltr">
<head>
<!-- Book generated using mdBook -->
<meta charset="UTF-8">
<title>Chapter 1 - docs</title>
<!-- Custom HTML head -->
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<body>
<div id="mdbook-help-container">
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<h2 class="mdbook-help-title">Keyboard shortcuts</h2>
<div>
<p>Press <kbd></kbd> or <kbd></kbd> to navigate between chapters</p>
<p>Press <kbd>S</kbd> or <kbd>/</kbd> to search in the book</p>
<p>Press <kbd>?</kbd> to show this help</p>
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let sidebar = localStorage.getItem('mdbook-sidebar');
if (theme.startsWith('"') && theme.endsWith('"')) {
localStorage.setItem('mdbook-theme', theme.slice(1, theme.length - 1));
}
if (sidebar.startsWith('"') && sidebar.endsWith('"')) {
localStorage.setItem('mdbook-sidebar', sidebar.slice(1, sidebar.length - 1));
}
} catch (e) { }
</script>
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<script>
const default_theme = window.matchMedia("(prefers-color-scheme: dark)").matches ? default_dark_theme : default_light_theme;
let theme;
try { theme = localStorage.getItem('mdbook-theme'); } catch(e) { }
if (theme === null || theme === undefined) { theme = default_theme; }
const html = document.documentElement;
html.classList.remove('light')
html.classList.add(theme);
html.classList.add("js");
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try { sidebar = localStorage.getItem('mdbook-sidebar'); } catch(e) { }
sidebar = sidebar || 'visible';
} else {
sidebar = 'hidden';
}
sidebar_toggle.checked = sidebar === 'visible';
html.classList.remove('sidebar-visible');
html.classList.add("sidebar-" + sidebar);
</script>
<nav id="sidebar" class="sidebar" aria-label="Table of contents">
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<button id="theme-toggle" class="icon-button" type="button" title="Change theme" aria-label="Change theme" aria-haspopup="true" aria-expanded="false" aria-controls="theme-list">
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<ul id="theme-list" class="theme-popup" aria-label="Themes" role="menu">
<li role="none"><button role="menuitem" class="theme" id="default_theme">Auto</button></li>
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</ul>
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</button>
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<div class="right-buttons">
<a href="print.html" title="Print this book" aria-label="Print this book">
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</a>
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<form id="searchbar-outer" class="searchbar-outer">
<input type="search" id="searchbar" name="searchbar" placeholder="Search this book ..." aria-controls="searchresults-outer" aria-describedby="searchresults-header">
</form>
<div id="searchresults-outer" class="searchresults-outer hidden">
<div id="searchresults-header" class="searchresults-header"></div>
<ul id="searchresults">
</ul>
</div>
</div>
<!-- Apply ARIA attributes after the sidebar and the sidebar toggle button are added to the DOM -->
<script>
document.getElementById('sidebar-toggle').setAttribute('aria-expanded', sidebar === 'visible');
document.getElementById('sidebar').setAttribute('aria-hidden', sidebar !== 'visible');
Array.from(document.querySelectorAll('#sidebar a')).forEach(function(link) {
link.setAttribute('tabIndex', sidebar === 'visible' ? 0 : -1);
});
</script>
<div id="content" class="content">
<main>
<h1 id="chapter-1"><a class="header" href="#chapter-1">Chapter 1</a></h1>
</main>
<nav class="nav-wrapper" aria-label="Page navigation">
<!-- Mobile navigation buttons -->
<div style="clear: both"></div>
</nav>
</div>
</div>
<nav class="nav-wide-wrapper" aria-label="Page navigation">
</nav>
</div>
<script>
window.playground_copyable = true;
</script>
<script src="elasticlunr.min.js"></script>
<script src="mark.min.js"></script>
<script src="searcher.js"></script>
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<script src="book.js"></script>
<!-- Custom JS scripts -->
</div>
</body>
</html>

