def collide_wall(self, p):
restitution = self.restitution * p.restitution
# First, check that we haven't crossed through the wall due to
# extreme speed and low framerate.
intersection = intersect_segments(self.p1, self.p2, p.last_pos, p.pos)
if intersection:
p.pos = p.last_pos
p.rebound(self.normal, intersection, restitution)
return
# Find vectors to each endpoint of the segment.
v1 = vec.vfrom(self.p1, p.pos)
v2 = vec.vfrom(self.p2, p.pos)
# Find a perpendicular vector from the wall to p.
v_dist = vec.proj(v1, self.normal)
# Test distance from the wall.
radius2 = p.radius**2
if vec.mag2(v_dist) > radius2:
return
# Test for collision with the endpoints of the segment.
# Check whether p is too far off the end of the segment, by checking
# the sign of the vector projection, then a radius check for the
# distance from the endpoint.
if vec.dot(v1, self.tangent) < 0:
if vec.mag2(v1) <= radius2:
p.rebound(v1, self.p1, restitution)
return
if vec.dot(v2, self.tangent) > 0:
if vec.mag2(v2) <= radius2:
p.rebound(v2, self.p2, restitution)
return
# Test that p is headed toward the wall.
if vec.dot(p.velocity, v_dist) >= c.epsilon:
return
# We are definitely not off the ends of the segment, and close enough
# that we are colliding.
p.rebound(self.normal, vec.sub(p.pos, v_dist), restitution)
def collide_wall(self, p):
restitution = self.restitution * p.restitution
# First, check that we haven't crossed through the wall due to
# extreme speed and low framerate.
intersection = intersect_segments(self.p1, self.p2, p.last_pos, p.pos)
if intersection:
p.pos = p.last_pos
p.rebound(self.normal, intersection, restitution)
return
# Find vectors to each endpoint of the segment.
v1 = vec.vfrom(self.p1, p.pos)
v2 = vec.vfrom(self.p2, p.pos)
# Find a perpendicular vector from the wall to p.
v_dist = vec.proj(v1, self.normal)
# Test distance from the wall.
radius2 = p.radius**2
if vec.mag2(v_dist) > radius2:
return
# Test for collision with the endpoints of the segment.
# Check whether p is too far off the end of the segment, by checking
# the sign of the vector projection, then a radius check for the
# distance from the endpoint.
if vec.dot(v1, self.tangent) < 0:
if vec.mag2(v1) <= radius2:
p.rebound(v1, self.p1, restitution)
return
if vec.dot(v2, self.tangent) > 0:
if vec.mag2(v2) <= radius2:
p.rebound(v2, self.p2, restitution)
return
# Test that p is headed toward the wall.
if vec.dot(p.velocity, v_dist) >= c.epsilon:
return
# We are definitely not off the ends of the segment, and close enough
# that we are colliding.
p.rebound(self.normal, vec.sub(p.pos, v_dist), restitution)
def intersect_circles(center1, radius1, center2, radius2):
radius1 = abs(radius1)
radius2 = abs(radius2)
if radius2 > radius1:
return intersect_circles(center2, radius2, center1, radius1)
transverse = vec.vfrom(center1, center2)
dist = vec.mag(transverse)
# Check for identical or concentric circles. These will have either
# no points in common or all points in common, and in either case, we
# return an empty list.
if points_equal(center1, center2):
return []
# Check for exterior or interior tangent.
radius_sum = radius1 + radius2
radius_difference = abs(radius1 - radius2)
if (float_equal(dist, radius_sum) or float_equal(dist, radius_difference)):
return [
vec.add(center1, vec.norm(transverse, radius1)),
]
# Check for non intersecting circles.
if dist > radius_sum or dist < radius_difference:
return []
