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<!DOCTYPE html>
<html>
<head>
<title><%= htmlWebpackPlugin.options.title %></title>
<meta name="viewport" content="width=device-width, initial-scale=1" />
</head>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Roboto:300,700&display=swap">
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans|Noto+Serif:400,400i,700,700i&display=swap" type="text/css" />
<link rel="stylesheet" href="curvenote.css" type="text/css">
<link rel="stylesheet" href="theme.css" type="text/css">
<body>
<nav class="popout centered">
<div>Documentation</div>
<ul>
<li><a href="/">curvenote.dev</a></li>
<li><a href="/introduction">Introduction</a></li>
<li><a href="/article">Article</a></li>
<li class="section">
<div>Components</div>
<ul>
<li><a href="/components">Introduction</a></li>
<li><a href="/components/variable">Variable</a></li>
<li><a href="/components/display">Display</a></li>
</ul>
</li>
<li><a href="/svg">Diagrams</a></li>
<li><a href="/runtime">Runtime</a></li>
</ul>
</nav>
<article id="myArticle" class="centered">
<h1 id="welcome">Welcome to @curvenote/article</h1>
<r-outline class="popout" for="myArticle"></r-outline>
<p>This is a paragraph, kinda simple. <code>code</code></p>
<aside class="callout">Hello world</aside>
<r-scope name="display">
<h2>Display Variables</h2>
<r-var name="x" value="1"></r-var>
<r-var name="y" value="5"></r-var>
<r-var name="xSquared" :value="x * x" description="The square of x."></r-var>
<p>To display an element create an <code>r-display</code>, which will just render the named variable as text.</p>
<r-code language="html" compact><r-display name="x"></r-display></r-code>
<p>
This is a number that is dynamic: <r-display bind="x"></r-display>.<br>
Try setting the value of $x$ with the range input: <r-range bind="x" max="5"></r-range>
</p>
<p>
You can also <code>transform</code> the value of a variable before you format it.
For example, you might want to say that the admission to a park is <code>'free'</code> when the <r-action
:click="{x:0}">value == 0</r-action>.
</p>
<aside><p>The <code>:transform</code> uses a <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Conditional_Operator">Conditional Operator</a> from javascript.</p></aside>
<r-demo>
<p>
The park admission is
<r-display :value="x" :transform="(value > 0)? value : 'free'" format="$.2f"></r-display>.
</p>
</r-demo>
<p>
You can also use this <code>transform</code> to say that the park admission is
<r-dynamic bind="x"
:transform="['free','real cheap','cheap','costly','expensive','real expensive'][Math.min(Math.max(value,0),5)]"
max="5"></r-dynamic>.<br>
This is also quite useful if you want to use the transform to index into an array <r-dynamic bind="x"
:transform="['😍','😄','😊','😐','😒','😔'][Math.min(Math.max(value,0),5)]"
max="5"></r-dynamic>, in this case emoji array - but it could be numeric too!
