![]() moving from the positive X axis through the first quadrant to the positive Y axis). It tells us that if we look from above, a positive rotation around the Z axis is an anticlockwise rotation (i.e. The right-hand grip rule comes into play here. Rather than thinking of them as just rotating points about the origin, we can think of them as rotating around the Z axis. Suddenly, this gives us a new approach to thinking about our 2D rotations. According to the right-hand rule, the Z direction is “out of the page” compared to the typical X-Y plane. When we add a third dimension, we add it in the Z direction. The first step that we’ll take in exploring 3D rotations is to simply imagine this flat plane existing within a 3D world. So far the rotations we have been looking at have been occurring in the X-Y plane, the normal 2D plane. However, the topic of 3D rotations in general is actually quite complicated and the maths can get a little mind-bending. Next, we saw that by using a 3x3 matrix and homogenous coordinates we are able to represent a translation in 2D, and in fact we can combine that with our rotation matrix to express any combination of rotation and translation in 2D using a single 3x3 matrix.īut we don’t live in a flat, two-dimensional paper world, we live in a 3D space where we can rotate things in all sorts of complicated ways! So how can we take what we’ve learnt about transformations in 2D and apply it to 3D problems? Extending into the third dimensionįor the rest of this post we’ll be exploring 3D rotation matrices, which aren’t too difficult to get the hang of once you’re on top of the 2D ones. We saw that using a single 2x2 matrix we can represent a whole host of transformations in the 2D plane - rotations in particular. First, let’s recap what we’ve covered so far.
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