def closest_point(self, p):
"""Return the point on the segment that is closest to p, and the distance to it"""
a, b = P.solve(self.dir, self.dir.perp(), p - self.p)
if 0 < a < 1:
return self.p + self.dir * a, self.dir.norm() * abs(b)
p_dist, q_dist = p.dist(self.p), p.dist(self.q)
if p_dist < q_dist:
return self.p, p_dist
else:
return self.q, q_dist
def intersect_with_circle(self, center_point, radius):
"""Intersection of segment object with circle. Returns a segment holding either the two
points intersecting the circle, the point intersecting and the endpoint contained within
the circle, or None (if no intersection exists)"""
# First find the closest point on the line.
# work in the frame of reference where self.p is zero
segment_direction = self.dir
segment_norm = segment_direction.norm()
perp = segment_direction.perp()
# solve the equation a*segment_direction+b*perp=center_point-self.p, where a and b are
# the coefficients of the vectors we are looking for. segment_direction and perp are
# perpendicular and so represent a basis in which we can define a linear combination of
# them to get center_point-self.p.
a, b = P.solve(segment_direction, perp, center_point - self.p)
height = abs(
b
) * segment_norm # the height of the triangle created by the intersection
# points and the center_point
if height > radius:
# no intersections
return None
base_size = np.sqrt(radius * radius - height *
height) / segment_norm # base_size is normalized
# to the size of segment_direction
# locations of intersections on the vector segment_direction
left = a - base_size
right = a + base_size
if right < 0 or left > 1:
# entire segment is outside of the circle
return None
# Return segment in absolute frame of reference, max and min used for cases where there
# is only one intersection
return S(self.p + segment_direction * max(0, left),
self.p + segment_direction * min(1, right))
def intersection_params(self, other):
a, neg_b = P.solve(self.dir, other.dir, other.p - self.p)
if not a:
return None, None
return a, -neg_b