[Algorithms] Direction+Up vector to Axis/angle

[Max G. <gi...@li...>]

Hello!

Question: how to convert direction and up vectors to axis/angle
rotation?
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Similar subject has been discussed recently in 'vector+angle' thread but
without any real answer.

In my solution I tried to duplicate Mesa3D sources but I must have done
something wrong... Can you explain me what should I do? Or maybe someone
could take a look at my code (I use Point3d class for both vertices and
vectors).

My camera is based on OpenGL scheme and is specified by: position,
axis/angle rotation, fov, near/far clipping planes.

public void lookAt(Point3d eye, Point3d target, Point3d up)
  {
  setPosition(eye); // updates camera position

  // this is based on Mesa3D's glu.c lookAt(...) method
  Point3d z = eye.sub(target).normalize();
  Point3d y = up;
  Point3d x = y.cross(z);
  y = z.cross(x).normalize();
  x.normalize();

  // converting to Axis/Angle
  Matrix3d m = new Matrix3d(x.x, x.y, x.z, y.x, y.y, y.z, z.x, z.y,
z.z);
  rotation = new AxisAngled(m).normalize();
  }

and from class AxisAngled:

 public void set(Matrix3d matrix)
  {
  // x, y and z must be computed prior to computing angle
  // (because of axisLength() which needs them)
  x = matrix.e8 - matrix.e6;
  y = matrix.e3 - matrix.e7;
  z = matrix.e4 - matrix.e2;
  a = Math.atan2(axisLength() / 2.0, (matrix.e1 + matrix.e5 + matrix.e9
- 1.0) / 2.0);
  }

Any suggestions / fixes?

Can this be done simpler (without intermediate matrix stage)? Do you
have *any* working code that converts vectors to axis/angle?

Help!

Bye,
Max


--
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Max Gilead                     gi...@li...
XMage library      http://xmage.sourceforge.net
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-- Sex on TV is bad. You might fall off...