def reflect( self, x, y ):
''' Calculates reflection between two circles. Returns the resulting momentum vector.
Takes the position of the reflection point as argument.
Test:
>>> from data import circle
>>> from data import vector2d
>>> c1 = circle.Circle()
>>> c1.position.x = -4
>>> c1.position.y = 2
>>> c1.radius = 2
>>> c1.momentum = vector2d.Vector2d( 4, 2 )
>>> c2 = circle.Circle()
>>> c2.position.x = 0
>>> c2.position.y = 2
>>> c2.radius = 2
>>> x = -2
>>> y = 2
>>> reflector = CircleCircleReflector( c1, c2 )
>>> v = reflector.reflect( x, y )
>>> print( '{0:.2f}, {1:.2f}'.format(v.x, v.y) )
-4.00, 2.00
'''
# Move reflection point to origin.
reflectionX = x - self._circle2.position.x
reflectionY = y - self._circle2.position.y
# Prepare comparison.
epsilon = 0.001
# Default values are used it the tangent line is vertical.
pointX1 = reflectionX
pointY1 = -1
pointX2 = reflectionX
pointY2 = 1
# Calculate tangent line y = mx + b
if not comparison.floatEqual( reflectionY, 0, epsilon ):
# Tangent line is perpendicular to the radius, so it's slope m will be a negative reciprocal
# of the slope of the line intersecting the reflection point.
m = -(reflectionX / reflectionY)
# Find b with the slope and the reflection point. Default value is used if tangent line is
# horizontal.
b = reflectionY
if not comparison.floatEqual( reflectionX, 0, epsilon ):
b = reflectionY / (m * reflectionX)
# Calculate tangent line points left and right of reflection point.
pointX1 = reflectionX - 1
pointY1 = m * pointX1 + b
pointX2 = reflectionX + 1
pointY2 = m * pointX2 + b
# Calculate result.
x, y = vector.reflectAtLine( self._circle1.momentum.x, self._circle1.momentum.y,
pointX1, pointY1, pointX2, pointY2 )
return vector2d.Vector2d( x, 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