How to rotate a path in 3D (computer sciences)

Question

I'm working on something in Unity3D (the game engine) where I have to modify a path/road in 3d space. The path consists of a collection of positions and quaternion-orientations (the orientation determines both the direction of the road, and the banking).

I'm having trouble rotating the the road the way I want it to.

I want to be able to rotate it using euler angles, rotating the path according to the startingpoint's orientation. (so the x-angle should rotate it around the first point's local x axis, etc.)

I thought the correct way to do this would be to do:

for (int i = 0; i < points.Count; i++)
{
   rotation = (Quaternion.Inverse(points[0].orientation) * Quaternion.Euler(eulerRotation) * points[0].orientation);
   points[i].orientation = rotation * points[i].orientation;
   points[i].position -= points[0].position;
   points[i].position = rotation * points[i].position;
   points[i].position += points[0].position;
}

But that doesn't seem to rotate it the way I want it to, the axes are wrong.

Any help?

Here's an image to show what I mean: roadscreenshot

It shows both the road before and after rotation (the upmoast road being its original orientation), It was supposed to rotate 30 degrees around the startingpoint's local x-axis, but clearly that's not how it rotated. The axes shown are the startingpoint's local axes, the x-axis is the red one.

Answer 1

If position and orientation of the points are given in global coordinate space, then you don't need to mix orientation into rotation as it has nothing to do with it.

rotationQuaternion = Quaternion.Euler(eulerRotation);
for (int i = 0; i < points.Count; i++)
{
   // If you use orientation as a rotation quaternion
   points[i].orientation = rotationQuaternion * points[i].orientation;
   points[i].position -= points[0].position;
   points[i].position = rotationQuaternion * points[i].position;
   points[i].position += points[0].position;
}

For better performance (at least I believe so), you might want to create Transform object from rotation and position of first point and apply it to positions of other points with one operation instead of three.