def __init__(self, density=1, pos=[0, 0], offsets=[], **kwargs):
sides = []
for o in offsets:
sides.append(Vector2(o))
polygon_mass_of_center_of_mass = Vector2(0)
total_polygon_mass = 0
total_polygon_momi = 0
for i in range(len(sides)):
triangle_area = (Vector2.cross(sides[i], sides[i - 1])) / 2
triangle_mass = density * triangle_area
total_polygon_mass += triangle_mass
triangle_momi = triangle_mass / 6 * (
sides[i - 1].magnitude()**2 + sides[i].magnitude()**2 +
Vector2.dot(sides[i - 1], sides[i]))
total_polygon_momi += triangle_momi
triangle_mass_of_center_of_mass = triangle_mass * (1 / 3) * (
sides[i - 1] + sides[i])
polygon_mass_of_center_of_mass += triangle_mass_of_center_of_mass
polygon_center_of_mass = polygon_mass_of_center_of_mass / total_polygon_mass
# move origin to center of mass
new_offsets = []
for o in offsets:
new_offsets.append(o - polygon_center_of_mass)
new_pos = pos + polygon_center_of_mass
momi_center_of_mass = total_polygon_momi - (
total_polygon_mass * polygon_center_of_mass.magnitude()**2)
# call superclass constructor
super().__init__(mass=total_polygon_mass,
momi=momi_center_of_mass,
pos=new_pos,
offsets=new_offsets,
**kwargs)
def project_shape(axis: Vector2,
points: list[Vector2]) -> tuple[float, float]:
dot_products = [axis.dot(point) for point in points]
return min(dot_products), max(dot_products)
