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8.4

How do a find quaternion rotation from local and world coordinate systems?

Asked by ImNotJimboJones in 3D Game Programming, OpenGL Graphics & Game Programming, Algorithms

Tags: quaternion lookat orientation, rotation vector coordinate, quaternion, opengl, orientation, glulookat, rotation

I am working with OpenGL, in the planning stages of a generic class describing 3D objects. I am trying to design the orientation control and have run into the following issue...

I'm not sure yet whether I will physically store an object's orientation based on rotation, or forward/up vectors, but in either case, I want to be able to get and set the object's orientation in terms of both.

I can't seem to figure out how to find quaternion (or axis/angle or Euler angle) rotation given forward/up vectors.

Regardless of chosen base reference, I will need this conversion to implement rotational get/set as well as a pseudo-gluLookAt equivalent. If I store orientation based on forward/up vector, I will need to convert during setOrientation(Quaternion quat) and if I store orientation based on rotation, I will need to convert in order to reference local axes (the forward vector, etc).

I've looked at the mesa source for gluLookAt, but it was of little help. The implementation converts the forward/up vectors directly to a transformation matrix. I have, however, included it as reference (maybe someone knows how to get a quaternion from gluLookAt's resulting matrix?).

thanks in advance for any insight.

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             void GLAPIENTRY
gluLookAt(GLdouble eyex, GLdouble eyey, GLdouble eyez,
	  GLdouble centerx, GLdouble centery, GLdouble centerz,
	  GLdouble upx, GLdouble upy, GLdouble upz)
{
   GLdouble m[16];
   GLdouble x[3], y[3], z[3];
   GLdouble mag;
 
   /* Make rotation matrix */
 
   /* Z vector */
   z[0] = eyex - centerx;
   z[1] = eyey - centery;
   z[2] = eyez - centerz;
   mag = sqrt(z[0] * z[0] + z[1] * z[1] + z[2] * z[2]);
   if (mag) {			/* mpichler, 19950515 */
      z[0] /= mag;
      z[1] /= mag;
      z[2] /= mag;
   }
 
   /* Y vector */
   y[0] = upx;
   y[1] = upy;
   y[2] = upz;
 
   /* X vector = Y cross Z */
   x[0] = y[1] * z[2] - y[2] * z[1];
   x[1] = -y[0] * z[2] + y[2] * z[0];
   x[2] = y[0] * z[1] - y[1] * z[0];
 
   /* Recompute Y = Z cross X */
   y[0] = z[1] * x[2] - z[2] * x[1];
   y[1] = -z[0] * x[2] + z[2] * x[0];
   y[2] = z[0] * x[1] - z[1] * x[0];
 
   /* mpichler, 19950515 */
   /* cross product gives area of parallelogram, which is < 1.0 for
    * non-perpendicular unit-length vectors; so normalize x, y here
    */
 
   mag = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
   if (mag) {
      x[0] /= mag;
      x[1] /= mag;
      x[2] /= mag;
   }
 
   mag = sqrt(y[0] * y[0] + y[1] * y[1] + y[2] * y[2]);
   if (mag) {
      y[0] /= mag;
      y[1] /= mag;
      y[2] /= mag;
   }
 
#define M(row,col)  m[col*4+row]
   M(0, 0) = x[0];
   M(0, 1) = x[1];
   M(0, 2) = x[2];
   M(0, 3) = 0.0;
   M(1, 0) = y[0];
   M(1, 1) = y[1];
   M(1, 2) = y[2];
   M(1, 3) = 0.0;
   M(2, 0) = z[0];
   M(2, 1) = z[1];
   M(2, 2) = z[2];
   M(2, 3) = 0.0;
   M(3, 0) = 0.0;
   M(3, 1) = 0.0;
   M(3, 2) = 0.0;
   M(3, 3) = 1.0;
#undef M
   glMultMatrixd(m);
 
   /* Translate Eye to Origin */
   glTranslated(-eyex, -eyey, -eyez);
 
}
           
         

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How do a find quaternion rotation from local and world coordinate systems?

Asked by ImNotJimboJones in 3D Game Programming, OpenGL Graphics & Game Programming, Algorithms

Tags: quaternion lookat orientation, rotation vector coordinate, quaternion, opengl, orientation, glulookat, rotation

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