Quaternion Explorer

The definition of Quaternion is a little more complex, but the use-case of a Quaternion is actually pretty easy to show. In this explorer, you’ll see how you define an axis with the sliders on the left then define the rotation around that axis with the slider on the right. This essentially shows you everything you need to create a Quaternion: an axis defined by three variables (x, y, z) and a rotation around that axis.

Please note that no matter what the axis is, if the rotation is zero, then the “Back” face of Cube looks straight at you. So try changing the axis sliders, scrub the rotation slider from 0 to 360 and back. Then change the axis sliders again, scrub from 0 to 360 again and you’ll notice how the rotation around the axis differs. Also, (0,0,0) isn’t an axis, so you can’t rotate around it

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Allow me to explain this a bit more. Here’s a few things to try to “orient” yourself

rotationX (x:1, y:0, z:0)

Move all the axis sliders to those values, then move the rotation slider from 0 – 360 and you’ll see your traditional rotationX (since it rotates around the X axis). You may be thinking to yourself, “Why do I need this? Why don’t I just use rotationX?” I would answer, “Because this way, you don’t limit yourself to just rotationX. You can define ANY rotation with these four numbers.” If you’ve ever tried to control a combination of rotationX, rotationY, and rotationZ at the same time, I’m sure you’ve run into difficulty.

Here are two other axes you’re familiar with:
rotationY (x:0, y:1, z:0)
rotationZ (x:0, y:0, z:1)

As a follow-up post, I’m working on a slerp explorer that will show you how to transition from any rotation to any other rotation which is where the power of Quaternions really shine.

As a final note, try leaving the rotation slider at 180 then adjusting the axis sliders. You will see the cube move at the same time as the axis, but it may look like it’s “lagging behind”. This effect comes from the cube adjusting itself to be rotated 180 around the axis. The cube is not following the axis in any way.

Don’t be distracted by the axis, it’s only there for reference. What’s important is the cube rotates around the axis.

Tags: quaternion