2018年1月16日火曜日

数学 - Python - JavaScript - 円の方程式 - 直交座標と極座標(三角関数(正弦、余弦))( @hyuki , @kdlvklv )結城浩さん、本気を出すまいくさんのツイート、リツイートより

• $\left(x,y\right)=\left(r\mathrm{cos}\theta ,r\mathrm{sin}\theta \right)$

関数が一つで済む。

• ${x}^{2}+{y}^{2}={r}^{2}$

間数が二つ必要になる。

コード(Emacs)

Python 3

#!/usr/bin/env python3
from sympy import pprint, symbols, solve, plot

r, x, y = symbols('r, x, y')
eq = x ** 2 + y ** 2 - r ** 2

for i, t in enumerate(solve(eq, y), 1):
print(f'{i}')
for s in [t, t.expand(), t.factor()]:
pprint(s)
print()
print()

p = plot(*[f.subs({r: 1}) for f in solve(eq, y)], show=False, legend=True)
for i, color in enumerate(['red', 'blue']):
p[i].line_color = color
p.save('sample.svg')


$./sample.py 1 _________________ -╲╱ (r - x)⋅(r + x) _________ ╱ 2 2 -╲╱ r - x ___________________ -╲╱ -(-r + x)⋅(r + x) 2 _________________ ╲╱ (r - x)⋅(r + x) _________ ╱ 2 2 ╲╱ r - x ___________________ ╲╱ -(-r + x)⋅(r + x)$


HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
<label for="r0">r = </label>
<input id="r0" type="number" min="0" value="0.5">
<label for="dx">dx = </label>
<input id="dx" type="number" min="0" step="0.001" value="0.001">
<br>
<label for="x1">x1 = </label>
<input id="x1" type="number" value="-5">
<label for="x2">x2 = </label>
<input id="x2" type="number" value="5">
<br>
<label for="y1">y1 = </label>
<input id="y1" type="number" value="-5">
<label for="y2">y2 = </label>
<input id="y2" type="number" value="5">
<br>
<label for="r1">r1 = </label>
<input id="r1" type="number" min="0" value="1">
<label for="r2">r2 = </label>
<input id="r2" type="number" min="0" value="2">

<button id="draw0">draw</button>
<button id="clear0">clear</button>

<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/d3/4.2.6/d3.min.js" integrity="sha256-5idA201uSwHAROtCops7codXJ0vja+6wbBrZdQ6ETQc=" crossorigin="anonymous"></script>

<script src="sample.js"></script>


JavaScript

let div0 = document.querySelector('#graph0'),
pre0 = document.querySelector('#output0'),
width = 600,
height = 600,
btn0 = document.querySelector('#draw0'),
btn1 = document.querySelector('#clear0'),
input_r = document.querySelector('#r0'),
input_dx = document.querySelector('#dx'),
input_x1 = document.querySelector('#x1'),
input_x2 = document.querySelector('#x2'),
input_y1 = document.querySelector('#y1'),
input_y2 = document.querySelector('#y2'),
input_r1 = document.querySelector('#r1'),
input_r2 = document.querySelector('#r2'),
inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2,
input_r1, input_r2],
p = (x) => pre0.textContent += x + '\n',
range = (start, end, step=1) => {
let res = [];
for (let i = start; i < end; i += step) {
res.push(i);
}
return res;
};

let draw = () => {
pre0.textContent = '';

let r = parseFloat(input_r.value),
dx = parseFloat(input_dx.value),
x1 = parseFloat(input_x1.value),
x2 = parseFloat(input_x2.value),
y1 = parseFloat(input_y1.value),
y2 = parseFloat(input_y2.value),
r1 = parseFloat(input_r1.value),
r2 = parseFloat(input_r2.value);

if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) {
return;
}

let points = [],
f = (x) => [r1 * Math.cos(x), r1 * Math.sin(x), 'green'],
g1 = (x) => Math.sqrt(r2 ** 2 - x ** 2),
g2 = (x) => -g1(x),
lines = [],
fns = [[g1, 'red'],
[g2, 'blue']];

for (let x0 = 0; x0 < 2 * Math.PI; x0 += dx) {
points.push(f(x0));
}

fns
.forEach((o) => {
let [f, color] = o;
for (let x = x1; x <= x2; x += dx) {
let y = f(x);

points.push([x, y, color]);
}
});

let xscale = d3.scaleLinear()
.domain([x1, x2])
let yscale = d3.scaleLinear()
.domain([y1, y2])

let xaxis = d3.axisBottom().scale(xscale);
let yaxis = d3.axisLeft().scale(yscale);
div0.innerHTML = '';
let svg = d3.select('#graph0')
.append('svg')
.attr('width', width)
.attr('height', height);

svg.selectAll('line')
.data([[x1, 0, x2, 0], [0, y1, 0, y2]].concat(lines))
.enter()
.append('line')
.attr('x1', (d) => xscale(d[0]))
.attr('y1', (d) => yscale(d[1]))
.attr('x2', (d) => xscale(d[2]))
.attr('y2', (d) => yscale(d[3]))
.attr('stroke', (d) => d[4] || 'black');

svg.selectAll('circle')
.data(points)
.enter()
.append('circle')
.attr('cx', (d) => xscale(d[0]))
.attr('cy', (d) => yscale(d[1]))
.attr('r', r)
.attr('fill', (d) => d[2] || 'green');

svg.append('g')
.attr('transform', translate(0, ${height - padding})) .call(xaxis); svg.append('g') .attr('transform', translate(${padding}, 0))
.call(yaxis);
};

inputs.forEach((input) => input.onchange = draw);
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();