</p>
<aside class="callout">
<p>
Properties of <code>r-display</code>:
<dl>
<dt><code>name</code></dt>
<dd>The variable to name to in the state.</dd>
<dt><code>format</code></dt>
<dd>A d3-format string. See the <a href="https://github.com/d3/d3-format" target="_blank">documentation</a>.</dd>
<dt><code>transform</code></dt>
<dd>Allows you to change or transform the value before formating: <code>format(transform(value))</code>. If the
value is a string after transformation, it will not be formatted.</dd>
</dl>
</p>
</aside>
</r-scope>
<div class="card-container">
<r-card class="flex-item" title="Variables" description="Reactive and variables and displays" img-src="/images/r-var.png" url="var"></r-card>
<r-card class="flex-item" title="Equations" description="Equations using KaTeX" img-src="/images/r-equation.gif" url="equation"></r-card>
<r-card class="flex-item" title="Charts" description="Reactive charts using d3" img-src="/images/r-chart.gif" url="chart"></r-card>
<r-card class="flex-item" title="Charts" description="Reactive charts using d3" img-src="/images/r-chart.gif" url="chart"></r-card>
<r-card class="flex-item" title="Charts" description="Reactive charts using d3" img-src="/images/r-chart.gif" url="chart"></r-card>
<r-card class="flex-item" title="Charts" description="Reactive charts using d3" img-src="/images/r-chart.gif" url="chart"></r-card>
</div>
<h2>There is code</h2>
<aside>The default aside happens, on the side!</aside>
<r-code language="python">
>>> import numpy as np
>>> a = np.arange(15).reshape(3, 5)
>>> a
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
</r-code>
<blockquote>
<p>I would have written a shorter letter, but I did not have the time.</p>
<footer>
<cite>Blaise Pascal</cite>
<time datetime="1656-12-04">December 4, 1656</time>
</footer>
</blockquote>
<h2>And Equations</h2>
<r-demo>
<script>
function prod(x, y) {
const prod = x * y;
return prod;
}
</script>
<r-var name="x" value="5"></r-var>
<r-var name="y" value="2"></r-var>
<r-var name="prod" :value="prod(x, y)"></r-var>
<p>
The product of
<r-dynamic bind="x"></r-dynamic>
and
<r-dynamic bind="y"></r-dynamic>
is
<r-display bind="prod"></r-display>
</p>
</r-demo>
<r-code language="javascript" copy>
</r-code>
<r-demo>
<r-var name="cookies" value="3" format=".4"></r-var>
<p>
When you eat
<r-dynamic bind="cookies" min="2" max="100"> cookies</r-dynamic>,
you consume
<r-display :value="cookies * 50" format=".0f" /></r-display>
calories.
</p>
</r-demo>
<r-demo>
<r-var name="index" value="1"></r-var>
<r-var name="MrTaylor"
:value="['f(x) \\approx f(a)', '\\frac {f^{\\prime}(a)}{1!} (x-a)', '\\frac{f^{\\prime\\prime}(a)}{2!} (x-a)^2', '\\frac{f^{(3)}(a)}{3!}(x-a)^3']">
</r-var>
Drag me to expand the Taylor Series:
<r-range bind="index" min="1" max="4"></r-range>
<r-equation :math="MrTaylor.slice(0, index).join(' + ') + ' + \\cdots'"></r-equation>
</r-demo>
<r-demo>
<r-equation>
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
</r-equation>
</r-demo>
<h2>And Demos</h2>
<r-svg-chart style="float: right" width="250" height="250" x-axis-location="origin" y-axis-location="origin" xlim="[-10,10]" ylim="[-10,10]">
<r-svg-eqn eqn="m*x + b" :listen="[m, b]"></r-svg-eqn>
<r-svg-node x="0" :y="b" :drag="{b: y}"></r-svg-node>
<r-svg-node x="5" :y="m*5 + b" :drag="{m: (y - b) / 5}"></r-svg-node>
</r-svg-chart>
<r-demo style="width: calc(100% - 250px)">
<r-var name="m" value="1"></r-var>
<r-var name="b" value="1"></r-var>
<p>$m$ = <r-range bind="m" step="0.1" min="-10" max="10"></r-range><r-display bind="m"></r-display></p>
<p>$b$ = <r-range bind="b" step="0.1" min="-10" max="10"></r-range><r-display bind="b"></r-display></p>
<r-equation aligned>
y &= m \times x + b \\
y &=
<r-display :value="m==-1 || m == 0 || m == 1? '' : m" format=".0f"></r-display>
<r-visible :visible="m == -1">-</r-visible>
<r-visible :visible="m !== 0">x</r-visible>
<r-display :value="b==0? '' : b" :format="m==0 ? '.0f' : '+.0f'">+1</r-display>
<r-visible :visible="m == 0 && b ==0">0</r-visible>
</r-equation>
</r-demo>
<r-scope name="radial">
<r-var name="a" value="1"></r-var>
<r-var name="b" value="1"></r-var>
<r-var name="cartesian" value="true" type="Boolean"></r-var>
<r-var name="showX" value="true" type="Boolean"></r-var>
<r-var name="radius" value="true" type="Boolean"></r-var>
<r-var name="r" :value="Math.sqrt(a*a + b*b)"></r-var>
<r-var name="theta" :value="Math.atan2(b, a) * 180 / Math.PI"></r-var>
<h3>Coordinate Transformation</h3>
<p>
A good example of this is <r-action :click="{cartesian: !cartesian}">changing</r-action> from a <r-action :click="{cartesian: false}">radial</r-action> coordinate system to <r-action :click="{cartesian: true}">Cartesian</r-action>.
