390 lines
29 KiB
HTML
390 lines
29 KiB
HTML
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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"/><meta name="viewport" content="width=device-width, initial-scale=1"/><title> <loganGatlin/> </title><link rel="icon" href="resources/favicon.svg" type="image/x-icon"/><style>
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/*!
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Pure v3.0.0
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Copyright 2013 Yahoo!
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Licensed under the BSD License.
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https://github.com/pure-css/pure/blob/master/LICENSE
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*/
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/*!
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normalize.css v | MIT License | https://necolas.github.io/normalize.css/
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Copyright (c) Nicolas Gallagher and Jonathan Neal
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*/
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/*! normalize.css v8.0.1 | MIT License | github.com/necolas/normalize.css */html{line-height:1.15;-webkit-text-size-adjust:100%}body{margin:0}main{display:block}h1{font-size:2em;margin:.67em 0}hr{box-sizing:content-box;height:0;overflow:visible}pre{font-family:monospace,monospace;font-size:1em}a{background-color:transparent}abbr[title]{border-bottom:none;text-decoration:underline;-webkit-text-decoration:underline dotted;text-decoration:underline dotted}b,strong{font-weight:bolder}code,kbd,samp{font-family:monospace,monospace;font-size:1em}small{font-size:80%}sub,sup{font-size:75%;line-height:0;position:relative;vertical-align:baseline}sub{bottom:-.25em}sup{top:-.5em}img{border-style:none}button,input,optgroup,select,textarea{font-family:inherit;font-size:100%;line-height:1.15;margin:0}button,input{overflow:visible}button,select{text-transform:none}[type=button],[type=reset],[type=submit],button{-webkit-appearance:button}[type=button]::-moz-focus-inner,[type=reset]::-moz-focus-inner,[type=submit]::-moz-focus-inner,button::-moz-focus-inner{border-style:none;padding:0}[type=button]:-moz-focusring,[type=reset]:-moz-focusring,[type=submit]:-moz-focusring,button:-moz-focusring{outline:1px dotted ButtonText}fieldset{padding:.35em .75em .625em}legend{box-sizing:border-box;color:inherit;display:table;max-width:100%;padding:0;white-space:normal}progress{vertical-align:baseline}textarea{overflow:auto}[type=checkbox],[type=radio]{box-sizing:border-box;padding:0}[type=number]::-webkit-inner-spin-button,[type=number]::-webkit-outer-spin-button{height:auto}[type=search]{-webkit-appearance:textfield;outline-offset:-2px}[type=search]::-webkit-search-decoration{-webkit-appearance:none}::-webkit-file-upload-button{-webkit-appearance:button;font:inherit}details{display:block}summary{display:list-item}template{display:none}[hidden]{display:none}html{font-family:sans-serif}.hidden,[hidden]{display:none!important}.pure-img{max-width:100%;height:auto;display:block}.pure-g{display:flex;flex-flow:row wrap;align-content:flex-start}.pure-u{display:inline-block;vertical-align:top}.pure-u-1,.pure-u-1-1,.pure-u-1-12,.pure-u-1-2,.pure-u-1-24,.pure-u-1-3,.pure-u-1-4,.pure-u-1-5,.pure-u-1-6,.pure-u-1-8,.pure-u-10-24,.pure-u-11-12,.pure-u-11-24,.pure-u-12-24,.pure-u-13-24,.pure-u-14-24,.pure-u-15-24,.pure-u-16-24,.pure-u-17-24,.pure-u-18-24,.pure-u-19-24,.pure-u-2-24,.pure-u-2-3,.pure-u-2-5,.pure-u-20-24,.pure-u-21-24,.pure-u-22-24,.pure-u-23-24,.pure-u-24-24,.pure-u-3-24,.pure-u-3-4,.pure-u-3-5,.pure-u-3-8,.pure-u-4-24,.pure-u-4-5,.pure-u-5-12,.pure-u-5-24,.pure-u-5-5,.pure-u-5-6,.pure-u-5-8,.pure-u-6-24,.pure-u-7-12,.pure-u-7-24,.pure-u-7-8,.pure-u-8-24,.pure-u-9-24{display:inline-block;letter-spacing:normal;word-spacing:normal;vertical-align:top;text-rendering:auto}.pure-u-1-24{width:4.1667%}.pure-u-1-12,.pure-u-2-24{width:8.3333%}.pure-u-1-8,.pure-u-3-24{width:12.5%}.pure-u-1-6,.pure-u-4-24{width:16.6667%}.pure-u-1-5{width:20%}.pure-u-5-24{width:20.8333%}.pure-u-1-4,.pure-u-6-24{width:25%}.pure-u-7-24{width:29.1667%}.pure-u-1-3,.pure-u-8-24{width:33.3333%}.pure-u-3-8,.pure-u-9-24{width:37.5%}.pure-u-2-5{width:40%}.pure-u-10-24,.pure-u-5-12{width:41.6667%}.pure-u-11-24{width:45.8333%}.pure-u-1-2,.pure-u-12-24{width:50%}.pure-u-13-24{width:54.1667%}.pure-u-14-24,.pure-u-7-12{width:58.3333%}.pure-u-3-5{width:60%}.pure-u-15-24,.pure-u-5-8{width:62.5%}.pure-u-16-24,.pure-u-2-3{width:66.6667%}.pure-u-17-24{width:70.8333%}.pure-u-18-24,.pure-u-3-4{width:75%}.pure-u-19-24{width:79.1667%}.pure-u-4-5{width:80%}.pure-u-20-24,.pure-u-5-6{width:83.3333%}.pure-u-21-24,.pure-u-7-8{width:87.5%}.pure-u-11-12,.pure-u-22-24{width:91.6667%}.pure-u-23-24{width:95.8333%}.pure-u-1,.pure-u-1-1,.pure-u-24-24,.pure-u-5-5{width:100%}.pure-button{display:inline-block;line-height:normal;white-space:nowrap;vertical-align:middle;text-align:center;cursor:pointer;-webkit-user-drag:none;-webkit-user-select:none;user-select:none;box-sizing:border-box}.pure-button::-moz-focus-inner{padding:0;border:0}.pure-button-group{letter-spacing:-.31em;text-rendering:optimizespeed}.opera-only :-o-
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</style><style>
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@font-face {
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font-family: Cascadia;
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src: url("/resources/CascadiaMonoPL.woff2");
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}
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body {
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color: #444;
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font-size: 1.2em;
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}
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.link {
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text-decoration: none;
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color: #1e90ff;
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}
