When I get done with this book, there are a few things I really want to wrap my poor brain around.
1. Quaternions. Apparently good for rotating things in 3D, avoids gimbal lock, which is something else I only vaguely understand, but think I know it when I see it. 🙂 Anyway, quaternions get into some complex concepts, like hyperspace and imaginary dimensions, the edge of the earth, and sea monsters. So I usually get scared and turn back.
2. Voronoi diagrams. They look like this:
Basically, each cell consists of all the points on the plane that are closer to the dot in that cell than to any other dot. I’ve actually accomplished this going through each pixel of a bitmap and measuring distances, but that seems pretty brute force. I know there are better ways, but it is more complex than it looks at first glance. Mario has had a go at this, and Robert has done beautiful stuff with them. I just want to understand them so I can do pretty things too.
There are probably more things, but those are on my mind now as things I’ve bumped into and bounced off of more than once.
Regarding quaternions, I think the deal is this…
If you don’t use quaternions and simply apply compound rotations around the x y and z axis, you get a wobbly rotation, which may not be what you want (sample below):
http://boing.urugate.com/esfera3d_wobbling.swf
Using Quaternions you can rotate around any fixed axis of your liking:
http://boing.urugate.com/esfera3d_fixed_axis.swf
Feel free to correct the hell out of me, cause I’m not a maths geek.
I had the very same feeling toward quaternions until recently. With the help of this book, I’ve understood the “why”, and that’s a big step foward for me.
The problem with the traditional “Euler way” is that, because you can express a rotation in more than one way, it’s hard to interpolate. For example, if you rotate an object by 90 on X, 90 on Y and -90 on Z (using xyz rotation order), you can end up at the same orientation that if you do only a rotation of 90 on Y. So you could interpolate between those two rotations and end up at the same visual orientation, and that’s not someting you want.
For the “how”, that’s still a bit mysterious to me…
Good Voronoi Diagram Resource: http://www.cs.berkeley.edu/~jrs/274/. Any of JRS’ topics are fairly well written.
Quaternions. Yes. Every time I’m doing something with Papervision I end up with the conclusion that I need to understand Quaternions.
So I bought two books last week:
http://www.amazon.de/gp/product/0691102988
http://www.amazon.de/gp/product/0486445186
Actually I didnt understand anything. They are written for maths geeks, not for me. Do you guys now a book which explains this stuff in an easy way?
Keith, cant you just understand everything and write a book about it? Im sure I would understand it 😉
Cheers,
Raphael
Quaternions are an interesting beast. Understanding the concept of Quaternions isn’t all that hard, however, I found it rather difficult to translate that concept into code.
In my experience, it helps to have a good spatial mind.
Out of all of the tutorials and lessons about Quaternions that I found online, back when they were new to me, this page helped me the most, and was most helpful in making the transition from theory to code.
http://www.cprogramming.com/tutorial/3d/quaternions.html
Hope it helps 😀
Hi all,
Keith, first congratulations for your ‘grand Oeuvre’, I’ve learnt so much reading your articles and following yours tutorials (and more recently reading your book ^^), it has always been inspiring and of a great help.
now I’d like to show you something. it’s about Delaunay triangulation and the Voronoï diagram in AS3 😉 http://en.nicoptere.net/?p=10
I wrote esppecially for you (mmmaaaaster) and I’m pretty sure you’ll find kick-ass graphic outputs for it 🙂
hope you’ll enjoy it.
+ big thanks to X for the link it’s indeed inspiring 😉
nicoptere, AWESOME. I can’t wait to dive into this and see what you’ve done. Unfortunately, that may have to wait a few weeks before I can really do much with it, but I’m sure I’ll have a peek. Thanks so much for sharing this. I love this community.
Hey Keith,
You might want to check out GCAL (http://www.cgal.org/). It’s an open-source computational geometry library which includes some code for generating voronoi diagrams. You may be able to get some ideas for a better algorithm there.
I love your book and your blog. Keep it up 🙂