Integral

One nice outil is integrate over the shape.

Since we describe the shapes by its boundaries, we transform the integral into a boundary integral by using Green’s theorem.

Fortunatelly, the user can use it directly by using the functions. If you want to know more, check out the Integral Theory.

from shapepy import Primitive, IntegrateShape

# Creates a square of side 2 and centered at origin (0, 0)
square = Primitive.square(side = 2)
IntegrateShape.area(square)  # 4

# Creates a circle of radius 1 and centered at origin (0, 0)
circle = Primitive.circle(radius = 1)
IntegrateShape.area(circle)  # 3.142221071689924

For any polynomial

from shapepy import Primitive, IntegrateShape

square = Primitive.square(side = 2, center = (3, 4))
area = IntegrateShape.polynomial(square, 0, 0)  # 4
momentum_x = IntegrateShape.polynomial(square, 1, 0)  # 12
momentum_y = IntegrateShape.polynomial(square, 0, 1)  # 16
inertia_xx = IntegrateShape.polynomial(square, 2, 0)  # 112/3
inertia_xy = IntegrateShape.polynomial(square, 1, 1)  # 48
inertia_yy = IntegrateShape.polynomial(square, 0, 2)  # 196/3