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<!DOCTYPE HTML>
<html lang="en" class="light sidebar-visible" dir="ltr">
<head>
<!-- Book generated using mdBook -->
<meta charset="UTF-8">
<title>docs</title>
<meta name="robots" content="noindex">
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<link rel="stylesheet" href="css/variables.css">
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<link rel="stylesheet" href="fonts/fonts.css">
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<link rel="stylesheet" id="highlight-css" href="highlight.css">
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<!-- Custom theme stylesheets -->
<!-- Provide site root and default themes to javascript -->
<script>
const path_to_root = "";
const default_light_theme = "light";
const default_dark_theme = "navy";
</script>
<!-- Start loading toc.js asap -->
<script src="toc.js"></script>
</head>
<body>
<div id="mdbook-help-container">
<div id="mdbook-help-popup">
<h2 class="mdbook-help-title">Keyboard shortcuts</h2>
<div>
<p>Press <kbd></kbd> or <kbd></kbd> to navigate between chapters</p>
<p>Press <kbd>S</kbd> or <kbd>/</kbd> to search in the book</p>
<p>Press <kbd>?</kbd> to show this help</p>
<p>Press <kbd>Esc</kbd> to hide this help</p>
</div>
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</div>
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<script>
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let theme = localStorage.getItem('mdbook-theme');
let sidebar = localStorage.getItem('mdbook-sidebar');
if (theme.startsWith('"') && theme.endsWith('"')) {
localStorage.setItem('mdbook-theme', theme.slice(1, theme.length - 1));
}
if (sidebar.startsWith('"') && sidebar.endsWith('"')) {
localStorage.setItem('mdbook-sidebar', sidebar.slice(1, sidebar.length - 1));
}
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</script>
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<script>
const default_theme = window.matchMedia("(prefers-color-scheme: dark)").matches ? default_dark_theme : default_light_theme;
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try { theme = localStorage.getItem('mdbook-theme'); } catch(e) { }
if (theme === null || theme === undefined) { theme = default_theme; }
const html = document.documentElement;
html.classList.remove('light')
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const sidebar_toggle = document.getElementById("sidebar-toggle-anchor");
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sidebar = sidebar || 'visible';
} else {
sidebar = 'hidden';
}
sidebar_toggle.checked = sidebar === 'visible';
html.classList.remove('sidebar-visible');
html.classList.add("sidebar-" + sidebar);
</script>
<nav id="sidebar" class="sidebar" aria-label="Table of contents">
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<mdbook-sidebar-scrollbox class="sidebar-scrollbox"></mdbook-sidebar-scrollbox>
<noscript>
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</noscript>
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<div class="sidebar-resize-indicator"></div>
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</nav>
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<div class="page">
<div id="menu-bar-hover-placeholder"></div>
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<div class="left-buttons">
<label id="sidebar-toggle" class="icon-button" for="sidebar-toggle-anchor" title="Toggle Table of Contents" aria-label="Toggle Table of Contents" aria-controls="sidebar">
<i class="fa fa-bars"></i>
</label>
<button id="theme-toggle" class="icon-button" type="button" title="Change theme" aria-label="Change theme" aria-haspopup="true" aria-expanded="false" aria-controls="theme-list">
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</button>
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<div class="right-buttons">
<a href="print.html" title="Print this book" aria-label="Print this book">
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<form id="searchbar-outer" class="searchbar-outer">
<input type="search" id="searchbar" name="searchbar" placeholder="Search this book ..." aria-controls="searchresults-outer" aria-describedby="searchresults-header">
</form>
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<ul id="searchresults">
</ul>
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<script>
document.getElementById('sidebar-toggle').setAttribute('aria-expanded', sidebar === 'visible');
document.getElementById('sidebar').setAttribute('aria-hidden', sidebar !== 'visible');
Array.from(document.querySelectorAll('#sidebar a')).forEach(function(link) {
link.setAttribute('tabIndex', sidebar === 'visible' ? 0 : -1);
});
</script>
<div id="content" class="content">
<main>
<h1 id="chapter-1"><a class="header" href="#chapter-1">Chapter 1</a></h1>
</main>
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</html>