</p>
<r-svg-chart style="float:right" xlim="[-5, 5]" ylim="[-5, 5]" height="300" width="300" x-axis-location="origin"
y-axis-location="origin">
<r-svg-path :visible="cartesian" :data="[[a,0], [a, b]]" :hover="{showX: true}" :stroke="showX ? 'red' : '#333'" strokeWidth="1.5"></r-svg-path>
<r-svg-path :visible="cartesian" :data="[[a, b], [0,b]]" :hover="{showX: false}" :stroke="!showX ? 'red' : '#333'" strokeWidth="1.5"></r-svg-path>
<r-svg-path :visible="!cartesian" :data="[[0,0], [a, b]]" :hover="{radius: true}" :stroke="radius ? 'red' : '#333'" strokeWidth="1.5"></r-svg-path>
<r-svg-eqn :visible="!cartesian && theta != 0" eqn="[Math.cos(t)*r, Math.sin(t)*r]" :domain="[0, theta * Math.PI / 180]" parameterize="t" :hover="{radius: false}" :stroke="!radius ? 'red' : '#333'" stroke="#333" strokeWidth="1.5"></r-svg-eqn>
<r-svg-node :x="a" :y="b" :drag="{a: x, b: y, cartesian: x > 0}"></r-svg-node>
</r-svg-chart>
<strong>Cartesian Coordinate System</strong>
<dl>
<dt>$x$</dt>
<dd>
<r-dynamic :value="a" :change="{a: value, cartesian: true, showX: true}" min="-5" :max="5" step="0.05"></r-dynamic>
</dd>
<dt>$y$</dt>
<dd>
<r-dynamic :value="b" :change="{b: value, cartesian: true, showX: false}" min="-5" :max="5" step="0.05"></r-dynamic>
</dd>
</dl>
<strong>Radial Coordinate System</strong>
<dl>
<dt>$r$</dt>
<dd>
<r-dynamic :value="Math.sqrt(a*a + b*b)" :change="{
a: value * Math.cos(Math.atan2(b, a)),
b: value * Math.sin(Math.atan2(b, a)),
cartesian: false, radius: true,
}" min="0.1" :max="5" step="0.05"></r-dynamic>
</dd>
<dt>$\theta$</dt>
<dd>
<r-dynamic :value="Math.atan2(b, a) * 180 / Math.PI" :change="{
a: Math.sqrt(a*a + b*b) * Math.cos(value * Math.PI / 180),
b: Math.sqrt(a*a + b*b) * Math.sin(value * Math.PI / 180),
cartesian: false, radius: false,
}" min="-180" :max="180" step="1" periodic="true">°</r-dynamic>
</dd>
</dl>
<r-visible :visible="cartesian && showX">
<strong style="text-decoration: underline;">Cartesian Update- $x$</strong>
<r-equation>
x = <r-display bind="a"></r-display>
</r-equation>
<r-code language="html">
<r-dynamic :value="x" :change="{x: value}"></r-dynamic>
</r-code>
</r-visible>
<r-visible :visible="cartesian && !showX">
<strong style="text-decoration: underline;">Cartesian Update - $y$</strong>
<r-equation>
y = <r-display bind="b"></r-display>
</r-equation>
<r-code language="html">
<r-dynamic :value="y" :change="{y: value}"></r-dynamic>
</r-code>
</r-visible>
<r-visible :visible="!cartesian && radius">
<strong>Radius Update</strong>
<r-equation aligned>
r &= \sqrt{x^2 + y^2} = <r-display bind="r"></r-display> \\
x &= r \cos(\operatorname{atan2}(y, x)) = <r-display bind="a"></r-display> \\
y &= r \sin(\operatorname{atan2}(y, x)) = <r-display bind="b"></r-display>
</r-equation>
<r-code language="html">
<r-dynamic :value="Math.sqrt(x*x + y*y)" :change="{
