839 lines
160 KiB
HTML
839 lines
160 KiB
HTML
<!doctype html>
|
||
<html>
|
||
<head>
|
||
<meta charset='UTF-8'><meta name='viewport' content='width=device-width initial-scale=1'>
|
||
|
||
<link href='https://fonts.loli.net/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext' rel='stylesheet' type='text/css' /><style type='text/css'>html {overflow-x: initial !important;}:root { --bg-color:#ffffff; --text-color:#333333; --select-text-bg-color:#B5D6FC; --select-text-font-color:auto; --monospace:"Lucida Console",Consolas,"Courier",monospace; --title-bar-height:20px; }
|
||
.mac-os-11 { --title-bar-height:28px; }
|
||
html { font-size: 14px; background-color: var(--bg-color); color: var(--text-color); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; -webkit-font-smoothing: antialiased; }
|
||
body { margin: 0px; padding: 0px; height: auto; inset: 0px; font-size: 1rem; line-height: 1.42857; overflow-x: hidden; background: inherit; tab-size: 4; }
|
||
iframe { margin: auto; }
|
||
a.url { word-break: break-all; }
|
||
a:active, a:hover { outline: 0px; }
|
||
.in-text-selection, ::selection { text-shadow: none; background: var(--select-text-bg-color); color: var(--select-text-font-color); }
|
||
#write { margin: 0px auto; height: auto; width: inherit; word-break: normal; overflow-wrap: break-word; position: relative; white-space: normal; overflow-x: visible; padding-top: 36px; }
|
||
#write.first-line-indent p { text-indent: 2em; }
|
||
#write.first-line-indent li p, #write.first-line-indent p * { text-indent: 0px; }
|
||
#write.first-line-indent li { margin-left: 2em; }
|
||
.for-image #write { padding-left: 8px; padding-right: 8px; }
|
||
body.typora-export { padding-left: 30px; padding-right: 30px; }
|
||
.typora-export .footnote-line, .typora-export li, .typora-export p { white-space: pre-wrap; }
|
||
.typora-export .task-list-item input { pointer-events: none; }
|
||
@media screen and (max-width: 500px) {
|
||
body.typora-export { padding-left: 0px; padding-right: 0px; }
|
||
#write { padding-left: 20px; padding-right: 20px; }
|
||
.CodeMirror-sizer { margin-left: 0px !important; }
|
||
.CodeMirror-gutters { display: none !important; }
|
||
}
|
||
#write li > figure:last-child { margin-bottom: 0.5rem; }
|
||
#write ol, #write ul { position: relative; }
|
||
img { max-width: 100%; vertical-align: middle; image-orientation: from-image; }
|
||
button, input, select, textarea { color: inherit; font: inherit; }
|
||
input[type="checkbox"], input[type="radio"] { line-height: normal; padding: 0px; }
|
||
*, ::after, ::before { box-sizing: border-box; }
|
||
#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p, #write pre { width: inherit; }
|
||
#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p { position: relative; }
|
||
p { line-height: inherit; }
|
||
h1, h2, h3, h4, h5, h6 { break-after: avoid-page; break-inside: avoid; orphans: 4; }
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||
p { orphans: 4; }
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||
h1 { font-size: 2rem; }
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||
h2 { font-size: 1.8rem; }
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||
h3 { font-size: 1.6rem; }
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||
h4 { font-size: 1.4rem; }
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||
h5 { font-size: 1.2rem; }
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||
h6 { font-size: 1rem; }
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||
.md-math-block, .md-rawblock, h1, h2, h3, h4, h5, h6, p { margin-top: 1rem; margin-bottom: 1rem; }
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||
.hidden { display: none; }
|
||
.md-blockmeta { color: rgb(204, 204, 204); font-weight: 700; font-style: italic; }
|
||
a { cursor: pointer; }
|
||
sup.md-footnote { padding: 2px 4px; background-color: rgba(238, 238, 238, 0.7); color: rgb(85, 85, 85); border-radius: 4px; cursor: pointer; }
|
||
sup.md-footnote a, sup.md-footnote a:hover { color: inherit; text-transform: inherit; text-decoration: inherit; }
|
||
#write input[type="checkbox"] { cursor: pointer; width: inherit; height: inherit; }
|
||
figure { overflow-x: auto; margin: 1.2em 0px; max-width: calc(100% + 16px); padding: 0px; }
|
||
figure > table { margin: 0px; }
|
||
tr { break-inside: avoid; break-after: auto; }
|
||
thead { display: table-header-group; }
|
||
table { border-collapse: collapse; border-spacing: 0px; width: 100%; overflow: auto; break-inside: auto; text-align: left; }
|
||
table.md-table td { min-width: 32px; }
|
||
.CodeMirror-gutters { border-right: 0px; background-color: inherit; }
|
||
.CodeMirror-linenumber { user-select: none; }
|
||
.CodeMirror { text-align: left; }
|
||
.CodeMirror-placeholder { opacity: 0.3; }
|
||
.CodeMirror pre { padding: 0px 4px; }
|
||
.CodeMirror-lines { padding: 0px; }
|
||
div.hr:focus { cursor: none; }
|
||
#write pre { white-space: pre-wrap; }
|
||
#write.fences-no-line-wrapping pre { white-space: pre; }
|
||
#write pre.ty-contain-cm { white-space: normal; }
|
||
.CodeMirror-gutters { margin-right: 4px; }
|
||
.md-fences { font-size: 0.9rem; display: block; break-inside: avoid; text-align: left; overflow: visible; white-space: pre; background: inherit; position: relative !important; }
|
||
.md-fences-adv-panel { width: 100%; margin-top: 10px; text-align: center; padding-top: 0px; padding-bottom: 8px; overflow-x: auto; }
|
||
#write .md-fences.mock-cm { white-space: pre-wrap; }
|
||
.md-fences.md-fences-with-lineno { padding-left: 0px; }
|
||
#write.fences-no-line-wrapping .md-fences.mock-cm { white-space: pre; overflow-x: auto; }
|
||
.md-fences.mock-cm.md-fences-with-lineno { padding-left: 8px; }
|
||
.CodeMirror-line, twitterwidget { break-inside: avoid; }
|
||
.footnotes { opacity: 0.8; font-size: 0.9rem; margin-top: 1em; margin-bottom: 1em; }
|
||
.footnotes + .footnotes { margin-top: 0px; }
|
||
.md-reset { margin: 0px; padding: 0px; border: 0px; outline: 0px; vertical-align: top; background: 0px 0px; text-decoration: none; text-shadow: none; float: none; position: static; width: auto; height: auto; white-space: nowrap; cursor: inherit; -webkit-tap-highlight-color: transparent; line-height: normal; font-weight: 400; text-align: left; box-sizing: content-box; direction: ltr; }
|
||
li div { padding-top: 0px; }
|
||
blockquote { margin: 1rem 0px; }
|
||
li .mathjax-block, li p { margin: 0.5rem 0px; }
|
||
li blockquote { margin: 1rem 0px; }
|
||
li { margin: 0px; position: relative; }
|
||
blockquote > :last-child { margin-bottom: 0px; }
|
||
blockquote > :first-child, li > :first-child { margin-top: 0px; }
|
||
.footnotes-area { color: rgb(136, 136, 136); margin-top: 0.714rem; padding-bottom: 0.143rem; white-space: normal; }
|
||
#write .footnote-line { white-space: pre-wrap; }
|
||
@media print {
|
||
body, html { border: 1px solid transparent; height: 99%; break-after: avoid; break-before: avoid; font-variant-ligatures: no-common-ligatures; }
|
||
#write { margin-top: 0px; padding-top: 0px; border-color: transparent !important; }