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.link :visited {
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color: #1e90ff;
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}
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table {
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display: block;
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margin-top: 1em;
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margin-bottom: 1em;
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margin-left: auto;
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margin-right: auto;
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width: 60%;
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text-align: left;
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border-collapse: collapse;
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}
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th {
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padding: 0.25em 0.25em 0.25em 0.25em;
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border: 2px solid;
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border-collapse: collapse;
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}
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td {
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padding: 0.25em 0.25em 0.25em 0.25em;
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border: 2px solid;
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border-collapse: collapse;
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}
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/* https://css-loaders.com/spinner/ */
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/* HTML: <div class="loader"></div> */
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.loading {
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width: 512px;
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padding: 8px;
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aspect-ratio: 1;
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border-radius: 50%;
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background: #25b09b;
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--_m:
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conic-gradient(#0000 10%,#000),
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linear-gradient(#000 0 0) content-box;
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-webkit-mask: var(--_m);
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mask: var(--_m);
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-webkit-mask-composite: source-out;
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mask-composite: subtract;
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animation: l3 1s infinite linear;
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}
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@keyframes l3 {to{transform: rotate(1turn)}}
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.centered {
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display: block;
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margin-top: 1em;
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margin-bottom: 1em;
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margin-left: auto;
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margin-right: auto;
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width: 50%;
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}
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.pure-img-responsive { max-width: 100%; height: auto;
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}
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.cascadia {
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font-family: Cascadia;
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}
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.home-menu {
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padding: 0.5em;
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text-align: center;
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box-shadow: 0 1px 1px rgba(0,0,0, 0.10);
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}
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.home-menu {
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background: #333;
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}
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.home-menu a {
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color: #ccc;
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}
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.home-menu li a:hover,
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.home-menu li a:focus {
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animation: menu-hover-anim 0.25s ease-out;
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animation-fill-mode: forwards;
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background: none;
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border: none;
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}
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.link {
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color: #00f;
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text-decoration: none;
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}
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.video {
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text-align: center;
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}
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.video iframe {
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width: 32em;
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height: 18em;
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frameborder: "0";
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}
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/*
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Add transition to containers so they can push in and out.