x: value * Math.cos(Math.atan2(y, x)),
y: value * Math.sin(Math.atan2(y, x))
}"></r-dynamic>
</r-code>
</r-visible>
<r-visible :visible="!cartesian && !radius">
<strong>Theta Update</strong>
<r-equation aligned>
\theta &= \operatorname{atan2}(y, x) = <r-display bind="theta"></r-display> \\
x &= \sqrt{x^2 + y^2} \cos( \theta ) = <r-display bind="a"></r-display> \\
y &= \sqrt{x^2 + y^2} \sin( \theta ) = <r-display bind="b"></r-display>
</r-equation>
<r-code language="html">
<r-dynamic :value="Math.atan2(y, x)" :change="{
x: Math.sqrt(x*x + y*y) * Math.cos(value),
y: Math.sqrt(x*x + y*y) * Math.sin(value)
}"></r-dynamic>
</r-code>
</r-visible>
</r-scope>
<r-scope name="sincos">
<r-var name="r" value="0.35"></r-var>
<r-var name="theta" value="0" format=".1f"></r-var>
<r-var name="xC" :value="Math.cos(theta)*r-0.5"></r-var>
<r-var name="yC" :value="Math.sin(theta)*r+0.5"></r-var>
<r-var name="sOrigin" value="false" type="Boolean"></r-var>
<r-var name="sRadius" value="false" type="Boolean"></r-var>
<r-var name="sAngle" value="false" type="Boolean"></r-var>
<r-var name="wR" value="1"></r-var>
<r-var name="wG" value="3"></r-var>
<r-var name="wB" value="1"></r-var>
<r-var name="wSin" value="3"></r-var>
<r-var name="wCos" value="3"></r-var>
<h3>Sin and Cos</h3>
<p>
In trigonometry, a
<r-action :hover="{wG:enter?8:3}"><strong style="color:green">unit circle</strong></r-action>
is the circle of
<r-action :hover="{sRadius:enter}"><strong style="color:#333">radius</strong></r-action>
one centered at the <r-action :hover="{sOrigin:enter}"><strong style="color:#333">origin</strong></r-action>
$(0, 0)$ in the Cartesian coordinate system. Let a
<r-action :hover="{sRadius:enter}"><strong style="color:#333">line</strong></r-action>
through the
<r-action :hover="{sOrigin:enter}"><strong style="color:#333">origin</strong></r-action>,
making an
<r-action :hover="{sAngle:enter}"><strong style="color:#333">angle</strong></r-action>,
of $\theta$=
<r-dynamic bind="theta" min="0" step="0.01" :max="Math.PI*2" periodic="true" :transform="value*180/Math.PI" after="º"></r-dynamic>
with the positive half of the x-axis, intersect the
<r-action :hover="{wG:enter?8:3}"><strong style="color:green">unit circle</strong></r-action>.
The
<r-action :hover="{wB:enter?3:1}"><strong style="color:blue">x-coordinates</strong></r-action>
and
<r-action :hover="{wR:enter?3:1}"><strong style="color:red">y-coordinates</strong></r-action>
of this point of intersection are equal to
<r-action :hover="{wCos:enter?8:3}"><strong style="color:blue">$\cos(\theta)$</strong></r-action>
and
<r-action :hover="{wSin:enter?8:3}"><strong style="color:red">$\sin(\theta)$</strong></r-action>,
respectively.
<a href="https://en.wikipedia.org/wiki/Sine#Unit_circle_definition" target="_blank">See Wikipedia</a>.
