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simulation/collision.py

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+def collide2d(a, b, e):
+    """Returns the velocities of balls a and b after collision. 
+
+    e is the *coefficient of restitution*, a parameter between 0 and 1 
+    which determines how much the objects bounce off each other. 
+    When e is 0, the two objects completely stick together. 
+    When e is 1, the two objects bounce off each other completely. 
+
+    This is a 2-dimensional collision because a and b each have a 2d 
+    velocity vector, like two balls moving on a plane. We can separate
+    each velocity vector into two components: a normal vector (pointed 
+    straight at the other ball) and a tangent vector (perpendicular to
+    the normal). The tangent vectors don't participate in the collision
+    at all, so we just need to calculate how the normal vectors change
+    after the collision. This is easier, since it's a 1-dimensional 
+    collision.
+
+    Afterwards we combine the updated normal vector with the tangent 
+    vector to get the resulting velocity vector for each ball.
+    """
+    a_to_b = b.position - a.position
+    av_normal = a.velocity.project(a_to_b)
+    av_tangent = a.velocity - av_normal
+    bv_normal = b.velocity.project(-a_to_b)
+    bv_tangent = b.velocity - bv_normal
+    av_normal_after, bv_normal_after = collide1d(av_normal, a.mass, bv_normal, b.mass, e)
+    av_after = av_normal_after + av_tangent
+    bv_after = bv_normal_after + bv_tangent
+    return av_after, bv_after
+
+def collide1d(av, am, bv, bm, e):
+    """Returns the velicoties of a and b after a 1-dimensional collision, 
+    where a and b are headed directly at each other. This formula is from Wikipedia: 
+    https://en.wikipedia.org/wiki/Elastic_collision#One-dimensional_Newtonian
+    """
+    velocity_center_of_mass = (av * am + bv * bm) / (am + bm)
+    av_after = velocity_center_of_mass * (1 + e) - av * e
+    bv_after = velocity_center_of_mass * (1 + e) - bv * e
+    return av_after, bv_after