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*/
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#layout,
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#menu,
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.menu-link {
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-webkit-transition: all 0.2s ease-out;
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-moz-transition: all 0.2s ease-out;
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-ms-transition: all 0.2s ease-out;
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-o-transition: all 0.2s ease-out;
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transition: all 0.2s ease-out;
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}
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/*
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This is the parent `<div>` that contains the menu and the content area.
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*/
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#layout {
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position: relative;
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left: 0;
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padding-left: 0;
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}
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#layout.active #menu {
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left: 150px;
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width: 150px;
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}
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#layout.active .menu-link {
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left: 150px;
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}
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/*
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The content `<div>` is where all your content goes.
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*/
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.content {
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margin: 0 auto;
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padding: 0 2em;
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max-width: 800px;
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margin-bottom: 50px;
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line-height: 1.6em;
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text-align: justify;
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}
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.header {
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margin: 0;
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color: #444;
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text-align: center;
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padding: 2.5em 4em 0;
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border-bottom: 1px solid #eee;
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}
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.header h1 {
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margin: 0.2em 0;
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font-size: 2.5em;
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font-weight: bold;
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}
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.header h2 {
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font-weight: 300;
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color: #888;
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padding: 0;
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margin-top: 0;
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}
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.distinct {
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background-color: #444;
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color: #fff;
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padding: 0.5em 0.5em 0.5em 0.5em;
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}
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@keyframes card-hover-anim {
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to {background-color: #ccc;}
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}
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@keyframes card-text-hover-anim {
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to {color: #222;}
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}
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.spaced {
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padding: 0.5em 0.5em 0.5em 0.5em;
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margin: 1em 0em 1em 0em;
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}
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h1 a svg {
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vertical-align: middle;
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}
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.card {
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background-color: #eee;
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text-decoration: none;
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text-align: left;
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}
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.card h1 {
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color: #444;
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}
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.card h2 {
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color: #777;
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}
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.card h3 {
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color: #999;
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}
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.card a {
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text-decoration: none;
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display: block;
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}
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.card:hover {
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animation: card-hover-anim 0.25s ease-out;
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animation-fill-mode: forwards;
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}
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/* .card:hover h3 { */
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/* animation: card-text-hover-anim 0.25s ease-out; */
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/* animation-fill-mode: forwards; */
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/* } */
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.card img {
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vertical-align: bottom;
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float: right;
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padding: 0em 0.1em 0em 0.1em;
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width: 60px;
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}
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.card svg {
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vertical-align: bottom;
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float: right;
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padding: 0em 0.1em 0em 0.1em;
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width: 3em;
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height: auto;
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}
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.content-subhead {
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margin: 50px 0 20px 0;
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font-weight: 300;
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color: #444;
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}
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code {
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font-family: Cascadia;
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}
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.code-block {
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/* background-color: #fdf6e3; */
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background-color: #eee;
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color: #002b36;
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font-family: Cascadia;
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font-size: 0.85em;
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padding: 0em 0.5em 0em 0.5em;
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margin: 1em 0em 1em 0em;
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page-break-inside: avoid;
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display: block;
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overflow: auto;
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word-wrap: break-word;
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max-width: 100%;
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}
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.code-block pre {
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display: block;
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margin: 0 0 0 0;
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padding: 0 0 0 0;
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}
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.code-block pre code {
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font-family: Cascadia;
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display: block;
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white-space: pre-wrap;
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}
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.code-block span {
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/* background-color: #fdf6e3; */
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background-color: #eee;
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}
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.keyword {
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color: #6c71c4;
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}
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.constant {
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color: #cb4b16;
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}
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.function {
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color: #268bd2;
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}
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.operator {
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color: #6c71c4;
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}
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.punctuation {
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color: #586e75;
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}
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.string {
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color: #859900;
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}
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.type {
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color: #2aa198;
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}
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.property {
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color: #586e75;
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}
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</style></head><body><div class="pure-g"><div class="pure-u-1-1"><div class="header"><h1> nd-range </h1><h2> Vector Math - Standard Library </h2></div><div class="content"><h2 class="distinct"> Motivation </h2>
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||
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The Rust standard library provides several 'Range' types which
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represent integers inside a given bounds (i.e. 1 ≤ n ≤ 100).