|
||
.typora-export * { -webkit-print-color-adjust: exact; }
|
||
.typora-export #write { break-after: avoid; }
|
||
.typora-export #write::after { height: 0px; }
|
||
.is-mac table { break-inside: avoid; }
|
||
.typora-export-show-outline .typora-export-sidebar { display: none; }
|
||
}
|
||
.footnote-line { margin-top: 0.714em; font-size: 0.7em; }
|
||
a img, img a { cursor: pointer; }
|
||
pre.md-meta-block { font-size: 0.8rem; min-height: 0.8rem; white-space: pre-wrap; background: rgb(204, 204, 204); display: block; overflow-x: hidden; }
|
||
p > .md-image:only-child:not(.md-img-error) img, p > img:only-child { display: block; margin: auto; }
|
||
#write.first-line-indent p > .md-image:only-child:not(.md-img-error) img { left: -2em; position: relative; }
|
||
p > .md-image:only-child { display: inline-block; width: 100%; }
|
||
#write .MathJax_Display { margin: 0.8em 0px 0px; }
|
||
.md-math-block { width: 100%; }
|
||
.md-math-block:not(:empty)::after { display: none; }
|
||
.MathJax_ref { fill: currentcolor; }
|
||
[contenteditable="true"]:active, [contenteditable="true"]:focus, [contenteditable="false"]:active, [contenteditable="false"]:focus { outline: 0px; box-shadow: none; }
|
||
.md-task-list-item { position: relative; list-style-type: none; }
|
||
.task-list-item.md-task-list-item { padding-left: 0px; }
|
||
.md-task-list-item > input { position: absolute; top: 0px; left: 0px; margin-left: -1.2em; margin-top: calc(1em - 10px); border: none; }
|
||
.math { font-size: 1rem; }
|
||
.md-toc { min-height: 3.58rem; position: relative; font-size: 0.9rem; border-radius: 10px; }
|
||
.md-toc-content { position: relative; margin-left: 0px; }
|
||
.md-toc-content::after, .md-toc::after { display: none; }
|
||
.md-toc-item { display: block; color: rgb(65, 131, 196); }
|
||
.md-toc-item a { text-decoration: none; }
|
||
.md-toc-inner:hover { text-decoration: underline; }
|
||
.md-toc-inner { display: inline-block; cursor: pointer; }
|
||
.md-toc-h1 .md-toc-inner { margin-left: 0px; font-weight: 700; }
|
||
.md-toc-h2 .md-toc-inner { margin-left: 2em; }
|
||
.md-toc-h3 .md-toc-inner { margin-left: 4em; }
|
||
.md-toc-h4 .md-toc-inner { margin-left: 6em; }
|
||
.md-toc-h5 .md-toc-inner { margin-left: 8em; }
|
||
.md-toc-h6 .md-toc-inner { margin-left: 10em; }
|
||
@media screen and (max-width: 48em) {
|
||
.md-toc-h3 .md-toc-inner { margin-left: 3.5em; }
|
||
.md-toc-h4 .md-toc-inner { margin-left: 5em; }
|
||
.md-toc-h5 .md-toc-inner { margin-left: 6.5em; }
|
||
.md-toc-h6 .md-toc-inner { margin-left: 8em; }
|
||
}
|
||
a.md-toc-inner { font-size: inherit; font-style: inherit; font-weight: inherit; line-height: inherit; }
|
||
.footnote-line a:not(.reversefootnote) { color: inherit; }
|
||
.md-attr { display: none; }
|
||
.md-fn-count::after { content: "."; }
|
||
code, pre, samp, tt { font-family: var(--monospace); }
|
||
kbd { margin: 0px 0.1em; padding: 0.1em 0.6em; font-size: 0.8em; color: rgb(36, 39, 41); background: rgb(255, 255, 255); border: 1px solid rgb(173, 179, 185); border-radius: 3px; box-shadow: rgba(12, 13, 14, 0.2) 0px 1px 0px, rgb(255, 255, 255) 0px 0px 0px 2px inset; white-space: nowrap; vertical-align: middle; }
|
||
.md-comment { color: rgb(162, 127, 3); opacity: 0.8; font-family: var(--monospace); }
|
||
code { text-align: left; vertical-align: initial; }
|
||
a.md-print-anchor { white-space: pre !important; border-width: initial !important; border-style: none !important; border-color: initial !important; display: inline-block !important; position: absolute !important; width: 1px !important; right: 0px !important; outline: 0px !important; background: 0px 0px !important; text-decoration: initial !important; text-shadow: initial !important; }
|
||
.os-windows.monocolor-emoji .md-emoji { font-family: "Segoe UI Symbol", sans-serif; }
|
||
.md-diagram-panel > svg { max-width: 100%; }
|
||
[lang="flow"] svg, [lang="mermaid"] svg { max-width: 100%; height: auto; }
|
||
[lang="mermaid"] .node text { font-size: 1rem; }
|
||
table tr th { border-bottom: 0px; }
|
||
video { max-width: 100%; display: block; margin: 0px auto; }
|
||
iframe { max-width: 100%; width: 100%; border: none; }
|
||
.highlight td, .highlight tr { border: 0px; }
|
||
mark { background: rgb(255, 255, 0); color: rgb(0, 0, 0); }
|
||
.md-html-inline .md-plain, .md-html-inline strong, mark .md-inline-math, mark strong { color: inherit; }
|
||
.md-expand mark .md-meta { opacity: 0.3 !important; }
|
||
mark .md-meta { color: rgb(0, 0, 0); }
|
||
@media print {
|
||
.typora-export h1, .typora-export h2, .typora-export h3, .typora-export h4, .typora-export h5, .typora-export h6 { break-inside: avoid; }
|
||
}
|
||
.md-diagram-panel .messageText { stroke: none !important; }
|
||
.md-diagram-panel .start-state { fill: var(--node-fill); }
|
||
.md-diagram-panel .edgeLabel rect { opacity: 1 !important; }
|
||
.md-require-zoom-fix { height: auto; margin-top: 16px; margin-bottom: 16px; }
|
||
.md-require-zoom-fix foreignobject { font-size: var(--mermaid-font-zoom); }
|
||
.md-fences.md-fences-math { font-size: 1em; }
|
||
.md-fences-advanced:not(.md-focus) { padding: 0px; white-space: nowrap; border: 0px; }
|
||
.md-fences-advanced:not(.md-focus) { background: inherit; }
|
||
.typora-export-show-outline .typora-export-content { max-width: 1440px; margin: auto; display: flex; flex-direction: row; }
|
||
.typora-export-sidebar { width: 300px; font-size: 0.8rem; margin-top: 80px; margin-right: 18px; }
|
||
.typora-export-show-outline #write { --webkit-flex:2; flex: 2 1 0%; }
|
||
.typora-export-sidebar .outline-content { position: fixed; top: 0px; max-height: 100%; overflow: hidden auto; padding-bottom: 30px; padding-top: 60px; width: 300px; }
|
||
@media screen and (max-width: 1024px) {
|
||
.typora-export-sidebar, .typora-export-sidebar .outline-content { width: 240px; }
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}
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@media screen and (max-width: 800px) {
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||
.typora-export-sidebar { display: none; }
|
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}
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||
.outline-content li, .outline-content ul { margin-left: 0px; margin-right: 0px; padding-left: 0px; padding-right: 0px; list-style: none; }
|
||
.outline-content ul { margin-top: 0px; margin-bottom: 0px; }
|
||
.outline-content strong { font-weight: 400; }
|
||
.outline-expander { width: 1rem; height: 1.42857rem; position: relative; display: table-cell; vertical-align: middle; cursor: pointer; padding-left: 4px; }
|
||
.outline-expander::before { content: ""; position: relative; font-family: Ionicons; display: inline-block; font-size: 8px; vertical-align: middle; }
|
||
.outline-item { padding-top: 3px; padding-bottom: 3px; cursor: pointer; }
|
||
.outline-expander:hover::before { content: ""; }
|
||
.outline-h1 > .outline-item { padding-left: 0px; }
|
||
.outline-h2 > .outline-item { padding-left: 1em; }
|
||
