Visualizing quaternions: An explorable video series

Post by adamnemecek » Sat, Oct 27, 2018, 4:07 PM UTC

yiyus wrote: post #22

adamnemecek wrote: post #5

I know I’m getting annoying with this but dual quaternions are even whackier. They are the best formalism for reasoning about 3D space developing over time. Here’s a cool demo http://www.chinedufn.com/dual-quaternion-shader-explained/ They seem to correspond to linear logic which is insanity.

You always write a similar comment but neither you or the page you link explain what is the advantage, or even the difference, of dual quaternions when compared to normal quaternions. However, the article linked in the site, actually gives a good explanation. Dual quaternions work not only rotations, but also translations. They provide a natural representation of rotations around arbitrary axis (not only around axis…

Post by yiyus » Sat, Oct 27, 2018, 7:51 PM UTC

adamnemecek wrote: post #31

yiyus wrote: post #22

Earlier quoted context omitted.

You always write a similar comment but neither you or the page you link explain what is the advantage, or even the difference, of dual quaternions when compared to normal quaternions. However, the article linked in the site, actually gives a good explanation. Dual quaternions work not only rotations, but also translations. They provide a natural representation of rotations around arbitrary axis (not only around axis…

I have posted it many times yes. You hit it on the head. They are very good for modeling for example rigid transformations or robot joints. They are a special case of GA. I used to very much into GA only to realize that dynamic 3D is the most interesting space, the other spaces are actually kinda boring.

Post by p0nce » Sun, Oct 28, 2018, 2:33 PM UTC

breatheoften wrote: post #32

p0nce wrote: post #23

Suppose you are standing anywhere on planet Earth, and you look at the horizon (not up, not down, so 360° of choice). A normalized quaternion encodes your position on the planet + the direction you are looking at on the horizon. It also encodes the rotation it would take to go from one such observer to another.

Does this assume the earth is a sphere? Can you keep the elegance of this coordinate encoding with convenient transformation operations and define somewhere a mapping from the quaternarion encoding of position into a non-homogenous oblate spheroid encoding like WGS84 ...?