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'use strict';
/* global Mark, elasticlunr, path_to_root */
window.search = window.search || {};
(function search() {
// Search functionality
//
// You can use !hasFocus() to prevent keyhandling in your key
// event handlers while the user is typing their search.
if (!Mark || !elasticlunr) {
return;
}
// eslint-disable-next-line max-len
// IE 11 Compatibility from https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/String/startsWith
if (!String.prototype.startsWith) {
String.prototype.startsWith = function(search, pos) {
return this.substr(!pos || pos < 0 ? 0 : +pos, search.length) === search;
};
}
const search_wrap = document.getElementById('search-wrapper'),
searchbar = document.getElementById('searchbar'),
searchresults = document.getElementById('searchresults'),
searchresults_outer = document.getElementById('searchresults-outer'),
searchresults_header = document.getElementById('searchresults-header'),
searchicon = document.getElementById('search-toggle'),
content = document.getElementById('content'),
// SVG text elements don't render if inside a <mark> tag.
mark_exclude = ['text'],
marker = new Mark(content),
URL_SEARCH_PARAM = 'search',
URL_MARK_PARAM = 'highlight';
let current_searchterm = '',
doc_urls = [],
search_options = {
bool: 'AND',
expand: true,
fields: {
title: {boost: 1},
body: {boost: 1},
breadcrumbs: {boost: 0},
},
},
searchindex = null,
results_options = {
teaser_word_count: 30,
limit_results: 30,
},
teaser_count = 0;
function hasFocus() {
return searchbar === document.activeElement;
}
function removeChildren(elem) {
while (elem.firstChild) {
elem.removeChild(elem.firstChild);
}
}
// Helper to parse a url into its building blocks.
function parseURL(url) {
const a = document.createElement('a');
a.href = url;
return {
source: url,
protocol: a.protocol.replace(':', ''),
host: a.hostname,
port: a.port,
params: (function() {
const ret = {};
const seg = a.search.replace(/^\?/, '').split('&');
for (const part of seg) {
if (!part) {
continue;
}
const s = part.split('=');
ret[s[0]] = s[1];
}
return ret;
})(),
file: (a.pathname.match(/\/([^/?#]+)$/i) || ['', ''])[1],
hash: a.hash.replace('#', ''),
path: a.pathname.replace(/^([^/])/, '/$1'),
};
}
// Helper to recreate a url string from its building blocks.
function renderURL(urlobject) {
let url = urlobject.protocol + '://' + urlobject.host;
if (urlobject.port !== '') {
url += ':' + urlobject.port;
}
url += urlobject.path;
let joiner = '?';
for (const prop in urlobject.params) {
if (Object.prototype.hasOwnProperty.call(urlobject.params, prop)) {
url += joiner + prop + '=' + urlobject.params[prop];
joiner = '&';
}
}
if (urlobject.hash !== '') {
url += '#' + urlobject.hash;
}
return url;
}
// Helper to escape html special chars for displaying the teasers
const escapeHTML = (function() {
const MAP = {
'&': '&amp;',
'<': '&lt;',
'>': '&gt;',
'"': '&#34;',
'\'': '&#39;',
};
const repl = function(c) {
return MAP[c];
};
return function(s) {
return s.replace(/[&<>'"]/g, repl);
};
})();
function formatSearchMetric(count, searchterm) {
if (count === 1) {
return count + ' search result for \'' + searchterm + '\':';
} else if (count === 0) {
return 'No search results for \'' + searchterm + '\'.';
} else {
return count + ' search results for \'' + searchterm + '\':';
}
}
function formatSearchResult(result, searchterms) {
const teaser = makeTeaser(escapeHTML(result.doc.body), searchterms);
teaser_count++;
// The ?URL_MARK_PARAM= parameter belongs inbetween the page and the #heading-anchor
const url = doc_urls[result.ref].split('#');
if (url.length === 1) { // no anchor found
url.push('');
}
// encodeURIComponent escapes all chars that could allow an XSS except
// for '. Due to that we also manually replace ' with its url-encoded
// representation (%27).
const encoded_search = encodeURIComponent(searchterms.join(' ')).replace(/'/g, '%27');
return '<a href="' + path_to_root + url[0] + '?' + URL_MARK_PARAM + '=' + encoded_search
+ '#' + url[1] + '" aria-details="teaser_' + teaser_count + '">'
+ result.doc.breadcrumbs + '</a>' + '<span class="teaser" id="teaser_' + teaser_count
+ '" aria-label="Search Result Teaser">' + teaser + '</span>';
}
function makeTeaser(body, searchterms) {
// The strategy is as follows:
// First, assign a value to each word in the document:
// Words that correspond to search terms (stemmer aware): 40
// Normal words: 2
// First word in a sentence: 8
// Then use a sliding window with a constant number of words and count the
// sum of the values of the words within the window. Then use the window that got the
// maximum sum. If there are multiple maximas, then get the last one.
// Enclose the terms in <em>.
const stemmed_searchterms = searchterms.map(function(w) {
return elasticlunr.stemmer(w.toLowerCase());
});
const searchterm_weight = 40;
const weighted = []; // contains elements of ["word", weight, index_in_document]
// split in sentences, then words
const sentences = body.toLowerCase().split('. ');
let index = 0;
let value = 0;
let searchterm_found = false;
for (const sentenceindex in sentences) {
const words = sentences[sentenceindex].split(' ');
value = 8;
for (const wordindex in words) {
const word = words[wordindex];
if (word.length > 0) {
for (const searchtermindex in stemmed_searchterms) {
if (elasticlunr.stemmer(word).startsWith(
stemmed_searchterms[searchtermindex])
) {
value = searchterm_weight;
searchterm_found = true;
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doc_urls = config.doc_urls;
searchindex = elasticlunr.Index.load(config.index);
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searchIconClickHandler();
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searchbarKeyUpHandler();
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document.addEventListener('keydown', e => {
globalKeyHandler(e);
}, false);
// If the user uses the browser buttons, do the same as if a reload happened
window.onpopstate = () => {
doSearchOrMarkFromUrl();
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// Suppress "submit" events so the page doesn't reload when the user presses Enter
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doSearchOrMarkFromUrl();
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config.hasFocus = hasFocus;
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function unfocusSearchbar() {
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const tmp = document.createElement('input');
tmp.setAttribute('style', 'position: absolute; opacity: 0;');
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tmp.remove();
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if (Object.prototype.hasOwnProperty.call(url.params, URL_SEARCH_PARAM)
&& url.params[URL_SEARCH_PARAM] !== '') {
showSearch(true);
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(url.params[URL_SEARCH_PARAM] + '').replace(/\+/g, '%20'));
searchbarKeyUpHandler(); // -> doSearch()
} else {
showSearch(false);
}
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const words = decodeURIComponent(url.params[URL_MARK_PARAM]).split(' ');
marker.mark(words, {
exclude: mark_exclude,
});
const markers = document.querySelectorAll('mark');
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marker.unmark();
}, 300);
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};
for (let i = 0; i < markers.length; i++) {
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// Eventhandler for keyevents on `document`
function globalKeyHandler(e) {
if (e.altKey ||
e.ctrlKey ||
e.metaKey ||
e.shiftKey ||
e.target.type === 'textarea' ||
e.target.type === 'text' ||
!hasFocus() && /^(?:input|select|textarea)$/i.test(e.target.nodeName)
) {
return;
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e.preventDefault();
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setSearchUrlParameters('',
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unfocusSearchbar();
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showSearch(true);
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script.onerror = error => {
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};
document.head.append(script);
}
loadScript(path_to_root + 'searchindex.js', 'search-index');
})(window.search);