.outline-h3 > .outline-item { padding-left: 2em; }
|
||
.outline-h4 > .outline-item { padding-left: 3em; }
|
||
.outline-h5 > .outline-item { padding-left: 4em; }
|
||
.outline-h6 > .outline-item { padding-left: 5em; }
|
||
.outline-label { cursor: pointer; display: table-cell; vertical-align: middle; text-decoration: none; color: inherit; }
|
||
.outline-label:hover { text-decoration: underline; }
|
||
.outline-item:hover { border-color: rgb(245, 245, 245); background-color: var(--item-hover-bg-color); }
|
||
.outline-item:hover { margin-left: -28px; margin-right: -28px; border-left: 28px solid transparent; border-right: 28px solid transparent; }
|
||
.outline-item-single .outline-expander::before, .outline-item-single .outline-expander:hover::before { display: none; }
|
||
.outline-item-open > .outline-item > .outline-expander::before { content: ""; }
|
||
.outline-children { display: none; }
|
||
.info-panel-tab-wrapper { display: none; }
|
||
.outline-item-open > .outline-children { display: block; }
|
||
.typora-export .outline-item { padding-top: 1px; padding-bottom: 1px; }
|
||
.typora-export .outline-item:hover { margin-right: -8px; border-right: 8px solid transparent; }
|
||
.typora-export .outline-expander::before { content: "+"; font-family: inherit; top: -1px; }
|
||
.typora-export .outline-expander:hover::before, .typora-export .outline-item-open > .outline-item > .outline-expander::before { content: "−"; }
|
||
.typora-export-collapse-outline .outline-children { display: none; }
|
||
.typora-export-collapse-outline .outline-item-open > .outline-children, .typora-export-no-collapse-outline .outline-children { display: block; }
|
||
.typora-export-no-collapse-outline .outline-expander::before { content: "" !important; }
|
||
.typora-export-show-outline .outline-item-active > .outline-item .outline-label { font-weight: 700; }
|
||
.md-inline-math-container mjx-container { zoom: 0.95; }
|
||
|
||
|
||
.CodeMirror { height: auto; }
|
||
.CodeMirror.cm-s-inner { background: inherit; }
|
||
.CodeMirror-scroll { overflow: auto hidden; z-index: 3; }
|
||
.CodeMirror-gutter-filler, .CodeMirror-scrollbar-filler { background-color: rgb(255, 255, 255); }
|
||
.CodeMirror-gutters { border-right: 1px solid rgb(221, 221, 221); background: inherit; white-space: nowrap; }
|
||
.CodeMirror-linenumber { padding: 0px 3px 0px 5px; text-align: right; color: rgb(153, 153, 153); }
|
||
.cm-s-inner .cm-keyword { color: rgb(119, 0, 136); }
|
||
.cm-s-inner .cm-atom, .cm-s-inner.cm-atom { color: rgb(34, 17, 153); }
|
||
.cm-s-inner .cm-number { color: rgb(17, 102, 68); }
|
||
.cm-s-inner .cm-def { color: rgb(0, 0, 255); }
|
||
.cm-s-inner .cm-variable { color: rgb(0, 0, 0); }
|
||
.cm-s-inner .cm-variable-2 { color: rgb(0, 85, 170); }
|
||
.cm-s-inner .cm-variable-3 { color: rgb(0, 136, 85); }
|
||
.cm-s-inner .cm-string { color: rgb(170, 17, 17); }
|
||
.cm-s-inner .cm-property { color: rgb(0, 0, 0); }
|
||
.cm-s-inner .cm-operator { color: rgb(152, 26, 26); }
|
||
.cm-s-inner .cm-comment, .cm-s-inner.cm-comment { color: rgb(170, 85, 0); }
|
||
.cm-s-inner .cm-string-2 { color: rgb(255, 85, 0); }
|
||
.cm-s-inner .cm-meta { color: rgb(85, 85, 85); }
|
||
.cm-s-inner .cm-qualifier { color: rgb(85, 85, 85); }
|
||
.cm-s-inner .cm-builtin { color: rgb(51, 0, 170); }
|
||
.cm-s-inner .cm-bracket { color: rgb(153, 153, 119); }
|
||
.cm-s-inner .cm-tag { color: rgb(17, 119, 0); }
|
||
.cm-s-inner .cm-attribute { color: rgb(0, 0, 204); }
|
||
.cm-s-inner .cm-header, .cm-s-inner.cm-header { color: rgb(0, 0, 255); }
|
||
.cm-s-inner .cm-quote, .cm-s-inner.cm-quote { color: rgb(0, 153, 0); }
|
||
.cm-s-inner .cm-hr, .cm-s-inner.cm-hr { color: rgb(153, 153, 153); }
|
||
.cm-s-inner .cm-link, .cm-s-inner.cm-link { color: rgb(0, 0, 204); }
|
||
.cm-negative { color: rgb(221, 68, 68); }
|
||
.cm-positive { color: rgb(34, 153, 34); }
|
||
.cm-header, .cm-strong { font-weight: 700; }
|
||
.cm-del { text-decoration: line-through; }
|
||
.cm-em { font-style: italic; }
|
||
.cm-link { text-decoration: underline; }
|
||
.cm-error { color: red; }
|
||
.cm-invalidchar { color: red; }
|
||
.cm-constant { color: rgb(38, 139, 210); }
|
||
.cm-defined { color: rgb(181, 137, 0); }
|
||
div.CodeMirror span.CodeMirror-matchingbracket { color: rgb(0, 255, 0); }
|
||
div.CodeMirror span.CodeMirror-nonmatchingbracket { color: rgb(255, 34, 34); }
|
||
.cm-s-inner .CodeMirror-activeline-background { background: inherit; }
|
||
.CodeMirror { position: relative; overflow: hidden; }
|
||
.CodeMirror-scroll { height: 100%; outline: 0px; position: relative; box-sizing: content-box; background: inherit; }
|
||
.CodeMirror-sizer { position: relative; }
|
||
.CodeMirror-gutter-filler, .CodeMirror-hscrollbar, .CodeMirror-scrollbar-filler, .CodeMirror-vscrollbar { position: absolute; z-index: 6; display: none; outline: 0px; }
|
||
.CodeMirror-vscrollbar { right: 0px; top: 0px; overflow: hidden; }
|
||
.CodeMirror-hscrollbar { bottom: 0px; left: 0px; overflow: auto hidden; }
|
||
.CodeMirror-scrollbar-filler { right: 0px; bottom: 0px; }
|
||
.CodeMirror-gutter-filler { left: 0px; bottom: 0px; }
|
||
.CodeMirror-gutters { position: absolute; left: 0px; top: 0px; padding-bottom: 10px; z-index: 3; overflow-y: hidden; }
|
||
.CodeMirror-gutter { white-space: normal; height: 100%; box-sizing: content-box; padding-bottom: 30px; margin-bottom: -32px; display: inline-block; }
|
||
.CodeMirror-gutter-wrapper { position: absolute; z-index: 4; background: 0px 0px !important; border: none !important; }
|
||
.CodeMirror-gutter-background { position: absolute; top: 0px; bottom: 0px; z-index: 4; }
|
||
.CodeMirror-gutter-elt { position: absolute; cursor: default; z-index: 4; }
|
||
.CodeMirror-lines { cursor: text; }
|
||
.CodeMirror pre { border-radius: 0px; border-width: 0px; background: 0px 0px; font-family: inherit; font-size: inherit; margin: 0px; white-space: pre; overflow-wrap: normal; color: inherit; z-index: 2; position: relative; overflow: visible; }
|
||
.CodeMirror-wrap pre { overflow-wrap: break-word; white-space: pre-wrap; word-break: normal; }
|
||
.CodeMirror-code pre { border-right: 30px solid transparent; width: fit-content; }
|
||
.CodeMirror-wrap .CodeMirror-code pre { border-right: none; width: auto; }
|
||
.CodeMirror-linebackground { position: absolute; inset: 0px; z-index: 0; }
|
||
.CodeMirror-linewidget { position: relative; z-index: 2; overflow: auto; }
|
||
.CodeMirror-wrap .CodeMirror-scroll { overflow-x: hidden; }
|
||
.CodeMirror-measure { position: absolute; width: 100%; height: 0px; overflow: hidden; visibility: hidden; }
|
||
.CodeMirror-measure pre { position: static; }
|
||
.CodeMirror div.CodeMirror-cursor { position: absolute; visibility: hidden; border-right: none; width: 0px; }
|
||
.CodeMirror div.CodeMirror-cursor { visibility: hidden; }
|
||
.CodeMirror-focused div.CodeMirror-cursor { visibility: inherit; }
|
||
.cm-searching { background: rgba(255, 255, 0, 0.4); }
|
||
span.cm-underlined { text-decoration: underline; }
|
||
span.cm-strikethrough { text-decoration: line-through; }
|
||
