def lies_behind(p, poly):
#draw a line from the viewer's position to p, and see if it intersects the plane formed by poly.
#formula courtesy of https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection
a,b,c = poly
n = cross_product(b-a, c-a)
p0 = a
l = Point(0,0,1)
l0 = p
if dot_product(l,n) == 0:
#I think this only happens when the poly is viewed edge-on.
return False
d = dot_product(p0 - l0, n) / dot_product(l,n)
return d < 0
def reflect_speeds(normal_vector, v1_vector, v2_vector, m_1, m_2):
"""
TODO
"""
v1_eff = geometry.dot_product(normal_vector, v1_vector)
v2_eff = geometry.dot_product(normal_vector, v2_vector)
new_v1_eff, new_v2_eff = elastic_collision(v1_eff, -v2_eff, m_1, m_2)
new_v1_eff = geometry.vector_product(normal_vector, new_v1_eff)
new_v2_eff = geometry.vector_product(normal_vector, new_v2_eff)
v1_perpendicular = geometry.components(normal_vector, v1_vector)[1]
v2_perpendicular = geometry.components(normal_vector, v2_vector)[1]
new_v1_vector = geometry.vector_diff(v1_perpendicular, new_v1_eff)
new_v2_vector = geometry.vector_sum(v2_perpendicular, new_v2_eff)
return (new_v1_vector[0], new_v1_vector[1], new_v2_vector[0],
new_v2_vector[1])
def reflect_speeds(normal_vector, v1_vector, v2_vector, m_1, m_2):
"""
TODO
"""
v1_eff = geometry.dot_product(normal_vector, v1_vector)
v2_eff = geometry.dot_product(normal_vector, v2_vector)
new_v1_eff, new_v2_eff = elastic_collision(v1_eff, -v2_eff, m_1, m_2)
new_v1_eff = geometry.vector_product(normal_vector, new_v1_eff)
new_v2_eff = geometry.vector_product(normal_vector, new_v2_eff)
v1_perpendicular = geometry.components(normal_vector, v1_vector)[1]
v2_perpendicular = geometry.components(normal_vector, v2_vector)[1]
new_v1_vector = geometry.vector_diff(v1_perpendicular, new_v1_eff)
new_v2_vector = geometry.vector_sum(v2_perpendicular, new_v2_eff)
return (new_v1_vector[0], new_v1_vector[1],
new_v2_vector[0], new_v2_vector[1])
def line_segment_intersection(a,b,c,d):
#a line can be expressed as the set of points p for which
#(p - p0) dot n = 0
#where p0 is a point on the line and n is a normal vector to the line.
#the vector equation for a line segment is
#p = f*c + (1-f)*d = f*c - f*d + d = f*(c-d) + d
#where f is a number between 0 and 1 inclusive.
#
#(f*(c-d) + d - p0) dot n = 0
#((f*(c-d)) dot n) - ((p0 - d) dot n) = 0
#((f*(c-d)) dot n) = ((p0 - d) dot n)
#f*((c-d) dot n) = ((p0 - d) dot n)
#f = ((p0 - d) dot n) / ((c-d) dot n)
p0 = a
n = exp(1, (a-b).angle() + math.radians(90))
f = dot_product(p0-d, n) / dot_product(c-d, n)
if 0 <= f <= 1:
return (c+d)*f - d
return None
def test_dot_product(self):
self.assertEqual(geometry.dot_product([1, 2, 1], [1, 1, 2]), 5)
def angle_3d(a,b):
return math.acos(dot_product(a,b) / (a.magnitude() * b.magnitude()))