Moving a Sphere so its Z-Axis faces a direction?

All right, I think I see what you mean. Take a ball-- you must have one lying around. Mark a spot on it to indicate an axis of interest.

Now pick a direction in which you want the axis to point. The trick is to rotate the ball in place to bring the axis to the right direction-- we'll get to the rolling in a minute. The obvious way is to move "directly", and if you do this a few times you'll notice that the axis around which you are rotating the ball is perpendicular to the axis you're trying to move.It's as if the spot is on the equator and you're rotating around the North-South axis.

Every time you pick a new direction, that direction and your marked axis determine the new equator. Also notice (this may be tricky) that you can draw a great circle (that's a circle that goes right around the sphere and divides it into equal halves) that goes between the mark and the destination, so that they're on opposite hemispheres, like mirror images. The poles are always on that circle.

Now suppose you're not free to choose the poles like that. You have a mark, you have a desired direction, so you have the great circle, and the north pole will be somewhere on the circle, but it could be anywhere. Imagine that someone else gets to choose it.

The mark will still rotate to the destination, but they won't be on the equator any more, they'll be at some other latitude. Now put the ball on the floor and roll it -- don't worry about the mark for now. Notice that it rotates around a horizontal axis, the poles, and touches the floor along a circle, the equator (which is now vertical).

The poles must be somewhere on the "waist" of the sphere, halfway up from the floor (don't call it the equator). If you pick the poles on that circle, you choose the direction of rolling. Now look at the marks, and draw the great circle that divides them.

The poles must be on that circle. Look where that circle crosses the "waist"; that's where your poles must be. Tell me if this makes sense, and we can put in the math.

Yep that makes sense. Did have to read it through a few times but I think I've got it now :) – Rob Hale Jun 12 at 16:14 1 @Rob Hale: good, that's enough to explain why the ball should roll in the (1,-1) direction in your second example. Now, are you familiar with the cross product of two vectors?

– Beta Jun 12 at 16:55 I've only ever used cross product to get the a perpendicular vector in world space. So Direction cross vect(0,0,1) for example I've not had to use it for anything more complex than that though. – Rob Hale Jun 12 at 17:28 OK it turns out the solution is far simpler than the explanation :) I ended up getting the Z-Axis of the sphere and adding the desired direction to it.

This gave me a direction the sphere could roll in that would result in it's Z-Axis pointing the correct way. – Rob Hale Jun 13 at 16:01 @Rob Hale: Umm... no, that won't work. Try your second example: the ball's Z-axis will rotate from Y to -X and back, never to X.

We still have a little ways to go; in a few hours I'll have time to edit my answer with the next part. – Beta Jun 13 at 16:16.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.