D Reflection

Some 3D object orientation cannot be obtained by rotation transformations and it requires additional reflection transformations. In 3D the reflection occurs on the plane. By analogy with the 2D reflection discussed earlier, 3D reflection of the plane is equivalent to a rotation around an axis in 4D space and back to the original 3D space.

Reflection about the xy plane changes only value of z for the object coordinate vector. In fact, they change the sign. Thus, the transformation matrix for reflection about the xy plane is:

(2.12)

For reflection about the yz plane:

(2.13)

For reflection about the xz plane:

(2.14)

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