




'''simple docstring'''







from __future__ import annotations

from math import pi, pow






def 		_lowercase		(	lowercase_  ):



		'''simple docstring'''







		if side_length < 0:
				raise ValueError("vol_cube() only accepts non-negative values"  )
		return pow(lowercase_						,							3  )






def 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if height < 0 or radius < 0:
				raise ValueError("vol_spherical_cap() only accepts non-negative values"  )
		# Volume is 1/3 pi * height squared * (3 * radius - height)
		return 1 / 3 * pi * pow(lowercase_						,							2  ) * (3 * radius - height)






def 		_lowercase		(	lowercase_						,							lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if radius_a < 0 or radius_a < 0 or centers_distance < 0:
				raise ValueError("vol_spheres_intersect() only accepts non-negative values"  )
		if centers_distance == 0:
				return vol_sphere(min(lowercase_						,							lowercase_  )  )

		_snake_case	       =       (
		    (radius_a - radius_a + centers_distance)
		    * (radius_a + radius_a - centers_distance)
		    / (2 * centers_distance)
		)
		_snake_case	       =       (
		    (radius_a - radius_a + centers_distance)
		    * (radius_a + radius_a - centers_distance)
		    / (2 * centers_distance)
		)

		return vol_spherical_cap(lowercase_						,							lowercase_  ) + vol_spherical_cap(lowercase_						,							lowercase_  )






def 		_lowercase		(	lowercase_						,							lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if radius_a <= 0 or radius_a <= 0 or centers_distance < 0:
				raise ValueError(
				    "vol_spheres_union() only accepts non-negative values, non-zero radius"  )

		if centers_distance == 0:
				return vol_sphere(max(lowercase_						,							lowercase_  )  )

		return (
		    vol_sphere(lowercase_  )
		    + vol_sphere(lowercase_  )
		    - vol_spheres_intersect(lowercase_						,							lowercase_						,							lowercase_  )
		)






def 		_lowercase		(	lowercase_						,							lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if width < 0 or height < 0 or length < 0:
				raise ValueError("vol_cuboid() only accepts non-negative values"  )
		return float(width * height * length  )






def 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if height < 0 or area_of_base < 0:
				raise ValueError("vol_cone() only accepts non-negative values"  )
		return area_of_base * height / 3.0






def 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if height < 0 or radius < 0:
				raise ValueError("vol_right_circ_cone() only accepts non-negative values"  )
		return pi * pow(lowercase_						,							2  ) * height / 3.0






def 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if height < 0 or area_of_base < 0:
				raise ValueError("vol_prism() only accepts non-negative values"  )
		return float(area_of_base * height  )






def 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if height < 0 or area_of_base < 0:
				raise ValueError("vol_pyramid() only accepts non-negative values"  )
		return area_of_base * height / 3.0






def 		_lowercase		(	lowercase_  ):



		'''simple docstring'''







		if radius < 0:
				raise ValueError("vol_sphere() only accepts non-negative values"  )
		# Volume is 4/3 * pi * radius cubed
		return 4 / 3 * pi * pow(lowercase_						,							3  )






def 		_lowercase		(	lowercase_  ):



		'''simple docstring'''







		if radius < 0:
				raise ValueError("vol_hemisphere() only accepts non-negative values"  )
		# Volume is radius cubed * pi * 2/3
		return pow(lowercase_						,							3  ) * pi * 2 / 3






def 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if height < 0 or radius < 0:
				raise ValueError("vol_circular_cylinder() only accepts non-negative values"  )
		# Volume is radius squared * height * pi
		return pow(lowercase_						,							2  ) * height * pi






def 		_lowercase		(	lowercase_						,							lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if inner_radius < 0 or outer_radius < 0 or height < 0:
				raise ValueError(
				    "vol_hollow_circular_cylinder() only accepts non-negative values"  )
		if outer_radius <= inner_radius:
				raise ValueError("outer_radius must be greater than inner_radius"  )
		return pi * (pow(lowercase_						,							2  ) - pow(lowercase_						,							2  )) * height






def 		_lowercase		(	lowercase_						,							lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if radius_a < 0 or radius_a < 0 or height < 0:
				raise ValueError("vol_conical_frustum() only accepts non-negative values"  )
		return (
		    1
		    / 3
		    * pi
		    * height
		    * (pow(lowercase_						,							2  ) + pow(lowercase_						,							2  ) + radius_a * radius_a)
		)






def 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''simple docstring'''







		if torus_radius < 0 or tube_radius < 0:
				raise ValueError("vol_torus() only accepts non-negative values"  )
		return 2 * pow(lowercase_						,							2  ) * torus_radius * pow(lowercase_						,							2  )






def 		_lowercase		(	):