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window.search = JSON.parse('{"doc_urls":["chapter_1.html#chapter-1"],"index":{"documentStore":{"docInfo":{"0":{"body":0,"breadcrumbs":4,"title":2}},"docs":{"0":{"body":"","breadcrumbs":"Chapter 1 » Chapter 1","id":"0","title":"Chapter 1"}},"length":1,"save":true},"fields":["title","body","breadcrumbs"],"index":{"body":{"root":{"1":{"df":1,"docs":{"0":{"tf":1.0}}},"c":{"df":0,"docs":{},"h":{"a":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":1,"docs":{"0":{"tf":1.0}}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"breadcrumbs":{"root":{"1":{"df":1,"docs":{"0":{"tf":1.7320508075688772}}},"c":{"df":0,"docs":{},"h":{"a":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":1,"docs":{"0":{"tf":1.7320508075688772}}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"title":{"root":{"1":{"df":1,"docs":{"0":{"tf":1.0}}},"c":{"df":0,"docs":{},"h":{"a":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":1,"docs":{"0":{"tf":1.0}}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}},"lang":"English","pipeline":["trimmer","stopWordFilter","stemmer"],"ref":"id","version":"0.9.5"},"results_options":{"limit_results":30,"teaser_word_count":30},"search_options":{"bool":"OR","expand":true,"fields":{"body":{"boost":1},"breadcrumbs":{"boost":1},"title":{"boost":2}}}}');