.cm-tw-syntaxerror { color: rgb(255, 255, 255); background-color: rgb(153, 0, 0); }
|
||
.cm-tw-deleted { text-decoration: line-through; }
|
||
.cm-tw-header5 { font-weight: 700; }
|
||
.cm-tw-listitem:first-child { padding-left: 10px; }
|
||
.cm-tw-box { border-style: solid; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; border-color: inherit; border-top-width: 0px !important; }
|
||
.cm-tw-underline { text-decoration: underline; }
|
||
@media print {
|
||
.CodeMirror div.CodeMirror-cursor { visibility: hidden; }
|
||
}
|
||
|
||
|
||
:root {
|
||
--side-bar-bg-color: #fafafa;
|
||
--control-text-color: #777;
|
||
}
|
||
|
||
@include-when-export url(https://fonts.loli.net/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext);
|
||
|
||
/* open-sans-regular - latin-ext_latin */
|
||
/* open-sans-italic - latin-ext_latin */
|
||
/* open-sans-700 - latin-ext_latin */
|
||
/* open-sans-700italic - latin-ext_latin */
|
||
html {
|
||
font-size: 16px;
|
||
-webkit-font-smoothing: antialiased;
|
||
}
|
||
|
||
body {
|
||
font-family: "Open Sans","Clear Sans", "Helvetica Neue", Helvetica, Arial, 'Segoe UI Emoji', sans-serif;
|
||
color: rgb(51, 51, 51);
|
||
line-height: 1.6;
|
||
}
|
||
|
||
#write {
|
||
max-width: 860px;
|
||
margin: 0 auto;
|
||
padding: 30px;
|
||
padding-bottom: 100px;
|
||
}
|
||
|
||
@media only screen and (min-width: 1400px) {
|
||
#write {
|
||
max-width: 1024px;
|
||
}
|
||
}
|
||
|
||
@media only screen and (min-width: 1800px) {
|
||
#write {
|
||
max-width: 1200px;
|
||
}
|
||
}
|
||
|
||
#write > ul:first-child,
|
||
#write > ol:first-child{
|
||
margin-top: 30px;
|
||
}
|
||
|
||
a {
|
||
color: #4183C4;
|
||
}
|
||
h1,
|
||
h2,
|
||
h3,
|
||
h4,
|
||
h5,
|
||
h6 {
|
||
position: relative;
|
||
margin-top: 1rem;
|
||
margin-bottom: 1rem;
|
||
font-weight: bold;
|
||
line-height: 1.4;
|
||
cursor: text;
|
||
}
|
||
h1:hover a.anchor,
|
||
h2:hover a.anchor,
|
||
h3:hover a.anchor,
|
||
h4:hover a.anchor,
|
||
h5:hover a.anchor,
|
||
h6:hover a.anchor {
|
||
text-decoration: none;
|
||
}
|
||
h1 tt,
|
||
h1 code {
|
||
font-size: inherit;
|
||
}
|
||
h2 tt,
|
||
h2 code {
|
||
font-size: inherit;
|
||
}
|
||
h3 tt,
|
||
h3 code {
|
||
font-size: inherit;
|
||
}
|
||
h4 tt,
|
||
h4 code {
|
||
font-size: inherit;
|
||
}
|
||
h5 tt,
|
||
h5 code {
|
||
font-size: inherit;
|
||
}
|
||
h6 tt,
|
||
h6 code {
|
||
font-size: inherit;
|
||
}
|
||
h1 {
|
||
font-size: 2.25em;
|
||
line-height: 1.2;
|
||
border-bottom: 1px solid #eee;
|
||
}
|
||
h2 {
|
||
font-size: 1.75em;
|
||
line-height: 1.225;
|
||
border-bottom: 1px solid #eee;
|
||
}
|
||
|
||
/*@media print {
|
||
.typora-export h1,
|
||
.typora-export h2 {
|
||
border-bottom: none;
|
||
padding-bottom: initial;
|
||
}
|
||
|
||
.typora-export h1::after,
|
||
.typora-export h2::after {
|
||
content: "";
|
||
display: block;
|
||
height: 100px;
|
||
margin-top: -96px;
|
||
border-top: 1px solid #eee;
|
||
}
|
||
}*/
|
||
|
||
h3 {
|
||
font-size: 1.5em;
|
||
line-height: 1.43;
|
||
}
|
||
h4 {
|
||
font-size: 1.25em;
|
||
}
|
||
h5 {
|
||
font-size: 1em;
|
||
}
|
||
h6 {
|
||
font-size: 1em;
|
||
color: #777;
|
||
}
|
||
p,
|
||
blockquote,
|
||
ul,
|
||
ol,
|
||
dl,
|
||
table{
|
||
margin: 0.8em 0;
|
||
}
|
||
li>ol,
|
||
li>ul {
|
||
margin: 0 0;
|
||
}
|
||
hr {
|
||
height: 2px;
|
||
padding: 0;
|
||
margin: 16px 0;
|
||
background-color: #e7e7e7;
|
||
border: 0 none;
|
||
overflow: hidden;
|
||
box-sizing: content-box;
|
||
}
|
||
|
||
li p.first {
|
||
display: inline-block;
|
||
}
|
||
ul,
|
||
ol {
|
||
padding-left: 30px;
|
||
}
|
||
ul:first-child,
|
||
ol:first-child {
|
||
margin-top: 0;
|
||
}
|
||
ul:last-child,
|
||
ol:last-child {
|
||
margin-bottom: 0;
|
||
}
|
||
blockquote {
|
||
border-left: 4px solid #dfe2e5;
|
||
padding: 0 15px;
|
||
color: #777777;
|
||
}
|
||
blockquote blockquote {
|
||
padding-right: 0;
|
||
}
|
||
table {
|
||
padding: 0;
|
||
word-break: initial;
|
||
}
|
||
table tr {
|
||
border: 1px solid #dfe2e5;
|
||
margin: 0;
|
||
padding: 0;
|
||
}
|
||
table tr:nth-child(2n),
|
||
thead {
|
||
background-color: #f8f8f8;
|
||
}
|
||
table th {
|
||
font-weight: bold;
|
||
border: 1px solid #dfe2e5;
|
||
border-bottom: 0;
|
||
margin: 0;
|
||
padding: 6px 13px;
|
||
}
|
||
table td {
|
||
border: 1px solid #dfe2e5;
|
||
margin: 0;
|
||
padding: 6px 13px;
|
||
}
|
||
table th:first-child,
|
||
table td:first-child {
|
||
margin-top: 0;
|
||
}
|
||
table th:last-child,
|
||
table td:last-child {
|
||
margin-bottom: 0;
|
||
}
|
||
|
||
.CodeMirror-lines {
|
||
padding-left: 4px;
|
||
}
|
||
|
||
.code-tooltip {
|
||
box-shadow: 0 1px 1px 0 rgba(0,28,36,.3);
|
||
border-top: 1px solid #eef2f2;
|
||
}
|
||
|
||
.md-fences,
|
||
code,
|
||
tt {
|
||
border: 1px solid #e7eaed;
|
||
background-color: #f8f8f8;
|
||
border-radius: 3px;
|
||
padding: 0;
|
||
padding: 2px 4px 0px 4px;
|
||
font-size: 0.9em;
|
||
}
|
||
|
||
code {
|
||
background-color: #f3f4f4;
|
||
padding: 0 2px 0 2px;
|
||
}
|
||
|
||
.md-fences {
|
||
margin-bottom: 15px;
|
||
margin-top: 15px;
|
||
padding-top: 8px;
|
||
padding-bottom: 6px;
|
||
}
|
||
|
||
|
||
.md-task-list-item > input {
|
||
margin-left: -1.3em;
|
||
}
|
||
|
||
@media print {
|
||
html {
|
||
font-size: 13px;
|
||
}
|
||
table,
|
||
pre {
|
||
page-break-inside: avoid;
|
||
}
|
||
pre {
|
||
word-wrap: break-word;
|
||
}
|
||
}
|
||
|
||
.md-fences {
|
||
background-color: #f8f8f8;
|
||
}
|
||
#write pre.md-meta-block {
|
||
padding: 1rem;
|
||
font-size: 85%;
|
||
line-height: 1.45;
|
||
background-color: #f7f7f7;
|
||
border: 0;
|
||
border-radius: 3px;
|
||
color: #777777;
|
||
margin-top: 0 !important;
|
||
}
|
||
|
||
.mathjax-block>.code-tooltip {
|
||
bottom: .375rem;
|
||
}
|
||
|
||
.md-mathjax-midline {
|
||
background: #fafafa;
|
||
}
|
||
|
||
#write>h3.md-focus:before{
|
||
left: -1.5625rem;
|
||
top: .375rem;
|
||
}
|
||
#write>h4.md-focus:before{
|
||
left: -1.5625rem;
|
||
top: .285714286rem;
|
||
}
|
||
#write>h5.md-focus:before{
|
||
left: -1.5625rem;
|
||
top: .285714286rem;
|
||
}
|
||
#write>h6.md-focus:before{
|
||
left: -1.5625rem;
|
||
top: .285714286rem;
|
||
}
|
||
.md-image>.md-meta {
|
||
/*border: 1px solid #ddd;*/
|
||
border-radius: 3px;
|
||
padding: 2px 0px 0px 4px;
|
||
font-size: 0.9em;
|
||
color: inherit;
|
||
}
|
||
|
||
.md-tag {
|
||
color: #a7a7a7;
|
||
opacity: 1;
|
||
}
|
||
|
||
.md-toc {
|
||
margin-top:20px;
|
||
padding-bottom:20px;
|
||
}
|
||
|
||
.sidebar-tabs {
|
||
border-bottom: none;
|
||
}
|
||
|
||
#typora-quick-open {
|
||
border: 1px solid #ddd;
|
||
background-color: #f8f8f8;
|
||
}
|
||
|
||
#typora-quick-open-item {
|
||
background-color: #FAFAFA;
|
||
border-color: #FEFEFE #e5e5e5 #e5e5e5 #eee;
|
||
border-style: solid;
|
||
border-width: 1px;
|
||
}
|
||
|
||
/** focus mode */
|
||
.on-focus-mode blockquote {
|
||
border-left-color: rgba(85, 85, 85, 0.12);
|
||
}
|
||
|
||
header, .context-menu, .megamenu-content, footer{
|
||
font-family: "Segoe UI", "Arial", sans-serif;
|
||
}
|
||
|
||
.file-node-content:hover .file-node-icon,
