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13.2: Matriz de transformación

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    Considera el siguiente conjunto de puntos:

    %matplotlib inline
import matplotlib.pylab as plt

x = [0.0,  0.0,  2.0,  8.0, 10.0, 10.0, 8.0, 4.0, 3.0, 3.0, 4.0, 6.0, 7.0, 7.0, 10.0, 
     10.0,  8.0,  2.0, 0.0, 0.0, 2.0, 6.0, 7.0,  7.0,  6.0,  4.0,  3.0, 3.0, 0.0]
y = [0.0, -2.0, -4.0, -4.0, -2.0,  2.0, 4.0, 4.0, 5.0, 7.0, 8.0, 8.0, 7.0, 6.0,  6.0,
     8.0, 10.0, 10.0, 8.0, 4.0, 2.0, 2.0, 1.0, -1.0, -2.0, -2.0, -1.0, 0.0, 0.0]

plt.plot(x,y, color='green');
plt.axis('equal');

    Podemos rotar estos puntos alrededor del origen usando el siguiente conjunto simple de ecuaciones:

    \[ x \cos(\theta) - y \sin(\theta) = x_{rotated} \nonumber \]

    \[ x \sin(\theta) + y \cos(\theta) = y_{rotated} \nonumber \]

    Esto puede ser reescrito como el siguiente sistema de matrices:

    \ [\ begin {split}
    \ left [
    \ begin {matrix}
    \ cos (\ theta) & -\ sin (\ theta)\\
    \ sin (\ theta) &\ cos (\ theta)
    \ end {matrix}
    \ derecha]
    \ izquierda [
    \ begin {matriz}
    x\\
    y
    \ end {matrix}
    \ right]
    =
    \ left [
    \ begin {matrix}
    x_ {rotada}\\
    y_ {rotada}
    \ end {matrix}
    \ right]
    \ end {split}\ nonumber\]

    Podemos rotar los puntos alrededor del origen por\(\pi/4\) (es decir\(45^o\)) de la siguiente manera:

    import numpy as np
import sympy as sym
sym.init_printing(use_unicode=True) # Trick to make matrixes look nice in jupyter

points = np.matrix([x,y])
    angle = np.pi/4
R = np.matrix([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]]);
sym.Matrix(R)
    p=R*points

plt.plot(p[0].T,p[1].T);
plt.axis('equal');

#print(p[0].T)

    Incluso podemos divertirnos un poco y seguir aplicando la misma rotación una y otra vez.

    # Apply R and plot 8 times
for i in range(0,8):
    p = R * p
    plt.plot(p[0].T,p[1].T);

plt.axis('equal');
    Pregunta

    En el código anterior ¿qué hace la llamada T en p [0] .T?

    This page titled 13.2: Matriz de transformación was last modified on Sun, 30 Oct 2022 15:33:25 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Dirk Colbry via source content that was edited to the style and standards of the LibreTexts platform.