		'''simple docstring'''







		print("Volumes:"  )
		print(f'''Cube: {vol_cube(2  ) = }'''  )  # = 8
		print(f'''Cuboid: {vol_cuboid(2						,							2						,							2  ) = }'''  )  # = 8
		print(f'''Cone: {vol_cone(2						,							2  ) = }'''  )  # ~= 1.33
		print(f'''Right Circular Cone: {vol_right_circ_cone(2						,							2  ) = }'''  )  # ~= 8.38
		print(f'''Prism: {vol_prism(2						,							2  ) = }'''  )  # = 4
		print(f'''Pyramid: {vol_pyramid(2						,							2  ) = }'''  )  # ~= 1.33
		print(f'''Sphere: {vol_sphere(2  ) = }'''  )  # ~= 33.5
		print(f'''Hemisphere: {vol_hemisphere(2  ) = }'''  )  # ~= 16.75
		print(f'''Circular Cylinder: {vol_circular_cylinder(2						,							2  ) = }'''  )  # ~= 25.1
		print(f'''Torus: {vol_torus(2						,							2  ) = }'''  )  # ~= 157.9
		print(f'''Conical Frustum: {vol_conical_frustum(2						,							2						,							4  ) = }'''  )  # ~= 58.6
		print(f'''Spherical cap: {vol_spherical_cap(1						,							2  ) = }'''  )  # ~= 5.24
		print(f'''Spheres intersetion: {vol_spheres_intersect(2						,							2						,							1  ) = }'''  )  # ~= 21.21
		print(f'''Spheres union: {vol_spheres_union(2						,							2						,							1  ) = }'''  )  # ~= 45.81
		print(
		    f'''Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1						,							2						,							3  ) = }'''  )  # ~= 28.3


if __name__ == "__main__":
						main()













"""simple docstring"""







import cva
import numpy as np

from digital_image_processing.filters.convolve import img_convolve
from digital_image_processing.filters.sobel_filter import sobel_filter

lowerCAmelCase_		:			List[Any]				   =					1_8_0






def 					_lowerCAmelCase				(					lowerCAmelCase		,					lowerCAmelCase						):







       '''simple docstring'''
       UpperCAmelCase					=	k_size // 2
       UpperCAmelCase			,				UpperCAmelCase					=	np.mgrid[0 - center : k_size - center, 0 - center : k_size - center]
       UpperCAmelCase					=	(
           1
           / (2 * np.pi * sigma)
           * np.exp(-(np.square(lowerCAmelCase						) + np.square(lowerCAmelCase						)) / (2 * np.square(lowerCAmelCase						))						)
       )
       return g






def 					_lowerCAmelCase				(					lowerCAmelCase		,					lowerCAmelCase		,					lowerCAmelCase						):







       '''simple docstring'''
       UpperCAmelCase					=	np.zeros(lowerCAmelCase						)

       for row in range(1		,					image_shape[0] - 1						):
              for col in range(1		,					image_shape[1] - 1						):
                     UpperCAmelCase					=	gradient_direction[row, col]

                     if (
                         0 <= direction < PI / 8
                         or 15 * PI / 8 <= direction <= 2 * PI
                         or 7 * PI / 8 <= direction <= 9 * PI / 8
                     ):
                            UpperCAmelCase					=	sobel_grad[row, col - 1]
                            UpperCAmelCase					=	sobel_grad[row, col + 1]
                            if sobel_grad[row, col] >= w and sobel_grad[row, col] >= e:
                                   UpperCAmelCase					=	sobel_grad[row, col]

