3D transformations use homogeneous coordinates and 4x4 matrices similarly to 2D transformations. There are basic transformations like identity, scale, translation, and mirroring as well as rotations around the X, Y, and Z axes represented by matrices. To reverse a rotation of q degrees, apply the inverse rotation R(-q) which has the same cosine elements but flipped sine elements, making it the transpose of the original rotation matrix.

2. 3D TransformationsSame idea as 2D transformationsHomogeneous coordinates: (x,y,z,w) 4x4 transformation matrices

3. Basic 3D TransformationsIdentityScaleTranslationMirror about Y/Z plane

4. Basic 3D TransformationsRotate around Z axis:Rotate around Y axis:Rotate around X axis:

5. Reverse RotationsQ: How do you undo a rotation of q, R(q)?A: Apply the inverse of the rotation… R-1(q) = R(-q) How to construct R-1(q) = R(-q)Inside the rotation matrix: cos(q) = cos(-q)The cosine elements of the inverse rotation matrix are unchangedThe sign of the sine elements will flipTherefore… R-1(q) = R(-q) = RT(q)