## 2018年1月28日日曜日

### 数学 - Python - JavaScript - 図形の変換の方法 - 線形写像・1次変換 – 1次変換による色々な図形の像 - 直線を像にもつ図形(逆像)

1. $\left(\begin{array}{cc}1& -2\\ 2& 3\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}x-2y\\ 2x+3y\end{array}\right)$
$2x+3y=0$

2. $\begin{array}{}2x+3y=x-2y\\ x+5y=0\end{array}$

3. $\begin{array}{}2x+3y=2\left(x-2y\right)-5\\ 7y+5=0\end{array}$

4. $\begin{array}{}3\left(x-2y\right)+2x+3y-4=0\\ 5x-3y-4=0\end{array}$

コード(Emacs)

Python 3

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

x, y = symbols('x, y')
x0, y0 = symbols('x0, y0')
d = {x0: x - 2 * y, y0: 2 * x + 3 * y}
fs = [y0, y0 - x0, y0 - 2 * x0 + 5, 3 * x0 + y0 - 4]
for i, f in enumerate(fs, 1):
print(f'({i})')
pprint(f.subs(d))

gs = [solve(f.subs(d), y)[0] for f in fs]
hs = [solve(f.subs({x0: x, y0: y}), y)[0] for f in fs]
for t in zip(hs, gs):
pprint(t)
p = plot(*hs, *gs, show=False, legend=True)
colors = ['red', 'green', 'blue', 'orange',
'brown', 'pink', 'purple', 'yellow']
for i, color in enumerate(colors):
p[i].line_color = color
p.save('sample17.svg')


$./sample17.py (1) 2⋅x + 3⋅y (2) x + 5⋅y (3) 7⋅y + 5 (4) 5⋅x - 3⋅y - 4 ⎛ -2⋅x ⎞ ⎜0, ─────⎟ ⎝ 3 ⎠ ⎛ -x ⎞ ⎜x, ───⎟ ⎝ 5 ⎠ (2⋅x - 5, -5/7) ⎛ 5⋅x 4⎞ ⎜-3⋅x + 4, ─── - ─⎟ ⎝ 3 3⎠$


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="0.005">
<br>
<label for="x1">x1 = </label>
<input id="x1" type="number" value="-10">
<label for="x2">x2 = </label>
<input id="x2" type="number" value="10">
<br>
<label for="y1">y1 = </label>
<input id="y1" type="number" value="-10">
<label for="y2">y2 = </label>
<input id="y2" type="number" value="10">

<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="sample17.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'),
inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2],
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 f1 = (x) => 0,
g1 = (x) => -2 / 3 * x,
f2 = (x) => x,
g2 = (x) => -1 / 5 * x,
f3 = (x) => 2 * x - 5,
g3 = (x) => - 7 / 5,
f4 = (x) => -3 * x + 4,
g4 = (x) => 5 / 3 * x - 4;

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);

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

let points = [],
lines = [],
fns = [[f1, 'red'],
[g1, 'green'],
[f2, 'blue'],
[g2, 'orange'],
[f3, 'brown'],
[g3, 'pink'],
[f4, 'purple'],
[g4, 'yellow']],
fns1 = [],
fns2 = [];

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

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

fns1
.forEach((o) => {
let [f, color] = o;

lines.push([x1, f(x1), x2, f(x2), color]);
});

fns2
.forEach((o) => {
let [f, color] = o;
for (let x = x1; x <= x2; x += dx0) {
let g = f(x);
lines.push([x1, g(x1), x2, g(x2), 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);

[fns, fns1, fns2].forEach((fs) => p(fs.join('\n')));
};

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