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# 2D Vehicle Physics
![force_diagram](images/force_diagram.svg)
Terminology:
$$
\begin{align}
CM &: \text{Center of Mass} \nonumber \\
A &: \text{Midpoint between front wheels} \nonumber \\
B &: \text{Midpoint between rear wheels} \nonumber \\
\vec F_A &: \text{Lateral force on the front wheels} \nonumber \\
\vec F_B &: \text{Lateral force on the rear wheels} \nonumber \\
\end{align}
$$
The relation of torque to angular acceleration and force is
$$
\begin{align}
\tau
&= \alpha I \nonumber \\
&= \vec r \times \vec F \nonumber \\
&= r_x F_y - r_y F_x \nonumber \\
\end{align}
$$
The acceleration of a point P is
$$
\begin{align}
\vec a_P
&= \frac{\vec F}{m} + |\vec P_{B/CM}| \cdot \alpha_{CM} \nonumber \\
\end{align}
$$
## Forces
### Force: Thrust
**Front-wheel drive:**
Positive force in the direction that the front wheels are facing (affected by steering).
**Rear-wheel drive:**
Positive force in the direction that the vehicle is facing.
### Force: Brakes/Reverse
**Front-wheel drive:**
Negative force in the direction that the front wheels are facing (affected by steering).
**Rear-wheel drive:**
Negative force in the direction that the vehicle is facing.
Stronger force if vehicle is moving "forward" (is braking).
Weaker force if vehicle is moving "backwards" (is reversing).
### Force: Lateral friction
Friction force,
$$
\begin{align}
F_{fric}
&= \mu \cdot s(\theta_{slip}) \nonumber \\
\end{align}
$$
where the slip function $s$ is
$$
s(\theta_{slip}) =
\begin{cases}
\theta_{slip} \cdot p & \text{for} \quad \theta_{slip} \leq 3\degree \nonumber \\
p & \text{for} \quad \theta_{slip} \gt 3\degree \nonumber \\
\end{cases}
$$
and $p$ is the peak.

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# Summary
- [2D Vehicle Physics](./2d_vehicle_physics.md)
- [Multiplayer](./multiplayer.md)

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# Chapter 1

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# Multiplayer
## Determinism
The `.powf` function used in `car.rs` is distinctly non-deterministic.

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<!DOCTYPE HTML>
<html lang="en" class="light" dir="ltr">
<head>
<!-- sidebar iframe generated using mdBook
This is a frame, and not included directly in the page, to control the total size of the
book. The TOC contains an entry for each page, so if each page includes a copy of the TOC,
the total size of the page becomes O(n**2).
The frame is only used as a fallback when JS is turned off. When it's on, the sidebar is
instead added to the main page by `toc.js` instead. The JavaScript mode is better
because, when running in a `file:///` URL, the iframed page would not be Same-Origin as
the rest of the page, so the sidebar and the main page theme would fall out of sync.
-->
<meta charset="UTF-8">
<meta name="robots" content="noindex">
<!-- Custom HTML head -->
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="theme-color" content="#ffffff">
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<body class="sidebar-iframe-inner">
<ol class="chapter"><li class="chapter-item expanded "><a href="chapter_1.html" target="_parent"><strong aria-hidden="true">1.</strong> Chapter 1</a></li></ol>
</body>
</html>

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// Populate the sidebar
//
// This is a script, and not included directly in the page, to control the total size of the book.
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super();
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var links = Array.prototype.slice.call(this.querySelectorAll("a"));
var l = links.length;
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sessionStorage.removeItem('sidebar-scroll');
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this.scrollTop = sidebarScrollTop;
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var activeSection = document.querySelector('#sidebar .active');
if (activeSection) {
activeSection.scrollIntoView({ block: 'center' });
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var sidebarAnchorToggles = document.querySelectorAll('#sidebar a.toggle');
function toggleSection(ev) {
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/* Original theme - https://github.com/chriskempson/tomorrow-theme */
/* https://github.com/jmblog/color-themes-for-highlightjs */
/* Tomorrow Comment */
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color: #969896;
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.hljs-tag,
.hljs-regexp,
.ruby .hljs-constant,
.xml .hljs-tag .hljs-title,
.xml .hljs-pi,
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color: #cc6666;
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.css .hljs-rule .hljs-attribute {
color: #f0c674;
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.hljs-value,
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.hljs-header,
.hljs-name,
.ruby .hljs-symbol,
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color: #b5bd68;
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/* Tomorrow Aqua */
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.hljs-section,
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color: #8abeb7;
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@ -21,6 +21,15 @@
rust.enable = true;
packages = [
pkgs.godot_4
pkgs.watchexec
pkgs.mdbook
pkgs.mdbook-katex
(pkgs.python3.withPackages (python-pkgs: [
python-pkgs.drawsvg
python-pkgs.ruff
python-pkgs.jedi-language-server
]))
];
};
};

