172 lines
4.9 KiB
Python
Executable File
172 lines
4.9 KiB
Python
Executable File
from decimal import Decimal, getcontext
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from vector import Vector
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getcontext().prec = 30
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class MyDecimal(Decimal):
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def is_near_zero(self, eps=1e-10):
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return abs(self) < eps
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class Plane(object):
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NO_NONZERO_ELTS_FOUND_MSG = 'No nonzero elements found'
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def __init__(self, normal_vector=None, constant_term=None):
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self.dimension = 3
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if not normal_vector:
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all_zeros = ['0'] * self.dimension
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normal_vector = Vector(all_zeros)
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self.normal_vector = normal_vector
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if not constant_term:
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constant_term = Decimal('0')
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self.constant_term = Decimal(constant_term)
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self.set_basepoint()
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def set_basepoint(self):
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try:
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n = self.normal_vector
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c = self.constant_term
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basepoint_coords = ['0'] * self.dimension
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initial_index = Plane.first_nonzero_index(n)
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initial_coefficient = n[initial_index]
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basepoint_coords[initial_index] = c / initial_coefficient
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self.basepoint = Vector(basepoint_coords)
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except Exception as e:
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if str(e) == Plane.NO_NONZERO_ELTS_FOUND_MSG:
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self.basepoint = None
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else:
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raise e
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def __str__(self):
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num_decimal_places = 3
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def write_coefficient(coefficient, is_initial_term=False):
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coefficient = round(coefficient, num_decimal_places)
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if coefficient % 1 == 0:
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coefficient = int(coefficient)
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output = ''
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if coefficient < 0:
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output += '-'
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if coefficient > 0 and not is_initial_term:
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output += '+'
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if not is_initial_term:
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output += ' '
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if abs(coefficient) != 1:
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output += '{}'.format(abs(coefficient))
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return output
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n = self.normal_vector
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try:
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initial_index = Plane.first_nonzero_index(n)
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terms = [write_coefficient(
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n[i], is_initial_term=(i == initial_index)) +
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'x_{}'.format(i + 1)
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for i in range(self.dimension)
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if round(n[i], num_decimal_places) != 0]
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output = ' '.join(terms)
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except Exception as e:
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if str(e) == self.NO_NONZERO_ELTS_FOUND_MSG:
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output = '0'
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else:
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raise e
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constant = round(self.constant_term, num_decimal_places)
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if constant % 1 == 0:
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constant = int(constant)
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output += ' = {}'.format(constant)
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return output
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def is_parallel(self, plane2):
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return self.normal_vector.is_parallel(plane2.normal_vector)
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def __eq__(self, plane2):
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if self.normal_vector.is_zero():
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if not plane2.normal_vector.is_zero():
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return False
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diff = self.constant_term - plane2.constant_term
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return MyDecimal(diff).is_near_zero()
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elif plane2.normal_vector.is_zero():
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return False
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if not self.is_parallel(plane2):
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return False
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basepoint_difference = self.basepoint.minus(plane2.basepoint)
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return basepoint_difference.is_orthogonal(self.normal_vector)
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def __iter__(self):
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self.current = 0
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return self
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def next(self):
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if self.current >= len(self.normal_vector):
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raise StopIteration
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else:
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current_value = self.normal_vector[self.current]
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self.current += 1
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return current_value
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def __len__(self):
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return len(self.normal_vector)
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def __getitem__(self, i):
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return self.normal_vector[i]
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@staticmethod
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def first_nonzero_index(iterable):
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for k, item in enumerate(iterable):
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if not MyDecimal(item).is_near_zero():
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return k
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raise Exception(Plane.NO_NONZERO_ELTS_FOUND_MSG)
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if __name__ == '__main__':
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# first system of planes:
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# -0.412x + 3.806y + 0.728z = -3.46
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# 1.03x - 9.515y - 1.82z = 8.65
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plane1 = Plane(Vector([-0.412, 3.806, 0.728]), -3.46)
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plane2 = Plane(Vector([1.03, -9.515, -1.82]), 8.65)
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print '1 is parallel: {}'.format(plane1.is_parallel(plane2))
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print '1 is equal: {}'.format(plane1 == plane2)
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# second system of planes:
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# 2.611x + 5.528y + 0.283z = 4.6
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# 7.715x + 8.306y + 5.342z = 3.76
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plane3 = Plane(Vector([2.611, 5.528, 0.283]), 4.6)
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plane4 = Plane(Vector([7.715, 8.306, 5.342]), 3.76)
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print '2 is parallel: {}'.format(plane3.is_parallel(plane4))
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print '2 is equal: {}'.format(plane3 == plane4)
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# third system of planes:
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# -7.926x + 8.625y - 7.212z = -7.952
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# -2.642x + 2.875y - 2.404z = -2.443
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plane5 = Plane(Vector([-7.926, 8.625, -7.212]), -7.952)
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plane6 = Plane(Vector([-2.642, 2.875, -2.404]), -2.443)
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print '3 is parallel: {}'.format(plane5.is_parallel(plane6))
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print '3 is equal: {}'.format(plane5 == plane6)
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