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Ranges can be iterated over, and used for bounds testing of numbers.
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In designing video games, it is often necessary to express 2 or 3
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dimensional quantities or bounds. Problems like iterating over
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voxels in a 3D world, or testing for an intersection between rectangles
|
||
|
|
lend themselves to the idea of Ranges.
|
||
|
|
<div class="code-block">
|
||
|
|
<pre><code>
|
||
|
|
<span class="comment">// A 3D array representing a 128x128x128 voxel world</span>
|
||
|
|
<span class="keyword storage">let</span> <span class="variable">world_data</span> <span class="operator">=</span> <span class="punctuation bracket">[</span><span class="punctuation bracket">[</span><span class="punctuation bracket">[</span><span class="constant numeric integer">0</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span>
|
||
|
|
<span class="comment">// The '0..128' here is a range from 0 to 127 inclusive</span>
|
||
|
|
<span class="keyword control repeat">for</span> <span class="variable">x</span> <span class="keyword control">in</span> <span class="constant numeric integer">0</span><span class="operator">..</span><span class="constant numeric integer">128</span> <span class="punctuation bracket">{</span>
|
||
|
|
<span class="keyword control repeat">for</span> <span class="variable">y</span> <span class="keyword control">in</span> <span class="constant numeric integer">0</span><span class="operator">..</span><span class="constant numeric integer">128</span> <span class="punctuation bracket">{</span>
|
||
|
|
<span class="keyword control repeat">for</span> <span class="variable">z</span> <span class="keyword control">in</span> <span class="constant numeric integer">0</span><span class="operator">..</span><span class="constant numeric integer">128</span> <span class="punctuation bracket">{</span>
|
||
|
|
<span class="keyword storage">let</span> <span class="variable">voxel</span> <span class="operator">=</span> <span class="operator">&</span><span class="variable">world</span><span class="punctuation bracket">[</span><span class="variable">x</span><span class="punctuation bracket">]</span><span class="punctuation bracket">[</span><span class="variable">y</span><span class="punctuation bracket">]</span><span class="punctuation bracket">[</span><span class="variable">z</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span>
|
||
|
|
<span class="comment">// Do something with voxel</span>
|
||
|
|
<span class="punctuation bracket">}</span>
|
||
|
|
<span class="punctuation bracket">}</span>
|
||
|
|
<span class="punctuation bracket">}</span>
|
||
|
|
</code></pre>
|
||
|
|
</div>
|
||
|
|
However, in these contexts the Range type is not particularly helpful.
|
||
|
|
I am forced to use three different ranges and a triple nested 'for' loop.
|
||
|
|
The idea for nd-range is to expand the native Range type so that it
|
||
|
|
can be used over arbitrary dimensions. This allows us to iterate over
|
||
|
|
X, Y, and Z coordinates in a single loop.
