"Bald Eagle" <cre### [at] netscapenet> wrote:

> So, I spent a bit of time working out how to do the "this object always faces
> the camera" thing,

And here's a bit more commentary to better explain how that works, and provide a
useful bit of code for future reference.

#macro FaceCamera (Object, CL)
 #local Min = min_extent (Object);
 #local Max = max_extent (Object);
 #local OL = Min + (Max-Min)/2;

 #declare CamL = CameraLocation;   // wherever you're putting it
 #declare CamD = vnormalize (OL-CamL);  // direction of camera view
  // One can alternately look at this as -Caml, translated to the object's
  // location by adding OL.  -CamL+OL = (OL-CamL)
 #declare CamR = vnormalize (vcross(y,CamD)); // to the right
  // The vector cross product gives a vector that is perpendicular to the two
  // given vectors.  If we're at the vertex (camera location) and we cross the
  // direction of view and the y-axis, we get a vector pointing out to the right
  // CamD and y are likely not perpendicular, so the resulting vcross is some
  // size != 1, so we normalize the size.
 #declare CamU = vnormalize (vcross(CamD,CamR)); // camera up
  // So now we have a view direction and a right vector, which are perpendicular
  // So we do another vector cross product, and get the new "up" vector
  // Which completes our new "frame of reference".
  // The tangent, normal, and binormal unit vectors, often called T, N, and B,


  // So now when we take the old x, y, and z basis vectors or normal POV-space
  // and move them to align with the new TNB vectors, your object whose
  // orientation was based upon x, y, and z is now based upon the new
  // T, N, and B vectors.
  // Since default camera points at z, and default orientation of most objects
  // is in the xy plane, the object is now in the same relative orientation
  // to the camera in the new TNB frame, and so always faces the camera.
 #declare Object_Transform =
 transform {
  matrix <
  CamR.x, CamR.y, CamR.z,
  CamU.x, CamU.y, CamU.z,
  CamD.x, CamD.y, CamD.z,
      0,      0,      0
  >
 }

 object {
  Object
  transform {Object_Transform}
 }
#end // end macro FaceCamera

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