class Line(object):
NO_NONZERO_ELTS_FOUND_MSG = 'No nonzero elements found'
def __init__(self, normal_vector=None, constant_term=None):
self.dimension = 2
if not normal_vector:
all_zeros = ['0']*self.dimension
normal_vector = Vector(all_zeros)
self.normal_vector = Vector(normal_vector)
if not constant_term:
constant_term = Decimal('0')
self.constant_term = Decimal(constant_term)
self.set_basepoint()
def set_basepoint(self):
try:
n = self.normal_vector.coordinates
c = self.constant_term
basepoint_coords = ['0']*self.dimension
initial_index = Line.first_nonzero_index(n)
initial_coefficient = n[initial_index]
basepoint_coords[initial_index] = c/initial_coefficient
self.basepoint = Vector(basepoint_coords)
except Exception as e:
if str(e) == Line.NO_NONZERO_ELTS_FOUND_MSG:
self.basepoint = None
else:
raise e
def is_parallel(self, vector2):
return self.normal_vector.is_parallel_to(vector2.normal_vector)
def __eq__(self, vector2):
if self.normal_vector.is_zero():
if not vector2.normal_vector.is_zero():
return False
else:
diff = self.constant_term - vector2.constant_term
return MyDecimal(diff).is_near_zero()
elif vector2.normal_vector.is_zero():
return False
# consists of the same set of points
if not self.is_parallel(vector2):
return False
direction_vector = self.basepoint - vector2.basepoint
return direction_vector.is_orthogonal(self.normal_vector)
def intersects(self, vector2):
if(self == vector2):
return 'The lines are equal, so there are infinite intersections.'
if(self.is_parallel(vector2) and not self == vector2):
return 'No intersection! The lines are parallel to each other.'
A, B = self.normal_vector.coordinates
C, D = vector2.normal_vector.coordinates
k1 = self.constant_term
k2 = vector2.constant_term
x = ((D * k1) - (B * k2)) / ((A * D) - (B * C))
y = ((-C * k1) + (A * k2)) / ((A * D) - (B * C))
return Vector([x,y])
def __str__(self):
num_decimal_places = 3
def write_coefficient(coefficient, is_initial_term=False):
coefficient = round(coefficient, num_decimal_places)
if coefficient % 1 == 0:
coefficient = int(coefficient)
output = ''
if coefficient < 0:
output += '-'
if coefficient > 0 and not is_initial_term:
output += '+'
if not is_initial_term:
output += ' '
if abs(coefficient) != 1:
output += '{}'.format(abs(coefficient))
return output
n = self.normal_vector.coordinates
try:
initial_index = Line.first_nonzero_index(n)
terms = [write_coefficient(n[i], is_initial_term=(i==initial_index)) + 'x_{}'.format(i+1)
for i in range(self.dimension) if round(n[i], num_decimal_places) != 0]
output = ' '.join(terms)
except Exception as e:
if str(e) == self.NO_NONZERO_ELTS_FOUND_MSG:
output = '0'
else:
raise e
constant = round(self.constant_term, num_decimal_places)
if constant % 1 == 0:
constant = int(constant)
output += ' = {}'.format(constant)
return output
@staticmethod
def first_nonzero_index(iterable):
for k, item in enumerate(iterable):
if not MyDecimal(item).is_near_zero():
return k
raise Exception(Line.NO_NONZERO_ELTS_FOUND_MSG)
class Plane(object):
NO_NONZERO_ELTS_FOUND_MSG = 'No nonzero elements found'
def __init__(self, normal_vector=None, constant_term=None):
self.dimension = 3
if not normal_vector:
all_zeros = ['0']*self.dimension
normal_vector = Vector(all_zeros)
self.normal_vector = Vector(normal_vector)
if not constant_term:
constant_term = Decimal('0')
self.constant_term = Decimal(constant_term)
self.set_basepoint()
def set_basepoint(self):
try:
n = self.normal_vector.coordinates
c = self.constant_term
basepoint_coords = ['0']*self.dimension
initial_index = Plane.first_nonzero_index(n)
initial_coefficient = n[initial_index]
basepoint_coords[initial_index] = c/initial_coefficient
self.basepoint = Vector(basepoint_coords)
except Exception as e:
if str(e) == Plane.NO_NONZERO_ELTS_FOUND_MSG:
self.basepoint = None
else:
raise e
def is_parallel(self, plane):
return self.normal_vector.is_parallel_to(plane.normal_vector)
def __eq__(self, plane):
if self.normal_vector.is_zero():
if not plane.normal_vector.is_zero():
return False
else:
diff = self.constant_term - plane.constant_term
return MyDecimal(diff).is_near_zero()
elif plane.normal_vector.is_zero():
return False
if not self.is_parallel(plane):
return False
direction_vector = self.basepoint - plane.basepoint
return direction_vector.is_orthogonal(self.normal_vector)
def __str__(self):
num_decimal_places = 3
def write_coefficient(coefficient, is_initial_term=False):
coefficient = round(coefficient, num_decimal_places)
if coefficient % 1 == 0:
coefficient = int(coefficient)
output = ''
if coefficient < 0:
output += '-'
if coefficient > 0 and not is_initial_term:
output += '+'
if not is_initial_term:
output += ' '
if abs(coefficient) != 1:
output += '{}'.format(abs(coefficient))
return output
n = self.normal_vector.coordinates
try:
initial_index = Plane.first_nonzero_index(n)
terms = [write_coefficient(n[i], is_initial_term=(i==initial_index)) + 'x_{}'.format(i+1)
for i in range(self.dimension) if round(n[i], num_decimal_places) != 0]
output = ' '.join(terms)
except Exception as e:
if str(e) == self.NO_NONZERO_ELTS_FOUND_MSG:
output = '0'
else:
raise e
constant = round(self.constant_term, num_decimal_places)
if constant % 1 == 0:
constant = int(constant)
output += ' = {}'.format(constant)
return output
@staticmethod
def first_nonzero_index(iterable):
for k, item in enumerate(iterable):
if not MyDecimal(item).is_near_zero():
return k
raise Exception(Plane.NO_NONZERO_ELTS_FOUND_MSG)