|
||
.file-node-content:hover .file-node-open-state{
|
||
visibility: visible;
|
||
}
|
||
|
||
.mac-seamless-mode #typora-sidebar {
|
||
background-color: #fafafa;
|
||
background-color: var(--side-bar-bg-color);
|
||
}
|
||
|
||
.md-lang {
|
||
color: #b4654d;
|
||
}
|
||
|
||
/*.html-for-mac {
|
||
--item-hover-bg-color: #E6F0FE;
|
||
}*/
|
||
|
||
#md-notification .btn {
|
||
border: 0;
|
||
}
|
||
|
||
.dropdown-menu .divider {
|
||
border-color: #e5e5e5;
|
||
opacity: 0.4;
|
||
}
|
||
|
||
.ty-preferences .window-content {
|
||
background-color: #fafafa;
|
||
}
|
||
|
||
.ty-preferences .nav-group-item.active {
|
||
color: white;
|
||
background: #999;
|
||
}
|
||
|
||
.menu-item-container a.menu-style-btn {
|
||
background-color: #f5f8fa;
|
||
background-image: linear-gradient( 180deg , hsla(0, 0%, 100%, 0.8), hsla(0, 0%, 100%, 0));
|
||
}
|
||
|
||
|
||
|
||
mjx-container[jax="SVG"] {
|
||
direction: ltr;
|
||
}
|
||
|
||
mjx-container[jax="SVG"] > svg {
|
||
overflow: visible;
|
||
min-height: 1px;
|
||
min-width: 1px;
|
||
}
|
||
|
||
mjx-container[jax="SVG"] > svg a {
|
||
fill: blue;
|
||
stroke: blue;
|
||
}
|
||
|
||
mjx-assistive-mml {
|
||
position: absolute !important;
|
||
top: 0px;
|
||
left: 0px;
|
||
clip: rect(1px, 1px, 1px, 1px);
|
||
padding: 1px 0px 0px 0px !important;
|
||
border: 0px !important;
|
||
display: block !important;
|
||
width: auto !important;
|
||
overflow: hidden !important;
|
||
-webkit-touch-callout: none;
|
||
-webkit-user-select: none;
|
||
-khtml-user-select: none;
|
||
-moz-user-select: none;
|
||
-ms-user-select: none;
|
||
user-select: none;
|
||
}
|
||
|
||
mjx-assistive-mml[display="block"] {
|
||
width: 100% !important;
|
||
}
|
||
|
||
mjx-container[jax="SVG"][display="true"] {
|
||
display: block;
|
||
text-align: center;
|
||
margin: 1em 0;
|
||
}
|
||
|
||
mjx-container[jax="SVG"][display="true"][width="full"] {
|
||
display: flex;
|
||
}
|
||
|
||
mjx-container[jax="SVG"][justify="left"] {
|
||
text-align: left;
|
||
}
|
||
|
||
mjx-container[jax="SVG"][justify="right"] {
|
||
text-align: right;
|
||
}
|
||
|
||
g[data-mml-node="merror"] > g {
|
||
fill: red;
|
||
stroke: red;
|
||
}
|
||
|
||
g[data-mml-node="merror"] > rect[data-background] {
|
||
fill: yellow;
|
||
stroke: none;
|
||
}
|
||
|
||
g[data-mml-node="mtable"] > line[data-line], svg[data-table] > g > line[data-line] {
|
||
stroke-width: 70px;
|
||
fill: none;
|
||
}
|
||
|
||
g[data-mml-node="mtable"] > rect[data-frame], svg[data-table] > g > rect[data-frame] {
|
||
stroke-width: 70px;
|
||
fill: none;
|
||
}
|
||
|
||
g[data-mml-node="mtable"] > .mjx-dashed, svg[data-table] > g > .mjx-dashed {
|
||
stroke-dasharray: 140;
|
||
}
|
||
|
||
g[data-mml-node="mtable"] > .mjx-dotted, svg[data-table] > g > .mjx-dotted {
|
||
stroke-linecap: round;
|
||
stroke-dasharray: 0,140;
|
||
}
|
||
|
||
g[data-mml-node="mtable"] > g > svg {
|
||
overflow: visible;
|
||
}
|
||
|
||
[jax="SVG"] mjx-tool {
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0;
|
||
height: 0;
|
||
}
|
||
|
||
[jax="SVG"] mjx-tool > mjx-tip {
|
||
position: absolute;
|
||
top: 0;
|
||
left: 0;
|
||
}
|
||
|
||
mjx-tool > mjx-tip {
|
||
display: inline-block;
|
||
padding: .2em;
|
||
border: 1px solid #888;
|
||
font-size: 70%;
|
||
background-color: #F8F8F8;
|
||
color: black;
|
||
box-shadow: 2px 2px 5px #AAAAAA;
|
||
}
|
||
|
||
g[data-mml-node="maction"][data-toggle] {
|
||
cursor: pointer;
|
||
}
|
||
|
||
mjx-status {
|
||
display: block;
|
||
position: fixed;
|
||
left: 1em;
|
||
bottom: 1em;
|
||
min-width: 25%;
|
||
padding: .2em .4em;
|
||
border: 1px solid #888;
|
||
font-size: 90%;
|
||
background-color: #F8F8F8;
|
||
color: black;
|
||
}
|
||
|
||
foreignObject[data-mjx-xml] {
|
||
font-family: initial;
|
||
line-height: normal;
|
||
overflow: visible;
|
||
}
|
||
|
||
mjx-container[jax="SVG"] path[data-c], mjx-container[jax="SVG"] use[data-c] {
|
||
stroke-width: 3;
|
||
}
|
||
|
||
g[data-mml-node="xypic"] path {
|
||
stroke-width: inherit;
|
||
}
|
||
|
||
.MathJax g[data-mml-node="xypic"] path {
|
||
stroke-width: inherit;
|
||
}
|
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<div id='write' class=''><h1 id='interpolacja-kwaternionów-1'><span>Interpolacja kwaternionów</span></h1><p><span>Celem tego zadania jest przećwiczenie interpolacji obrotów przy użyciu kwaternionów. </span></p><h2 id='opis-projektu'><span>Opis projektu </span></h2><p><span>Plik </span><code>main7</code><span> rysuje futurystyczne miasto i latające samochody, które startują z jednego wieżowca, okrążają miasto i lądują na drugim. Jeżeli rysowanie miasta jest zbyt wymagające dla komputera, to w funkcji </span><code>initModels</code><span> można podmienić model na mniej złożony, zmniejszenie wartości dla multisamplingu też powinno poprawić wydajność (linijka </span><code>glutSetOption(GLUT_MULTISAMPLE, 4);</code><span>). Do ładowania obiektów jest wykorzystywana biblioteka Assimp z prostą obsługą materiałów. </span></p><p><span>Statki poruszają się po krzywej wyznaczonej przez punkty kontrolne zapisane w </span><code>keyPoints</code><span> i interpolowane liniowo. Nie mają one zdefiniowanych obrotów, zadaniem jest wyliczenie im obrotów. </span></p><p><span>Dla łatwiejszego debugowania kamera została rozwinięta o następujące opcje:</span></p><ul><li><span>obroty przy pomocy kwaternionów </span></li><li><span>przyciski </span><strong><span>q</span></strong><span> i </span><strong><span>e</span></strong><span> przenoszą kamerę w okolicę następnego/poprzedniego punktu kontrolnego</span></li><li><span>przycisk </span><strong><span>0</span></strong><span> przenosi do pierwszego punktu kontrolnego</span></li><li><span>przycisk </span><strong><span>1</span></strong><span> przyczepia kamerę do statku. </span></li></ul><h1 id='materiały-i-graf-sceny'><span>Materiały i graf sceny</span></h1><h2 id='import'><span>Import</span></h2><p><span>modele które importujemy w trakcie tych zajęć mają rozszerzenie </span><strong><span>fbx</span></strong><span> są to dużo bardziej skomplikowane pliki, mogą one zawierać więcej niż jeden </span><em><span>mesh</span></em><span> lokalne macierze transformacji i informację o materiałach. </span></p><h2 id='materiały'><span>Materiały</span></h2><p><span>Do tej pory ręcznie wybieraliśmy program, którym rysowaliśmy. wiązało się to z tym, że trzeba było pamiętać jakie parametry należy przesłać do danego obiektu. Rozwiązaniem jest przechowywanie w materiałach. W projekcie w klasie </span><code>RenderContext</code><span> jest wskaźnik na zmienną typu </span><code>Material</code><span>, której zadaniem jest przechowywanie tej informacji.