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godot/car.tscn Normal file
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[ext_resource type="Texture2D" uid="uid://by4cbmcpktbmf" path="res://assets/car.png" id="1_7822p"]
[sub_resource type="RectangleShape2D" id="RectangleShape2D_37kl0"]
size = Vector2(194, 493)
[node name="Car" type="Car"]
mass = 1300.0
inertia = 5e+07
[node name="CollisionShape2D" type="CollisionShape2D" parent="."]
shape = SubResource("RectangleShape2D_37kl0")
[node name="Sprite2D" type="Sprite2D" parent="."]
scale = Vector2(0.265446, 0.265446)
texture = ExtResource("1_7822p")

11
godot/game.tscn Normal file
View File

@ -0,0 +1,11 @@
[gd_scene load_steps=2 format=3 uid="uid://7713s03g7nxw"]
[ext_resource type="PackedScene" uid="uid://ukvcgdjxtkqw" path="res://car.tscn" id="1_80nbo"]
[node name="Node2D" type="Node2D"]
[node name="Camera2D" type="Camera2D" parent="."]
position = Vector2(0, -1)
zoom = Vector2(0.077, 0.077)
[node name="Car" parent="." instance=ExtResource("1_80nbo")]

View File

@ -11,7 +11,7 @@ config_version=5
[application]
config/name="Grand Theft Arena"
run/main_scene="uid://y1wcwxtxgsy5"
run/main_scene="uid://7713s03g7nxw"
config/features=PackedStringArray("4.4", "Forward Plus")
config/icon="res://icon.svg"
@ -37,3 +37,14 @@ turn_right={
"events": [Object(InputEventKey,"resource_local_to_scene":false,"resource_name":"","device":0,"window_id":0,"alt_pressed":false,"shift_pressed":false,"ctrl_pressed":false,"meta_pressed":false,"pressed":false,"keycode":0,"physical_keycode":4194321,"key_label":0,"unicode":0,"location":0,"echo":false,"script":null)
]
}
handbrake={
"deadzone": 0.2,
"events": [Object(InputEventKey,"resource_local_to_scene":false,"resource_name":"","device":-1,"window_id":0,"alt_pressed":false,"shift_pressed":false,"ctrl_pressed":false,"meta_pressed":false,"pressed":false,"keycode":0,"physical_keycode":32,"key_label":0,"unicode":32,"location":0,"echo":false,"script":null)
]
}
[physics]
2d/default_gravity=0.0
2d/default_linear_damp=0.0
2d/default_angular_damp=0.0

View File

@ -1,8 +0,0 @@
[gd_scene load_steps=2 format=3 uid="uid://y1wcwxtxgsy5"]
[ext_resource type="Texture2D" uid="uid://by4cbmcpktbmf" path="res://assets/car.png" id="1_37kl0"]
[node name="MyNode" type="Player"]
position = Vector2(582, 324)
scale = Vector2(0.143817, 0.143817)
texture = ExtResource("1_37kl0")

View File

@ -12,3 +12,20 @@ fmt:
# Perform automated fixes
fix:
bc-fix
# Launch the editor
ed:
godot godot/project.godot
# Launch the game
run:
cargo build
godot --path godot
# mdbook serve
serve-docs:
mdbook serve docs
# Regenerate docs figures on changes
watch-figures:
watchexec --exts=py --restart --watch docs python3 docs/figures.py

