def length(self):
""" Calculates the length of a vector.
Test:
>>> print( '{0:.3f}'.format(Vector2d( 1, 1 ).length()) )
1.414
>>> print( '{0:.3f}'.format(Vector2d( 45, 127 ).length()) )
134.737
>>> print( '{0:.3f}'.format(Vector2d( 5, 3 ).length()) )
5.831
>>> print( '{0:.3f}'.format(Vector2d( -1, 1 ).length()) )
1.414
>>> print( '{0:.3f}'.format(Vector2d( 45, -127 ).length()) )
134.737
>>> print( '{0:.3f}'.format(Vector2d( -5, -3 ).length()) )
5.831
"""
return pythagorean.solveC(self.x, self.y)
def reflectAtLine( x1, y1, x2, y2, x3, y3 ):
''' Reflects vector 1 at the line between vectors 2 and 3. Returns the x-component
and y-component of the reflected vector in this order: reflectAtLine() => x, y
Parameter:
x1 -- The x-coordinate of the vector to reflect.
y1 -- The y-coordinate of the vector to reflect.
x2 -- The x-coordinate of the first point of the line.
y2 -- The y-coordinate of the first point of the line.
x3 -- The x-coordinate of the second point of the line.
y3 -- The y-coordinate of the second point of the line.
Test:
>>> x, y = reflectAtLine( -2, -7, -2, 3, 4, -2 )
>>> print( '{0:.2f}, {1:.2f}'.format(x, y) )
6.52, 3.23
>>> x, y = reflectAtLine( -4, 2, 0, -2, 0, 2 )
>>> print( '{0:.2f}, {1:.2f}'.format(x, y) )
4.00, 2.00
'''
# Vector between both points aka the line.
dx = x3 - x2
dy = y3 - y2
# Calculate normal with unit length.
length = pythagorean.solveC( dy, dx )
nx = -dy
ny = dx
if not comparison.floatEqual( length, 0, 0.00001 ):
nx /= length
ny /= length
# Dot product of vector 1 and normal.
dotProduct = x1 * nx + y1 * ny
# The reflected vector.
x = x1 - 2 * nx * dotProduct
y = y1 - 2 * ny * dotProduct
return x, y