</span></p><h2 id='graf-sceny'><span>Graf sceny</span></h2><p><span>Sceny w bardziej złożonych projektach potrafią być skomplikowane. Obiekty w scenie są umieszczane hierarchicznie. przykładowo bohater posiada ręce, które poruszają się razem z nim (z reguły) jednak mogą same z siebie się poruszać, gdy postać atakuje. w ręku tej postaci może znajdować się miecz lub inna broń i ta broń będzie poruszać zawsze gdy bohater się się będzie przemieszczać, ale też gdy się zamachnie. W poprzednich projektach przykładem takich zależności była planeta i krążący wokół niej księżyc. Takich zależności może być więcej i pamiętanie wszystkich poprzednich interakcji staje się kłopotliwe. Rozwiązaniem, które pozwala wprowadzić taką hierarchię jest graf sceny. Graf sceny jest drzewem, w którym każdy węzeł jest jakimś obiektem w grze oraz zawiera informację o lokalnej transformacji względem obiektu nadrzędnego-ojca. To rozwiązanie pozwala myśleć tylko o lokalnych transformacjach, a globalne pobrać z nadrzędnych węzłów. </span></p><h3 ><span> </span></h3><p><span>W naszym projekcie graf sceny jest zrealizowany w formie tablicy. To znaczy w projekcie znajdują się 2 tablice </span><code>city</code><span> i </span><code>car</code><span>. Odpowiadają one za grafy dla miasta i pojazdu, jak nazwa wskazuje. Tablice zawierają struktury </span><code>Core::Node</code><span>:</span></p><pre class="md-fences md-end-block ty-contain-cm modeLoaded" spellcheck="false" lang="c++"><div class="CodeMirror cm-s-inner cm-s-null-scroll CodeMirror-wrap" lang="c++"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 9.5px; left: 8px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-keyword">struct</span> <span class="cm-def">Node</span> {</span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-variable">std::vector</span><span class="cm-operator"><</span><span class="cm-variable">RenderContext</span><span class="cm-operator">></span> <span class="cm-variable">renderContexts</span>;</span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-variable">glm::mat4</span> <span class="cm-variable">matrix</span>;</span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-variable-3">int</span> <span class="cm-variable">parent</span>;</span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span>};</span></pre></div></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 115px;"></div><div class="CodeMirror-gutters" style="display: none; height: 115px;"></div></div></div></pre><p><span>Zawiera ona RenderContexty, które składają się na ten obiekt, macierz transformacji oraz indeks obiektu nadrzędnego, czyli np dla </span><code>car[3]</code><span> jego ojcem będzie </span><code>car[car[3].parent]</code><span>, jeżeli atrybut </span><code>parent</code><span> jest równy -1 to znaczy, że dotarliśmy do korzenia, czyli obiektu który już nie ma nadrzędnego. </span></p><h3 id='zadanie-1'><span>Zadanie </span></h3><p><span>Prześledź jak ładowane są obiekty w funkcji </span><code>initModels()</code><span>. </span></p><p><span>W tej chwili nic się nie wyświetla. Jak wciśniesz </span><strong><span>r</span></strong><span> to kamera zostanie przeniesiona do centrum, gdzie znajdują się wszystkie obiekty. Wynika to z tego, że funkcja</span><code>renderRecursive</code><span> jest niekompletna. Dopisz obliczanie macierzy transformacji. Najpierw przypisz do niej macierz transformacji z obecnego węzła </span><code>node</code><span>, następnie w pętli domnóż od lewej macierz transformacji nadrzędnego węzła, nadrzędnego nadrzędnego węzła i tak aż do korzenia. Po wykonaniu powinna pojawić scena, która zwiera miasto i latające statki. W następnych zadaniach skupimy się na poprawieniu ich zachowania.</span></p><h1 id='interpolacja-1'><span>Interpolacja</span></h1><p><span>Większość pracy będzie się dziać w funkcji </span><code>animationMatrix</code><span>, ma ona zmienną </span><code>speed</code><span>, która może być pomocna przy debugowaniu.</span></p><h2 id='interpolacja-krzywej'><span>Interpolacja krzywej</span></h2><p><span>W tej punkty kontrolne są interpolowane liniowo w funkcji </span><code>animationMatrix</code><span>. Funkcja ta oblicza na podstawie otrzymanego czasu oblicza macierz transformacji obiektu (statku) poruszającego się po krzywej. Oblicza ona pomiędzy jakimi puntami powinien znajdować się obiekt (zmienna </span><code>i</code><span>) oraz parametr </span><code>t</code><span> który określa jaki punkt pomiędzy punktami kontrolnymi </span><code>i</code><span> oraz </span><code>i+1</code><span>wybrać. Zastąp interpolację liniową na Catmull-Roma w linii: </span></p><pre lang="C++" spellcheck="false" class="md-fences md-end-block ty-contain-cm modeLoaded"><div class="CodeMirror cm-s-inner cm-s-null-scroll CodeMirror-wrap" lang="c++"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 9.5px; left: 8px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-variable">glm::vec3</span> <span class="cm-variable">pos</span> <span class="cm-operator">=</span> (<span class="cm-variable">keyPoints</span>[<span class="cm-variable">std::max</span>(<span class="cm-number">0</span>, <span class="cm-variable">index</span>)] <span class="cm-operator">*</span> <span class="cm-variable">t</span> <span class="cm-operator">+</span> <span class="cm-variable">keyPoints</span>[<span class="cm-variable">std::min</span>(<span class="cm-variable">size</span>, <span class="cm-variable">index</span> <span class="cm-operator">+</span> <span class="cm-number">1</span>)] <span class="cm-operator">*</span> (<span class="cm-number">1</span> <span class="cm-operator">-</span> <span class="cm-variable">t</span>));</span></pre></div></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 23px;"></div><div class="CodeMirror-gutters" style="display: none; height: 23px;"></div></div></div></pre><p> </p><p><span> Użyj funkcji glm::catmullRom(). Przyjmuje ona cztery argumenty typu glm::vec3 (v1, v2, v3, v4) i jeden argument typu float (s). Zwraca ona glm::vec3, w którym znajduje się zinterpolowana pozycja między punktami v2 i v3 (parametr s wybiera punkt na ścieżce; dla s=0 zwracane jest v2, dla s=1 zwracane jest v3, dla 0<s<1 zwracana jest zinterpolowana pozycja na ścieżce). Punkty v1 i v4 są dodatkowymi punktami kontrolującymi krzywiznę ścieżki. Dla krzywych Catmulla-Roma, należy jako v1,v2,v3,v4 podać po prostu cztery kolejne punkty ze zbioru punktów kontrolnych</span></p><h2 id='interpolacja-kwaternionów-2'><span>Interpolacja kwaternionów</span></h2><p><span>Celem tego zadania jest przećwiczenie interpolacji obrotów przy użyciu kwaternionów. </span></p><p> </p><h2 id='obliczenie-kierunków'><span>Obliczenie kierunków </span></h2><p><span>W pierwszej kolejności potrzebujemy obliczyć kwaterniony odpowiadające obrotom statków między kolejnymi punktami kontrolnymi. Chcemy, żeby statek był skierowany w kierunku lotu. Najpierw musimy uzyskać znormalizowany wektor kierunkowy dla każdej pary 2 kolejnych punktów kontrolnych jak na rysunku poniżej. </span></p><p><img src="vectors.jpg" referrerpolicy="no-referrer" alt="wektory">
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<span>Nastęnie należy obliczyć kwaterniony odpowiadające za obrót z początkowej orientacji statku (opisywanej przez wektor (0,0,1)) do orientaci wyznaczonej przez wektory kietunkowe.</span>
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<span>Żeby obliczyć obrót między jednym wektorem a drugim, należy obliczyć oś obrotu, oblicza się go za pomocą iloczynu wektorowego, oraz kąt obrotu, oblicza się za pomocą iloczynu skalarnego. </span>