View File

@ -0,0 +1,266 @@
//! Implements a vehicle model based on the bicycle model.
use godot::classes::IRigidBody2D;
use godot::classes::RigidBody2D;
use godot::global::deg_to_rad;
use godot::prelude::*;
use std::f32::consts::PI;
#[derive(GodotClass)]
#[class(base=RigidBody2D)]
struct Car {
engine_force: f32,
brake_force: f32,
air_drag_coefficient: f32,
mechanical_drag: f32,
max_cornering_force: f32,
front_wheel: Wheel,
rear_wheel: Wheel,
/// Unit: radians
max_steering_angle: f32,
base: Base<RigidBody2D>,
}
struct Wheel {
/// Distance from center of mass.
y_distance: f32,
/// Whether the wheels have static (good) grip or are slipping (as in drifting)
// TODO
has_grip: bool,
}
impl Wheel {
/// Returns position vector to wheel.
fn world_offset(&self, rotation: f32) -> Vector2 {
Vector2::new(0.0, self.y_distance).rotated(rotation)
}
}
#[godot_api]
impl IRigidBody2D for Car {
fn init(base: Base<RigidBody2D>) -> Self {
let engine_force = 4000000.0;
let brake_force = 2.5 * engine_force;
let max_cornering_force = 7000000.0;
Self {
base,
engine_force,
brake_force,
air_drag_coefficient: 0.05,
mechanical_drag: 2000.0,
max_steering_angle: deg_to_rad(32.0) as f32,
max_cornering_force,
front_wheel: Wheel {
y_distance: 200.0,
has_grip: true,
},
rear_wheel: Wheel {
y_distance: -200.0,
has_grip: true,
},
}
}
fn physics_process(&mut self, _delta: f64) {
// self.base_mut().set_mass(1300.0);
// self.base_mut().set_inertia(260000000000.0);
let input = Input::singleton();
let move_forward = input.is_action_pressed("move_forward");
let move_backward = input.is_action_pressed("move_backward");
let turn_left = input.is_action_pressed("turn_left");
let turn_right = input.is_action_pressed("turn_right");
// TODO: Handbrake
let _handbrake = input.is_action_pressed("handbrake");
let rotation = self.base().get_rotation();
let forward = self.forward();
let front_wheel_velocity = self.wheel_velocity(&self.front_wheel);
let rear_wheel_velocity = self.wheel_velocity(&self.rear_wheel);
let front_wheel_angle = match (turn_left, turn_right) {
(true, false) => self.steering_angle(),
(false, true) => -self.steering_angle(),
(true, true) | (false, false) => 0.0,
};
let front_wheel_position = self.front_wheel.world_offset(rotation);
let rear_wheel_position = self.rear_wheel.world_offset(rotation);
let front_wheels_direction = forward.rotated(front_wheel_angle);
let rear_wheels_direction = forward;
// Engine/thrust force
let thrust_force = match (move_forward, move_backward) {
(true, false) => self.engine_force * front_wheels_direction,
(false, true) => {
if forward.dot(self.base().get_linear_velocity()) > 0.0 {
// Moving ahead, so use brakes
-self.brake_force * front_wheels_direction
} else {
// Moving backwards, so reverse
-0.5 * self.engine_force * front_wheels_direction
}
}
_ => Vector2::default(),
};
// front wheel drive
self.base_mut().apply_force_ex(thrust_force).position(front_wheel_position).done();
let front_slip_angle = front_wheels_direction.angle_to(front_wheel_velocity);
let rear_slip_angle = rear_wheels_direction.angle_to(rear_wheel_velocity);
let speed_is_negligible = self.speed_is_negligible();
if speed_is_negligible {
self.base_mut().set_linear_velocity(Vector2::default());
}
// Cornering forces
if !speed_is_negligible {
self.apply_cornering_force(front_wheel_position, front_slip_angle);
self.apply_cornering_force(rear_wheel_position, rear_slip_angle);
};
// Air drag
self.apply_air_drag();
// Mechanical friction
self.apply_mechanical_drag();
}
}
impl Car {
fn apply_cornering_force(&mut self, wheel_position: Vector2, slip_angle: f32) {
let right = self.right();
let a = slip_angle.abs();
let a = if a > PI / 2.0 { PI - a } else { a };
let f = cornering_force(self.max_cornering_force, a);
let force_vector = -slip_angle.sign() * right * f;
self.base_mut().apply_force_ex(force_vector).position(wheel_position).done();
}
/// Returns normal vector in the direction the car is facing.
fn forward(&self) -> Vector2 {
let rotation = self.base().get_rotation();
Vector2::UP.rotated(rotation)
}
/// Returns normal vector to the right of where the car is facing.
fn right(&self) -> Vector2 {
let rotation = self.base().get_rotation();
Vector2::RIGHT.rotated(rotation)
}
/// Returns velocity vector of a wheel.
fn wheel_velocity(&self, wheel: &Wheel) -> Vector2 {
let vel = self.base().get_linear_velocity();
let ang_vel = self.base().get_angular_velocity();
let rot = self.base().get_rotation();
vel + ang_vel * wheel.world_offset(rot).rotated(PI / 2.0)
}
/// Returns current speed.
// TODO: in what unit?
fn speed(&self) -> f32 {
self.base().get_linear_velocity().length()
}
/// Returns true if current speed is low enough that lateral friction on wheels etc should not be calculated.
fn speed_is_negligible(&self) -> bool {
// Touch and feel value
const THRESHOLD: f32 = 10.0;
self.speed() < THRESHOLD
}
/// Returns steering angle, which is reduced from the max steering angle, the faster the car goes.
fn steering_angle(&self) -> f32 {
// Steering angle as function of speed s.
// f(0) = 1
// f(s) -> 0 as s -> infinity
// Model:
// f(s) = 1 / (1 + s^q)
// where q controls dropoff aggressiveness.
let s = self.speed();
let scale = 1800.0;
let s = s / scale;
let q = 1.5;
let f = 1.0 / (1.0 + s.powf(q));
self.max_steering_angle * f
}
fn apply_air_drag(&mut self) {
let vel = self.base().get_linear_velocity();
if let Some(direction) = vel.try_normalized() {
let drag = self.air_drag_coefficient * vel.length_squared();
let drag = -direction * drag;
self.base_mut().apply_force(drag);
}
}
/// Mechanical loss.
///
/// Sublinear force. Intented to slow the car when it is already at low speed.
fn apply_mechanical_drag(&mut self) {
let vel = self.base().get_linear_velocity();
if let Some(direction) = vel.try_normalized() {
// TODO: Note in book that powf is non-deterministic.
let f = self.mechanical_drag * vel.length().powf(0.8);
let f_vec = -direction * f;
self.base_mut().apply_force(f_vec);
}
}
}
/// Lateral wheel force as a function of slip angle in radians
///
/// Takes positive slip angle in [0; pi/2]
///
/// Returns a non-negative value.
fn cornering_force(peak: f32, slip_angle: f32) -> f32 {
debug_assert!(slip_angle >= 0.0);
debug_assert!(slip_angle <= PI / 2.0);
// TODO: Where should the peak be?
// Sources say
// - 3 degrees
// - 5-6 degrees for street tires and 8 degrees for racing ties.
// - 11 degrees for road tires with smooth curve, 6 degrees for semi-slick/competition track tires with faster drop past peak. Slick tires: 3 degrees for competitive racing.
//
// TODO what about when the input angle is more than 90 degrees? Still return peak then?
let peak_angle = deg_to_rad(6.0) as f32;
let magnitude = if slip_angle < peak_angle {
slip_angle * peak
} else {
// TODO: falloff after peak
// Past the peak street tires fall off slower and racing tires fall off faster.
let c = 0.5;
peak - c * peak * (slip_angle - peak_angle) / deg_to_rad(90.0) as f32
};
// dbg!(rad_to_deg(slip_angle as f64), peak, magnitude);
debug_assert!(magnitude >= 0.0);
debug_assert!(peak >= magnitude);
magnitude
}

