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Cálculo do comprimento ideal de uma rede de dormir
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| #!/usr/bin/env python | |
| from sympy import sinh, acosh, sqrt, nsolve, Symbol, Float | |
| def calcular_rede(altura_rede, altura_ganchos, distancia_ganchos): | |
| H = distancia_ganchos | |
| h = altura_ganchos - altura_rede | |
| a = Symbol('a') | |
| L = Symbol('L') | |
| # https://en.wikipedia.org/wiki/Catenary#Determining_parameters | |
| eqs = ( | |
| 2*a*sinh(H/(2*a)) - L, | |
| 2*a*acosh((h+a)/a) - H, | |
| ) | |
| a, L = nsolve(eqs, (a, L), (1, 1)) | |
| hmin = altura_ganchos - sqrt(L**2/4 - distancia_ganchos**2/4) | |
| return a, L, hmin | |
| def plotar_rede(altura_rede, altura_ganchos, distancia_ganchos, a, hmin): | |
| import matplotlib.pyplot as plt | |
| import numpy as np | |
| x = np.linspace(-distancia_ganchos/2, distancia_ganchos/2, 1024) | |
| y = altura_rede - a + a*np.cosh(x/a) | |
| plt.plot(x, y, 'g') | |
| plt.plot([-distancia_ganchos/2, 0, distancia_ganchos/2], | |
| [altura_ganchos, hmin, altura_ganchos], 'r') | |
| plt.xlim([-distancia_ganchos/2, distancia_ganchos/2]) | |
| plt.ylim([0, altura_ganchos]) | |
| plt.tight_layout() | |
| plt.show() | |
| if __name__ == '__main__': | |
| import argparse | |
| import json | |
| parser = argparse.ArgumentParser() | |
| parser.add_argument('--altura_rede', type=Float, default=Float('0.60')) | |
| parser.add_argument('--plot', action=argparse.BooleanOptionalAction) | |
| parser.add_argument('altura_ganchos', type=Float) | |
| parser.add_argument('distancia_ganchos', type=Float) | |
| args = parser.parse_args() | |
| a, L, hmin = calcular_rede( | |
| args.altura_rede, | |
| args.altura_ganchos, | |
| args.distancia_ganchos) | |
| print(json.dumps({ | |
| "comprimento": float(L), | |
| "altura_minima": float(hmin) | |
| }, indent=4)) | |
| if args.plot: | |
| plotar_rede(float(args.altura_rede), | |
| float(args.altura_ganchos), | |
| float(args.distancia_ganchos), | |
| float(a), | |
| float(hmin)) |
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