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<span>Może być kuszące policzenie wektora obrotu pomiędzy początkowym wektorem kierunkowym a kolejnymi wektorami, ale takie rozwiązanie może prowadzić do niepożądanych zachowań. Dlatego należy obliczać obroty pomiędzy kolejnymi wektorami i je akumulować.</span></p><h3 id='zadanie-2'><span>Zadanie</span></h3><p><span>Uzupełnij funkcję </span><code>initKeyRoation</code><span> o wypełnienie </span><code>std::vector<glm::quat> keyRotation</code><span> kwaternionami. </span></p><ol start='' ><li><p><span>Zainicjalizuj zmienną </span><code>glm::vec3 oldDirection</code><span> wektorem o współrzędnych (0,0,1), czyli początkowej orientacji pojazdu</span></p></li><li><p><span>Zainicjalizuj zmienną </span><code>glm::quat oldRotationCamera</code><span> kwaternionem identycznościom (1,0,0,0).</span></p></li><li><p><span>W pętli for po i od 0 do liczba keyPoints odjąć 1.</span></p><ol start='' ><li><span>Oblicz nowy kierunek: odejmij od punktu końcowego: </span><code>keyPoints[i+1]</code><span> punkt początkowy: </span><code>keyPoints[i]</code><span>.</span></li><li><span>Oblicz nową rotację, skorzystaj z funkcji </span><code>glm::rotationCamera</code><span> przemnóż jej wynik przez </span><code>oldRotationCamera</code><span> od prawej i całość znormalizuj.</span></li><li><span>Dodaj nowy obrót do </span><code>keyRotation</code><span>.</span></li><li><span>Podmień </span><code>oldDritection</code><span> na nowy kierunek i </span><code>oldRotationCamera</code><span> na nowy obrót.</span></li></ol></li><li><p><span>Po wszystkim kwaternionów jest o jeden mniej niż punktów dodaj jeszcze jeden o wartościach (1,0,0,0) na koniec.</span></p></li></ol><h2 id='interpolacja-2'><span>Interpolacja </span></h2><p><span>Do interpolacji użyjemy funkcji </span><code>slerp</code><span> opisanej wzorem</span></p><p><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="41.164ex" height="3.607ex" role="img" focusable="false" viewBox="0 -1047.1 18194.6 1594.2" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.238ex;"><defs><path id="MJX-19-TEX-I-1D460" d="M131 289Q131 321 147 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transform="translate(1217.6,0)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mover"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-20-TEX-I-1D45E"></use></g><g data-mml-node="mo" transform="translate(316.8,16) translate(-250 0)"><use data-c="5E" xlink:href="#MJX-20-TEX-N-5E"></use></g></g></g><g data-mml-node="TeXAtom" transform="translate(479,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D456" xlink:href="#MJX-20-TEX-I-1D456"></use></g><g data-mml-node="mo" transform="translate(345,0)"><use data-c="2B" xlink:href="#MJX-20-TEX-N-2B"></use></g><g data-mml-node="mn" transform="translate(1123,0)"><use data-c="31" xlink:href="#MJX-20-TEX-N-31"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mover><msub><mi>q</mi><mi>i</mi></msub><mo stretchy="false">^</mo></mover></mrow><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo stretchy="false">^</mo></mover></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>+</mo><mn>1</mn></mrow></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">\hat{q_i},\hat{q}_{i+1}</script><span> są interpolowanymi kwaternionami, </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="0.817ex" height="1.441ex" role="img" focusable="false" viewBox="0 -626 361 637" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-27-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D461" xlink:href="#MJX-27-TEX-I-1D461"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">t</script><span> jest parametrem od 0 do 1, natomiast </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.348ex" height="2.034ex" role="img" focusable="false" viewBox="0 -694 596 899" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.464ex;"><defs><path id="MJX-22-TEX-I-1D719" d="M409 688Q413 694 421 694H429H442Q448 688 448 686Q448 679 418 563Q411 535 404 504T392 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\phi</script><span> można otrzymać z wzoru </span>
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data-c="1D464" xlink:href="#MJX-23-TEX-I-1D464"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>s</mi><mi>ϕ</mi><mo>=</mo><msub><mi>q</mi><mi>x</mi></msub><msub><mi>r</mi><mi>x</mi></msub><mo>+</mo><msub><mi>q</mi><mi>y</mi></msub><msub><mi>r</mi><mi>y</mi></msub><mo>+</mo><msub><mi>q</mi><mi>z</mi></msub><msub><mi>r</mi><mi>z</mi></msub><mo>+</mo><msub><mi>q</mi><mi>w</mi></msub><msub><mi>r</mi><mi>w</mi></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">cos\phi = q_xr_x+q_yr_y+q_zr_z+q_wr_w</script><span>. dla </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.109ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3584.2 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-24-TEX-I-1D461" d="M26 385Q19 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fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D461" xlink:href="#MJX-24-TEX-I-1D461"></use></g><g data-mml-node="mo" transform="translate(638.8,0)"><use data-c="2208" xlink:href="#MJX-24-TEX-N-2208"></use></g><g data-mml-node="mrow" transform="translate(1583.6,0)"><g data-mml-node="mo"><use data-c="5B" xlink:href="#MJX-24-TEX-N-5B"></use></g><g data-mml-node="mn" transform="translate(278,0)"><use data-c="30" xlink:href="#MJX-24-TEX-N-30"></use></g><g data-mml-node="mo" transform="translate(778,0)"><use data-c="2C" xlink:href="#MJX-24-TEX-N-2C"></use></g><g data-mml-node="mn" transform="translate(1222.7,0)"><use data-c="31" xlink:href="#MJX-24-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(1722.7,0)"><use data-c="5D" xlink:href="#MJX-24-TEX-N-5D"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>∈</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">]</mo></mrow></math></mjx-assistive-mml></mjx-container><script type="math/tex">t\in\left[0,1\right]</script><span> </span><code>slerp</code><span> oblicza najkrótszą ścieżkę pomiędzy kwaternionami p i q w przestrzeni kwaternionów jednostkowych. Nie będziemy jej obliczać samodzielnie, skorzystamy z implementacji </span><code>glm::slerp</code><span>.</span></p><p><span>W funkcji </span><code>animationMatrix</code><span> dodaj interpolację kwaternionów </span></p><pre class="md-fences md-end-block ty-contain-cm modeLoaded" spellcheck="false" lang="C++" style="break-inside: unset;"><div class="CodeMirror cm-s-inner cm-s-null-scroll CodeMirror-wrap" lang="c++"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 9.5px; left: 8px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
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</span></span></pre></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable">glm::mat4</span> <span class="cm-def">animationMatrix</span>(<span class="cm-variable-3">float</span> <span class="cm-variable">time</span>) {</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ...</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-comment">//index of first keyPoint</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-variable-3">int</span> <span class="cm-variable">index</span> <span class="cm-operator">=</span> <span class="cm-number">0</span>;</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
