def intersection_line_and_circle(cp: Position, cr: float, lp1: Position,
lp2: Position) -> List[Position]:
# Based on http://mathworld.wolfram.com/Circle-LineIntersection.html
lp1 = lp1.copy() - cp
lp2 = lp2.copy() - cp
d = lp2 - lp1
det = lp1.x * lp2.y - lp2.x * lp1.y
delta = cr**2 * d.norm**2 - det**2
if delta < 0:
return [] # No intersection
x1 = (det * d.y + np.sign(d.y) * d.x * np.sqrt(delta)) / (d.norm**2)
y1 = (-det * d.x + abs(d.y) * np.sqrt(delta)) / (d.norm**2)
if delta == 0:
return [Position(x1, y1) + cp] # Tangential
x2 = (det * d.y - np.sign(d.y) * d.x * np.sqrt(delta)) / (d.norm**2)
y2 = (-det * d.x - abs(d.y) * np.sqrt(delta)) / (d.norm**2)
return [Position(x1, y1) + cp, Position(x2, y2) + cp]
def normalize(vec: Position) -> Position:
if vec.norm == 0:
raise ZeroDivisionError
return vec.copy() / vec.norm