</p>
<r-demo>
<r-svg-chart xlim="[-1, 2]" ylim="[-1, 1]" height="400" width="600" x-axis-location="hidden" y-axis-location="hidden">
<!-- Create Axis -->
<r-svg-path :data="[[-1,0],[2, 0],[],[0, -1], [0, 1]]" stroke="#ddd" stroke-width="2"></r-svg-path>
<r-svg-path :data="[[-1, 0.5-r],[2, 0.5-r],[],[-1, 0.5], [2, 0.5],[],[-1, 0.5+r],[2, 0.5+r]]" stroke="#ddd" stroke-width="0.5"></r-svg-path>
<r-svg-path :data="[[ 0,-0.5-r],[2,-0.5-r],[],[ 0,-0.5], [2,-0.5],[],[ 0,-0.5+r],[2,-0.5+r]]" stroke="#ddd" stroke-width="0.5"></r-svg-path>
<r-svg-path :data="[[-0.5-r,1],[-0.5-r,0],[],[-0.5,1], [-0.5,0],[],[-0.5+r,1],[-0.5+r,0]]" stroke="#ddd" stroke-width="0.5"></r-svg-path>
<!-- Three equations for the bottom-left curve -->
<r-svg-eqn eqn="[-Math.cos(t)*(-0.5-r), -Math.sin(t)*(-0.5-r)]" parameterize="t" :domain="[Math.PI, Math.PI*1.5]" stroke="#ddd" stroke-width="0.5"></r-svg-eqn>
<r-svg-eqn eqn="[-Math.cos(t)/-2, -Math.sin(t)/-2]" parameterize="t" :domain="[Math.PI, Math.PI*1.5]" stroke="#ddd" stroke-width="0.5"></r-svg-eqn>
<r-svg-eqn eqn="[-Math.cos(t)*(-0.5+r), -Math.sin(t)*(-0.5+r)]" parameterize="t" :domain="[Math.PI, Math.PI*1.5]" stroke="#ddd" stroke-width="0.5"></r-svg-eqn>
<!-- Guidelines from the current point (xC,yC) -->
<r-svg-path :data="[[xC, yC], [0, yC]]" stroke="red" :stroke-width="wR"></r-svg-path>
<r-svg-path :data="[[xC, yC], [xC, 0]]" stroke="blue" :stroke-width="wB"></r-svg-path>
<r-svg-eqn eqn="[-Math.cos(t)*xC, -Math.sin(t)*xC]" parameterize="t" :domain="[Math.PI, Math.PI*1.5]" stroke="blue" :stroke-width="wB"></r-svg-eqn>
<!-- Text labels -->
<r-svg-text text="sin(θ)" x="1.75" :y=" 0.43-r" fill="red"></r-svg-text>
<r-svg-text text="cos(θ)" x="1.75" :y="-0.57-r" fill="blue"></r-svg-text>
<!-- Origin, radius and angle: default is hidden -->
<r-svg-circle x="-0.5" y="0.5" :visible="sOrigin" fill="#333"></r-svg-circle>
<r-svg-path :data="[[-0.5, 0.5], [xC,yC]]" :visible="sRadius" stroke="#333" stroke-width="3"></r-svg-path>
<r-svg-eqn eqn="[Math.cos(t)*0.1 - 0.5, Math.sin(t)*0.1 + 0.5]" parameterize="t" :domain="[0, theta]" :visible="sAngle" stroke="#333" stroke-width="3"></r-svg-eqn>
<r-svg-path :data="[[xC,yC], [-0.5, 0.5], [-0.5 + r,0.5]]" :visible="sAngle" stroke="#333" stroke-width="2"></r-svg-path>
<!-- A circle! -->
<r-svg-eqn eqn="[Math.cos(t)*r-0.5, Math.sin(t)*r+0.5]" parameterize="t" :domain="[0, Math.PI*2]" stroke="green" :stroke-width="wG"></r-svg-eqn>
<!-- Offset sin and cos waves -->
<r-svg-eqn eqn="Math.sin(x* Math.PI+theta)*r + 0.5" domain="[0, 2]" stroke="red" :stroke-width="wSin"></r-svg-eqn>
<r-svg-eqn eqn="Math.cos(x* Math.PI+theta)*r - 0.5" domain="[0, 2]" stroke="blue" :stroke-width="wCos"></r-svg-eqn>
<!-- A drag node to change the offset -->
<r-svg-node :x="xC" :y="yC" fill="#333" :drag="{theta: (Math.PI * 2 + Math.atan2(y-0.5, x+0.5)) % (Math.PI * 2)}"></r-svg-node>
</r-svg-chart>
</r-demo>
</r-scope>
</article>
</body>
</html>