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</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-keyword">while</span> (<span class="cm-variable">distances</span>[<span class="cm-variable">index</span>] <span class="cm-operator"><=</span> <span class="cm-variable">time</span>) {</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-variable">time</span> <span class="cm-operator">=</span> <span class="cm-variable">time</span> <span class="cm-operator">-</span> <span class="cm-variable">distances</span>[<span class="cm-variable">index</span>];</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-variable">index</span> <span class="cm-operator">+=</span> <span class="cm-number">1</span>;</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span>}</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
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</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-comment">//t coefitient between 0 and 1 for interpolation</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-variable-3">float</span> <span class="cm-variable">t</span> <span class="cm-operator">=</span> <span class="cm-variable">time</span> <span class="cm-operator">/</span> <span class="cm-variable">distances</span>[<span class="cm-variable">index</span>];</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> ...</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-comment">//implement corect animation</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-keyword">auto</span> <span class="cm-variable">animationRotation</span> <span class="cm-operator">=</span> <span class="cm-variable">glm::quat</span>(<span class="cm-number">1</span>,<span class="cm-number">0</span>,<span class="cm-number">0</span>,<span class="cm-number">0</span>);</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
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</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-variable">glm::mat4</span> <span class="cm-variable">result</span> <span class="cm-operator">=</span> <span class="cm-variable">glm::translate</span>(<span class="cm-variable">pos</span>) <span class="cm-operator">*</span> <span class="cm-variable">glm::mat4_cast</span>(<span class="cm-variable">animationRotation</span>);</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
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</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
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</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-keyword">return</span> <span class="cm-variable">result</span>;</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
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</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">}</span></pre></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 529px;"></div><div class="CodeMirror-gutters" style="display: none; height: 529px;"></div></div></div></pre><p><span>Pobierz z </span><code>keyRotation</code><span> kwaterniony o indeksach </span><code>index</code><span> i </span><code>index+1</code><span> wywołaj </span><code>glm::slerp</code><span> z nimi jako argumentami. Trzecim parametrem powinna być wartość </span><code>t</code><span>.</span></p><blockquote><p><span>Uwaga! pobierając wartości z wektora </span><code>keyRotation</code><span> pamiętaj, żeby nie wyjść poza jego zakres, najlepiej weż maksimum z indeksu i zera oraz minimum z indeksu i rozmiaru wektora.</span></p></blockquote><p><span>Otrzymana animacja będzie ciągła, ale w punktach kontrolnych będzie widoczne szarpnięcie wywołane przez to, że funkcja slerp nie jest gładka, gdy przechodzimy do kolejnej pary kwaternionów. By zniwelować ten efekt użyjemy funkcji </span><code>glm::squat</code><span>.</span></p><p><span>Funkcja squat podobnie jak Catmull-Rom przyjmuje 4 wartości jednak zamiast przyjmować 4 kolejne wektory, przyjmuje 2 kwaterniony interpolowane i 2 kwaterniony pośrednie. opisana jes</span>
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xmlns="http://www.w3.org/2000/svg" width="0.817ex" height="1.441ex" role="img" focusable="false" viewBox="0 -626 361 637" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-27-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D461" xlink:href="#MJX-27-TEX-I-1D461"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">t</script><span> to parametr od 0 do 1. Natomiast </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="6.924ex" height="2.301ex" role="img" focusable="false" viewBox="0 -809 3060.3 1017" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.471ex;"><defs><path id="MJX-28-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-28-TEX-N-5E" d="M112 560L249 694L257 686Q387 562 387 560L361 531Q359 532 303 581L250 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data-mjx-texclass="ORD"><mover><mi>q</mi><mo stretchy="false">^</mo></mover></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>+</mo><mn>2</mn></mrow></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">\hat{q}_{i+2}</script><span> z </span><code>keyRotation</code><span> (</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="0.781ex" height="1.52ex" role="img" focusable="false" viewBox="0 -661 345 672" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-34-TEX-I-1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D456" xlink:href="#MJX-34-TEX-I-1D456"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">i</script><span> odpowiada zmiennej </span><code>index</code><span> jak poprzednio), oblicz </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.937ex" height="2.187ex" role="img" focusable="false" viewBox="0 -809 856 966.8" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-35-TEX-I-1D44E" d="M33 157Q33 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data-c="2B" xlink:href="#MJX-36-TEX-N-2B"></use></g><g data-mml-node="mn" transform="translate(1123,0)"><use data-c="31" xlink:href="#MJX-36-TEX-N-31"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow data-mjx-texclass="ORD"><mover><mi>a</mi><mo stretchy="false">^</mo></mover></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>+</mo><mn>1</mn></mrow></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">\hat{a}_{i+1}</script><span>, funkcje, które będą potrzebne to </span><code>glm::inverse</code><span>, </span><code>glm::exp</code><span>, </span><code>glm::log</code><span>. Na koniec podmień </span><code>slerp</code><span> na </span><code>squat</code><span>.</span></p><p><span>Teraz przejścia między obrotami powinny być gładkie. Jedna rzecz, która pozostaje, to poprawić moment lądowania. Ustaw ręcznie kilka ostatnich kwaternionów tak, żeby statek lądował poziomo.</span></p></div></div>
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