# If we've reached this point, we know that the two circles intersect
# in two distinct points.
# Reference:
# http://mathworld.wolfram.com/Circle-CircleIntersection.html
# Pretend that the circles are arranged along the x-axis.
# Find the x-value of the intersection points, which is the same for both
# points. Then find the chord length "a" between the two intersection
# points, and use vector math to find the points.
dist2 = vec.mag2(transverse)
x = (dist2 - radius2**2 + radius1**2) / (2 * dist)
a = ((1 / dist) * sqrt(
(-dist + radius1 - radius2) * (-dist - radius1 + radius2) *
(-dist + radius1 + radius2) * (dist + radius1 + radius2)))
chord_middle = vec.add(
center1,
vec.norm(transverse, x),
)
perp = vec.perp(transverse)
return [
vec.add(chord_middle, vec.norm(perp, a / 2)),
vec.add(chord_middle, vec.norm(perp, -a / 2)),
]
def rebound(self, normal, point=None, restitution=1):
# Split into normal and tangential components.
tangent = vec.perp(normal)
v_tangent = vec.proj(self.velocity, tangent)
v_normal = vec.proj(self.velocity, normal)
# Invert normal component and recombine, with restitution.
v_normal = vec.neg(v_normal)
self.velocity = vec.add(v_tangent, vec.mul(v_normal, restitution))
# If the particle is partially inside the wall, move it out.
if point is not None:
v = vec.vfrom(point, self.pos)
if vec.mag2(v) < self.radius ** 2:
v = vec.norm(v, self.radius)
self.pos = vec.add(point, v)
def rebound(self, normal, point=None, restitution=1):
# Split into normal and tangential components.
tangent = vec.perp(normal)
v_tangent = vec.proj(self.velocity, tangent)
v_normal = vec.proj(self.velocity, normal)
# Invert normal component and recombine, with restitution.
v_normal = vec.neg(v_normal)
self.velocity = vec.add(
v_tangent,
vec.mul(v_normal, restitution),
)
# If the particle is partially inside the wall, move it out.
if point is not None:
v = vec.vfrom(point, self.pos)
if vec.mag2(v) < self.radius**2:
v = vec.norm(v, self.radius)
self.pos = vec.add(point, v)
def intersect(p1, p2):
distance2 = vec.mag2(vec.vfrom(p1.pos, p2.pos))
return distance2 <= (p1.radius + p2.radius) ** 2
def closest_point_to(target, points):
return min(
points,
key=lambda p: vec.mag2(vec.vfrom(target, p))
)
def intersect_circles(center1, radius1, center2, radius2):
radius1 = abs(radius1)
radius2 = abs(radius2)
if radius2 > radius1:
return intersect_circles(center2, radius2, center1, radius1)
transverse = vec.vfrom(center1, center2)
dist = vec.mag(transverse)
# Check for identical or concentric circles. These will have either
# no points in common or all points in common, and in either case, we
# return an empty list.
if points_equal(center1, center2):
return []
# Check for exterior or interior tangent.
radius_sum = radius1 + radius2
radius_difference = abs(radius1 - radius2)
if (
float_equal(dist, radius_sum) or
float_equal(dist, radius_difference)
):
return [
vec.add(
center1,
vec.norm(transverse, radius1)
),
]
# Check for non intersecting circles.
if dist > radius_sum or dist < radius_difference:
return []
# If we've reached this point, we know that the two circles intersect
# in two distinct points.
# Reference:
# http://mathworld.wolfram.com/Circle-CircleIntersection.html
# Pretend that the circles are arranged along the x-axis.
# Find the x-value of the intersection points, which is the same for both
# points. Then find the chord length "a" between the two intersection
# points, and use vector math to find the points.
dist2 = vec.mag2(transverse)
x = (dist2 - radius2**2 + radius1**2) / (2 * dist)
a = (
(1 / dist) *
sqrt(
(-dist + radius1 - radius2) *
(-dist - radius1 + radius2) *
(-dist + radius1 + radius2) *
(dist + radius1 + radius2)
)
)
chord_middle = vec.add(
center1,
vec.norm(transverse, x),
)
perp = vec.perp(transverse)
return [
vec.add(chord_middle, vec.norm(perp, a / 2)),
vec.add(chord_middle, vec.norm(perp, -a / 2)),
]
def closest_point_to(target, points):
return min(points, key=lambda p: vec.mag2(vec.vfrom(target, p)))
def intersect(p1, p2):
distance2 = vec.mag2(vec.vfrom(p1.pos, p2.pos))
return distance2 <= (p1.radius + p2.radius)**2