# How can I apply transformations to a geometry?#

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2023-12-06 21:43:10

Structures

In Tidy3D, all geometries can be translated, rotated, and scaled. These methods create a new copy of the original geometry with a transformation applied. For example, you can start with a tidy3d.Box centered at the origin and create a copy of it rotated around the z-axis:


box = tidy3d.Box(size=(2, 1, 1))

rotated_box = box.rotated(np.pi / 6, axis=2)

_ = rotated_box.plot(z = 0)



Transformed geometries can be further transformed. Composing transformations is as simple as cascading the method calls. In the following example, we create an ellipsoidal prism by scaling a primitive tidy3d.Cylinder and rotating it.


ellipsoid = tidy3d.Cylinder(radius=0.5, length=0.5, axis=1).scaled(x=2, y=1, z=1).rotated(np.pi / 4, axis=1)

_ = ellipsoid.plot(y=0)



A tidy3d.Transformed object contains an inner geometry and a transformation, written as a 4 x 4 matrix and applied to the (homogeneous) coordinates of the inner geometry. It is possible to define a Transformed object directly from the inner geometry and the transformation. To help create the most usual transformation matrices, the Transformed class has 3 static methods for translation, rotation, and scaling that can be used and combined (the @ operator can be used for matrix multiplication with numpy arrays).


rot = tidy3d.Transformed.rotation(np.pi / 3, axis=(1, 1, 1))
trans = tidy3d.Transformed.translation(1, 2, 0)
scale = tidy3d.Transformed.scaling(1, 1.25, 1)

# The box is first rotated, then translated, and finally scaled
transformed = td.Transformed(geometry=td.Box(size=(1, 1, 1)), transform=scale @ trans @ rot)