2017年8月22日火曜日

学習環境

解析入門 原書第3版 (S.ラング(著)、松坂 和夫(翻訳)、片山 孝次(翻訳)、岩波書店)の第2部(微分と基本的な関数)、第6章(曲線をえがくこと)、4(極座標)、練習問題7、8、9.を取り組んでみる。


  1. cos2θ= cos 2 θ sin 2 θ =12 sin 2 θ y=rsinθ sinθ= y x 2 + y 2 x 2 + y 2 =| 1 2 y 2 x 2 + y 2 |

  2. sin3θ=sin2θcosθ+cos2θsinθ =2sinθcosθcosθ+( cos 2 θ sin 2 θ )sinθ =2sinθ( 1 sin 2 θ )+( 12 sin 2 θ )sinθ =2sinθ2 sin 3 θ+sinθ2 sin 3 θ =3( sinθ sin 3 θ ) =3( y x 2 + y 2 y 3 ( x 2 + y 2 ) x 2 + y 2 ) x 2 + y 2 =3( y x 2 + y 2 y 3 ( x 2 + y 2 ) x 2 + y 2 ) x 2 + y 2 =3( y x 2 + y 2 y 3 ( x 2 + y 2 ) 2 ) ( x 2 + y 2 ) 3 =3( y( x 2 + y 2 ) y 3 )

  3. sin3θ=sin2θcosθ+cos2θsinθ =2sinθcosθcosθ+( cos 2 θ sin 2 θ )sinθ =2sinθ( 1 sin 2 θ )+( 12 sin 2 θ )sinθ =2sinθ2 sin 3 θ+sinθ2 sin 3 θ =3( sinθ sin 3 θ ) =3( y x 2 + y 2 y 3 ( x 2 + y 2 ) x 2 + y 2 ) x 2 + y 2 =3| y x 2 + y 2 y 3 ( x 2 + y 2 ) x 2 + y 2 | x 2 + y 2 =3| y x 2 + y 2 y 3 ( x 2 + y 2 ) 2 |

コード(Emacs)

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="dΘ">dΘ = </label>
<input id="dΘ" type="number" min="0" step="0.0001" value="0.001">
<br>
<label for="x1">x1 = </label>
<input id="x1" type="number" value="-1.5">
<label for="x2">x2 = </label>
<input id="x2" type="number" value="1.5">
<br>
<label for="y1">y1 = </label>
<input id="y1" type="number" value="-1.5">
<label for="y2">y2 = </label>
<input id="y2" type="number" value="1.5">

<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="sample7.js"></script>    

JavaScript

let div0 = document.querySelector('#graph0'),
    pre0 = document.querySelector('#output0'),
    width = 600,
    height = 600,
    padding = 50,
    btn0 = document.querySelector('#draw0'),
    btn1 = document.querySelector('#clear0'),
    input_r = document.querySelector('#r0'),
    input_dΘ = document.querySelector('#dΘ'),
    input_x1 = document.querySelector('#x1'),
    input_x2 = document.querySelector('#x2'),
    input_y1 = document.querySelector('#y1'),
    input_y2 = document.querySelector('#y2'),
    inputs = [input_r, input_dΘ, 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 f7 = (Θ) => Math.abs(Math.cos(2 * Θ)),
    f8 = (Θ) => Math.sin(3 * Θ),
    f9 = (Θ) => Math.abs(Math.sin(3 * Θ));
        
let draw = () => {
    pre0.textContent = '';

    let r = parseFloat(input_r.value),= parseFloat(input_dΘ.value),
        x1 = parseFloat(input_x1.value),
        x2 = parseFloat(input_x2.value),
        y1 = parseFloat(input_y1.value),
        y2 = parseFloat(input_y2.value);

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

    let points = [],
        lines = [],
        fns = [[f7, 'red'],
               [f8, 'green'],
               [f9, 'blue']],
        fns1 = [],
        fns2 = [];

    fns
        .forEach((o) => {
            let [f, color] = o;
            for (let Θ = 0; Θ <= 2 * Math.PI; Θ +=) {
                let r = f(Θ),
                    x = r * Math.cos(Θ),
                    y = r * Math.sin(Θ);

                points.push([x, y, 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])
        .range([padding, width - padding]);
    let yscale = d3.scaleLinear()
        .domain([y1, y2])
        .range([height - padding, padding]);

    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();







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