|
||
|
|
<div class="code-block">
|
||
|
|
<pre><code>
|
||
|
|
<span class="keyword storage">let</span> <span class="variable">world_data</span> <span class="operator">=</span> <span class="punctuation bracket">[</span><span class="punctuation bracket">[</span><span class="punctuation bracket">[</span><span class="constant numeric integer">0</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span>
|
||
|
|
<span class="keyword control repeat">for</span> <span class="punctuation bracket">[</span><span class="variable">x</span><span class="punctuation delimiter">,</span> <span class="variable">y</span><span class="punctuation delimiter">,</span> <span class="variable">z</span><span class="punctuation bracket">]</span> <span class="keyword control">in</span> <span class="function macro">nrange</span><span class="function macro">!</span><span class="punctuation bracket">(</span><span class="constant numeric integer">0</span><span class="operator"><span class="punctuation delimiter">.</span><span class="punctuation delimiter">.</span></span><span class="constant numeric integer">128</span><span class="punctuation delimiter">,</span> <span class="constant numeric integer">0</span><span class="operator"><span class="punctuation delimiter">.</span><span class="punctuation delimiter">.</span></span><span class="constant numeric integer">128</span><span class="punctuation delimiter">,</span> <span class="constant numeric integer">0</span><span class="operator"><span class="punctuation delimiter">.</span><span class="punctuation delimiter">.</span></span><span class="constant numeric integer">128</span><span class="punctuation bracket">)</span><span class="punctuation delimiter"></span> <span class="punctuation bracket">{</span>
|
||
|
|
<span class="keyword storage">let</span> <span class="variable">voxel</span> <span class="operator">=</span> <span class="operator">&</span><span class="variable">world</span><span class="punctuation bracket">[</span><span class="variable">x</span><span class="punctuation bracket">]</span><span class="punctuation bracket">[</span><span class="variable">y</span><span class="punctuation bracket">]</span><span class="punctuation bracket">[</span><span class="variable">z</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span>
|
||
|
|
<span class="comment">// Do something with voxel</span>
|
||
|
|
<span class="punctuation bracket">}</span>
|
||
|
|
</code></pre>
|
||
|
|
</div><h2 class="distinct"> Approach </h2>
|
||
|
|
An nd-range is similar in concept to an axis-aligned bounding box,
|
||
|
|
or AABB. These are common abstractions used in game development,
|
||
|
|
and there are well established algorithms that test for overlap.
|
||
|
|
Iterating over is slightly more complex, requiring some vector
|
||
|
|
algebra. If we interpret the range of values over each axis as a
|
||
|
|
vector, we can apply the cartesian product algorithm to find every
|
||
|
|
position within the bounded space. Below is a diagram from Wikipedia
|
||
|
|
(CC BY-SA 3.0).
|
||
|
|
<img class="centered" src="https://upload.wikimedia.org/wikipedia/commons/4/4e/Cartesian_Product_qtl1.svg"/>
|
||
|
|
Because a range is contiguous by definition, generating a cartesian
|
||
|
|
product is simple and performant. The iterator object has a space
|
||
|
|
complexity of O(N), where n is the number of dimensions. Rust's const generics
|
||
|
|
allow the entire struct to exist on the stack, which is a boon to performance.
|
||
|
|
<h2 class="distinct"> Performance </h2>
|
||
|
|
My points of comparison are the itertools and cartesian crates, which provide
|
||
|
|
comparable algorithms. Despite its popularity, I was shocked to discover how
|
||
|
|
slow the itertools implementation of the cartesian product is. The cartesian-rs
|
||
|
|
crate is lesser known, and uses a creative macro-based solution. I benchmarked
|
||
|
|
all three approaches, as well as the nested for-loop base case, over a 100x100x100
|
||
|
|
range.
|
||
|
|
<table class="striped"><thead><th scope="col"> Implementation </th><th scope="col"> Average Time (ns) </th><th scope="col"> Error (+/- ns) </th></thead><tbody><tr><th scope="row"><a href="https://docs.rs/itertools/latest/itertools/trait.Itertools.html#method.cartesian_product">
|
||
|
|
itertools
|
||
|
|
</a></th><td> 1,821,573 </td><td> 31,501 </td></tr><tr><th scope="row"><a href="https://crates.io/crates/cartesian">
|
||
|
|
cartesian-rs
|
||
|
|
</a></th><td> 989,242 </td><td> 50,835 </td></tr><tr><th scope="row"> nd-range </th><td> 968,853 </td><td> 15,792 </td></tr><tr><th scope="row"> nested loops </th><td> 911,853 </td><td> 46,066 </td></tr></tbody></table><h2 class="distinct"> Pros and Cons</h2>
|
||
|
|
My implementation is competitive with, and possibly faster than
|
||
|
|
its competitors for my use case. While nd-range only works for
|
||
|
|
ranges of contiguous integers, itertools and cartesian-rs work
|
||
|
|
for any iterators. However, by restricting my use case I can
|
||
|
|
extract more performance gains and integrate better with the Rust
|
||
|
|
standard library.
|
||
|
|
</div></div></div></body></html>
|