angle and axis of rotation given initial and final positions

[fabrival]

Hello, inside my application I need to detect collisions of a number of possible paths with terrain.
Every path is a collection of capsules and I know the position of every capsule in 3D space.
I need to use only the Bullet Collision Detection Library.
The btCapsuleShape represents a capsule around the Y axis. Now I need to place the associated Collision Objects in the right positions.
I suppose that, after some manipulation, the problem can be reduced to map one vector onto another in 3D space through a rotation around an axis.
In the examples that I've seen the axis is known and the final position is unknown. I need to do the inverse in the most efficient way because this operation will be performed for a great number of times.

What is the most efficient way of finding the angle and axis of rotation which map one vector onto another?

I've seen that a quaternion can be efficiently used to apply a rotation to a vector, but I haven't found examples for the inverse situation. Could anyone indicate such an example? Would it be as efficient as the direct approach?

Thanks in advance.

Fabrizio

[Erwin Coumans]

What API are you using? The btCollisionWorld::convexSweepTest takes a start and end transform.

Given a start and end orientation you can compute the axis and angle between both using btTransformUtil::calculateDiffAxisAngleQuaternion. See src\LinearMath\btTransformUtil.h

Is that what you need?
Thanks,
Erwin

[fabrival]

Thanks for your answer, Erwin!

With it I have realized that I made a wrong assumption: dealing with static paths (no time involved) I started working with the basic collision shapes and btCollisionWorld::contactPairTest(). Any hit, no matter if the closest one or not, would have stopped the test and discarded the path.
Now I see that btCollisionWorld::convexSweepTest () and btTransformUtil can be successfully used also in my case.

Thanks

Fabrizio