



from math import factorial, pi






def      _A				(UpperCamelCase		:      float      ,			UpperCamelCase		:      int = 30 )  ->float:



			'''simple docstring'''







			if not isinstance(UpperCamelCase      ,			(int, float) ):
						raise ValueError("""maclaurin_sin() requires either an int or float for theta""" )

			if not isinstance(UpperCamelCase      ,			UpperCamelCase ) or accuracy <= 0:
						raise ValueError("""maclaurin_sin() requires a positive int for accuracy""" )

			lowerCamelCase__ :      Dict								=		float(UpperCamelCase )
			lowerCamelCase__ :      int								=		theta // (2 * pi)
			theta -= 2 * div * pi
			return sum(
			    (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1 ) for r in range(UpperCamelCase ) )






def      _A				(UpperCamelCase		:      float      ,			UpperCamelCase		:      int = 30 )  ->float:



			'''simple docstring'''







			if not isinstance(UpperCamelCase      ,			(int, float) ):
						raise ValueError("""maclaurin_cos() requires either an int or float for theta""" )

			if not isinstance(UpperCamelCase      ,			UpperCamelCase ) or accuracy <= 0:
						raise ValueError("""maclaurin_cos() requires a positive int for accuracy""" )

			lowerCamelCase__ :      int								=		float(UpperCamelCase )
			lowerCamelCase__ :      Optional[int]								=		theta // (2 * pi)
			theta -= 2 * div * pi
			return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r ) for r in range(UpperCamelCase ) )


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				print(maclaurin_sin(10))
				print(maclaurin_sin(-10))
				print(maclaurin_sin(10, 15))
				print(maclaurin_sin(-10, 15))

				print(maclaurin_cos(5))
				print(maclaurin_cos(-5))
				print(maclaurin_cos(10, 15))
				print(maclaurin_cos(-10, 15))








from pathlib import Path

import cva
import numpy as np
from matplotlib import pyplot as plt






def      _A				(UpperCamelCase		:      np.ndarray      ,			UpperCamelCase		:      np.ndarray      ,			UpperCamelCase		:      np.ndarray      ,			UpperCamelCase		:      int      ,			UpperCamelCase		:      int )  ->np.ndarray:



			'''simple docstring'''







			lowerCamelCase__ :      Union[str, Any]								=		cva.getAffineTransform(UpperCamelCase      ,			UpperCamelCase )
			return cva.warpAffine(UpperCamelCase      ,			UpperCamelCase      ,			(rows, cols) )


if __name__ == "__main__":
				# read original image
				_lowercase     							=						cva.imread(
				    str(Path(__file__).resolve().parent.parent / '''image_data''' / '''lena.jpg''')
				)
				# turn image in gray scale value
				_lowercase     							=						cva.cvtColor(image, cva.COLOR_BGR2GRAY)
				# get image shape
				_lowercase							,				_lowercase     							=						gray_img.shape

				# set different points to rotate image
				_lowercase     							=						np.array([[50, 50], [2_00, 50], [50, 2_00]], np.floataa)
				_lowercase     							=						np.array([[10, 1_00], [2_00, 50], [1_00, 2_50]], np.floataa)
				_lowercase     							=						np.array([[50, 50], [1_50, 50], [1_20, 2_00]], np.floataa)
				_lowercase     							=						np.array([[10, 1_00], [80, 50], [1_80, 2_50]], np.floataa)

				# add all rotated images in a list
				_lowercase     							=						[
				    gray_img,
				    get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
				    get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
				    get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
				]

				# plot different image rotations
				_lowercase     							=						plt.figure(1)
				_lowercase     							=						['''Original''', '''Rotation 1''', '''Rotation 2''', '''Rotation 3''']
				for i, image in enumerate(images):
								plt.subplot(2, 2, i + 1), plt.imshow(image, '''gray''')
								plt.title(titles[i])
								plt.axis('''off''')
								plt.subplots_adjust(left=0.0, bottom=0.05, right=1.0, top=0.95)
				plt.show()



