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import matplotlib.pyplot as plt
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import numpy as np
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import math
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def get_shear_matrix_for_factor_x(factor_x: int):
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shear_m=np.empty((2,2),np.float)
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shear_m[0,:] = np.array([1,factor_x])
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shear_m[1, :] = np.array([0,1])
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return shear_m
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def get_rotation_matrix_for_angle(angle: float):
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theta = angle
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rotation_matrix = np.array([[math.cos(theta), -math.sin(theta)], [math.sin(theta), math.cos(theta)]], np.float)
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return rotation_matrix
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def get_new_point(point: tuple, angle: float):
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"""
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:param point: a point in 2D, with coordinates x, y
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:param angle: in radians
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:return: tuple representing a point with ratoted coordinates
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"""
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rotation_matrix = get_rotation_matrix_for_angle(angle)
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point_vector=np.empty((2,1),float)
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point_vector[0,0]=point[0]
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point_vector[1,0]=point[1]
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new_point = np.matmul(rotation_matrix, point)
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x = int(new_point[0])
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y = int(new_point[1])
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return (x,y)
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def display_plot(points):
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"""
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:param points: np.matrix
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"""
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point_list_x = points[:, 0] #
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point_list_y = points[:, 1] # [
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plt.plot(point_list_x, point_list_y)
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plt.show()
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def get_my_T():
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points=np.empty((9,2),np.float)
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points[:,0] = np.array([20,25,25,35,35,10,10,20,20])
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points[:,1] = np.array([ 0, 0,30,30,35,35,30,30, 0])
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return points
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def display_three_letters_on_same_plot(p_1: np.matrix , p_2: np.matrix, p_3: np.matrix):
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plt.plot(p_1[:,0], p_1[:,1],color="red")
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plt.plot(p_2[:, 0], p_2[:, 1], color="yellow")
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plt.plot(p_3[:, 0], p_3[:, 1], color="green")
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plt.xlim([-100,100])
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plt.ylim([-100,100])
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plt.show()
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def display_two_letters_on_same_plot(p_1: np.matrix , p_2: np.matrix):
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plt.plot(p_1[:,0], p_1[:,1],color="red")
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plt.plot(p_2[:, 0], p_2[:, 1], color="yellow")
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plt.show()
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def display_points(points):
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plt.plot(points[:,0], points[:,1])
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plt.show()
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def rotate_a_letter_by_angle(letter:np.matrix,angle:np.float):
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m,n=letter.shape
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new_points = np.empty((m,n),np.float)
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for i in range(m):
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new_points[i,:] = get_new_point(letter[i,:],angle)
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return new_points
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def shear_a_letter_by_factor_x(letter:np.matrix,factor_x:np.int):
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m,n=letter.shape
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new_letter = np.empty((m,n),np.float)
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shear_matrix=get_shear_matrix_for_factor_x(factor_x)
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for i in range(m):
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new_letter[i,:] = np.matmul(shear_matrix,letter[i,:])
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return new_letter
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p=get_my_T()
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p_1=rotate_a_letter_by_angle(get_my_T(), np.pi/2)
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p_2=shear_a_letter_by_factor_x(p,1)
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# display_two_letters_on_same_plot(p,p_2)
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display_three_letters_on_same_plot(p,p_1,p_2)
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# display_points(p_2)
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