Python - 数学 - データをグラフで可視化する(投射軌跡比較プログラムの拡張)

Pythonからはじめる数学入門
原著

開発環境

• OS X El Capitan - Apple (OS)
• Emacs (Text Editor)
• Python 3.5 (プログラミング言語)

Pythonからはじめる数学入門 (Amit Saha (著)、黒川 利明 (翻訳)、オライリージャパン)の2章(データをグラフで可視化する)、2.6(プログラミングチャレンジ)、問題2-3(投射軌跡比較プログラムの拡張)を取り組んでみる。

問題2-3(投射軌跡比較プログラムの拡張)

コード(Emacs)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import matplotlib.pyplot as plt
import math


def draw_graph(x, y):
    plt.plot(x, y)
    plt.xlabel('x-coordinate')
    plt.ylabel('y-coordinate')
    plt.title('Projectile motion of a ball')


def frange(start, final, interval):
    numbers = []
    while start < final:
        numbers.append(start)
        start += interval
    return numbers


def draw_trajectory(u, theta, t_flight):
    intervals = frange(0, t_flight, 0.001)
    x = [u * math.cos(theta) * t for t in intervals]
    y = [u * math.sin(theta) * t - 0.5 * g * t * t for t in intervals]
    draw_graph(x, y)

if __name__ == '__main__':
    plt.figure(figsize=(5, 5))
    g = 9.8
    velocities = []
    angles = []
    try:
        n = int(input('How many trajectories? '))
        for i in range(n):
            u = float(
                input('Enter the initial velocity {0} (m/s): '.format(i + 1))
            )
            theta = float(
                input(
                    'Enter the angle of projection {0} (degrees): '.format(
                        i + 1
                    )
                )
            )
            velocities.append(u)
            angles.append(theta)
    except ValueError as err:
        print('You entered an invalid input')
        print(err)
    else:
        legends = []
        for i, velocity in enumerate(velocities):
            angle = angles[i]
            rad = math.radians(angle)
            legends.append((velocity, angle))
            t_flight = 2 * velocity * math.sin(rad) / g
            x = velocity * math.cos(rad) * t_flight
            t = t_flight / 2
            y = velocity * math.sin(rad) * t - 0.5 * g * t * t
            print('velocity: {0}, angle: {1}\n\ttime: {2}, x: {3}, y:{4}'.
                  format(velocity, angle, t_flight, x, y))
            draw_trajectory(velocity, rad, t_flight)

        plt.legend(legends)
        plt.savefig('trajectory.png')
        plt.show()

入出力結果(Terminal, IPython)

$ ./sample3.py
How many trajectories? 3
Enter the initial velocity 1 (m/s): 45
Enter the angle of projection 1 (degrees): 45
Enter the initial velocity 2 (m/s): 60
Enter the angle of projection 2 (degrees): 45
Enter the initial velocity 3 (m/s): 45
Enter the angle of projection 3 (degrees): 80
velocity: 45.0, angle: 45.0
 time: 6.493837786407068, x: 206.6326530612245, y:51.658163265306115
velocity: 60.0, angle: 45.0
 time: 8.65845038187609, x: 367.3469387755101, y:91.83673469387752
velocity: 45.0, angle: 80.0
 time: 9.044152833785583, x: 70.6725296157632, y:100.20095808906795
$