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3D Matrix Transformations

Does anybody have a method to figuring out how a matrix relates to a 3D transformation for further maths, ie reflections and rotations. I’ve tried using a cardboard box to visualise it but this doesn’t help. Anybody have any ideas? :smile:

Reply 1

mqb2766

Original post by Mitchchambo

For rotations, just rotate in the plane where the angle is defined. So a rotation about the x-axis is a rotation in the y-z plane
https://en.wikipedia.org/wiki/Rotation_matrix
Remember to get the direction (sign) correct. This is a fairly common matrix transformation as multiple rotations just correspond to multiplying matrices and are another repesentation of the basic angle sum trig relationships.

For simple reflections, say in the plane defined by the x & y axis, flip the sign of the z value. More generally
http://www.math.niu.edu/~beachy/courses/240/02fall/sim_ex.pdf
(not verified fully) note the reflection plane passes through the origin.

Edit: to "derive" / verify, think about what happens to each of tthe unit vectors (1,0,0), (0,1,0), (0,0,1) when you multiply by the matrix.