                     elif (
                         PI / 8 <= direction < 3 * PI / 8
                         or 9 * PI / 8 <= direction < 11 * PI / 8
                     ):
                            UpperCAmelCase					=	sobel_grad[row + 1, col - 1]
                            UpperCAmelCase					=	sobel_grad[row - 1, col + 1]
                            if sobel_grad[row, col] >= sw and sobel_grad[row, col] >= ne:
                                   UpperCAmelCase					=	sobel_grad[row, col]

                     elif (
                         3 * PI / 8 <= direction < 5 * PI / 8
                         or 11 * PI / 8 <= direction < 13 * PI / 8
                     ):
                            UpperCAmelCase					=	sobel_grad[row - 1, col]
                            UpperCAmelCase					=	sobel_grad[row + 1, col]
                            if sobel_grad[row, col] >= n and sobel_grad[row, col] >= s:
                                   UpperCAmelCase					=	sobel_grad[row, col]

                     elif (
                         5 * PI / 8 <= direction < 7 * PI / 8
                         or 13 * PI / 8 <= direction < 15 * PI / 8
                     ):
                            UpperCAmelCase					=	sobel_grad[row - 1, col - 1]
                            UpperCAmelCase					=	sobel_grad[row + 1, col + 1]
                            if sobel_grad[row, col] >= nw and sobel_grad[row, col] >= se:
                                   UpperCAmelCase					=	sobel_grad[row, col]

       return destination






def 					_lowerCAmelCase				(					lowerCAmelCase		,					lowerCAmelCase		,					lowerCAmelCase		,					lowerCAmelCase		,					lowerCAmelCase		,					lowerCAmelCase						):







       '''simple docstring'''
       for row in range(1		,					image_shape[0] - 1						):
              for col in range(1		,					image_shape[1] - 1						):
                     if destination[row, col] >= threshold_high:
                            UpperCAmelCase					=	strong
                     elif destination[row, col] <= threshold_low:
                            UpperCAmelCase					=	0
                     else:
                            UpperCAmelCase					=	weak






def 					_lowerCAmelCase				(					lowerCAmelCase		,					lowerCAmelCase		,					lowerCAmelCase		,					lowerCAmelCase						):







       '''simple docstring'''
       for row in range(1		,					image_shape[0]						):
              for col in range(1		,					image_shape[1]						):
                     if destination[row, col] == weak:
                            if 255 in (
                                destination[row, col + 1],
                                destination[row, col - 1],
                                destination[row - 1, col],
                                destination[row + 1, col],
                                destination[row - 1, col - 1],
                                destination[row + 1, col - 1],
                                destination[row - 1, col + 1],
                                destination[row + 1, col + 1],
                            ):
                                   UpperCAmelCase					=	strong
                            else:
                                   UpperCAmelCase					=	0






def 					_lowerCAmelCase				(					lowerCAmelCase		,					lowerCAmelCase=15		,					lowerCAmelCase=30		,					lowerCAmelCase=128		,					lowerCAmelCase=255						):







       '''simple docstring'''
       # gaussian_filter
       UpperCAmelCase					=	img_convolve(lowerCAmelCase		,					gen_gaussian_kernel(9		,					sigma=1.4						)						)
       # get the gradient and degree by sobel_filter
       UpperCAmelCase			,				UpperCAmelCase					=	sobel_filter(lowerCAmelCase						)
       UpperCAmelCase					=	PI + np.radadeg(lowerCAmelCase						)

       UpperCAmelCase					=	suppress_non_maximum(image.shape		,					lowerCAmelCase		,					lowerCAmelCase						)

       detect_high_low_threshold(
           image.shape		,					lowerCAmelCase		,					lowerCAmelCase		,					lowerCAmelCase		,					lowerCAmelCase		,					lowerCAmelCase						)

       track_edge(image.shape		,					lowerCAmelCase		,					lowerCAmelCase		,					lowerCAmelCase						)

       return destination


if __name__ == "__main__":
 # read original image in gray mode
 lowerCAmelCase_		:			Optional[Any]				   =					cva.imread(R'''../image_data/lena.jpg''', 0)
 # canny edge detection
 lowerCAmelCase_		:			Dict				   =					canny(lena)
 cva.imshow('''canny''', canny_destination)
 cva.waitKey(0)