View File

@ -1,61 +1,10 @@
//! Grand Theft Arena
use godot::classes::ISprite2D;
use godot::classes::Sprite2D;
use godot::prelude::*;
mod car;
struct MyExtension;
#[gdextension]
unsafe impl ExtensionLibrary for MyExtension {}
#[derive(GodotClass)]
#[class(base=Sprite2D)]
struct Player {
speed: f64,
angular_speed: f64,
base: Base<Sprite2D>,
}
#[godot_api]
impl ISprite2D for Player {
fn init(base: Base<Sprite2D>) -> Self {
Self {
speed: 400.0,
angular_speed: std::f64::consts::PI,
base,
}
}
fn physics_process(&mut self, delta: f64) {
let input = Input::singleton();
let speed = self.speed;
let angular_speed = self.angular_speed;
let mut base = self.base_mut();
// Rotation
if input.is_action_pressed("turn_left") {
let radians = -angular_speed * delta;
base.rotate(radians as f32);
}
if input.is_action_pressed("turn_right") {
let radians = angular_speed * delta;
base.rotate(radians as f32);
}
// Movement
let mut velocity = Vector2::ZERO;
if input.is_action_pressed("move_forward") {
let forward = Vector2::UP.rotated(base.get_rotation());
velocity += forward * speed as f32;
}
if input.is_action_pressed("move_backward") {
let backward = Vector2::UP.rotated(base.get_rotation());
velocity -= backward * speed as f32;
}
base.translate(velocity * delta as f32);
}
}