How to efficiently rotate and translate a plane in 3D?

You need to be careful because normals don't necessarily transform like points do, and the distance is the perpendicular distance to the origin, so you have to compute d'= d + n. V . If all you're doing is translation and rotation, then you can rotate the normal and compute a new perpendicular distance.

But, if you're scaling your axes differently, or doing a general projective transformation, then you need to treat things differently.

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