Camera parameters for "ideal" camera?

Hello,

Recently I've been looking into an error characterization of the
ARToolKit, using OpenGL to render images of markers into a framebuffer,
which is then fed back into ARToolKit as if the framebuffer had come from
an ideal camera.

If I understand the meanings of the camera parameters correctly, a
rectangular viewport with dimensions (w,h) subtending theta degrees
horizontally, e.g., the viewpoint given by

  double w, h, theta;

  glViewport(0, 0, (GLsizei) w, (GLsizei) h);
  glMatrixMode(GL_PROJECTION);
  glLoadIdentity();
  gluPerspective(theta, w / h, 1.0, 100.0);

should have a corresponding intrinsic camera matrix as follows:

  {{ a,   0.0, w / 2.0},
   { 0.0, a,   h / 2.0},
   { 0.0, 0.0, 1.0    }}

where a = (w / 2.0) * tan((M_PI * theta / 180.0) / 2.0).  Distortion
parameters are {0.0, 0.0, 1.0, 1.0}.  (I've arbitrarily chosen a focal
distance of 1.0.)

Now, if my windows are square (w = h), this is great: the outputs more or
less match the inputs, up to a linear scale and offset.  When w != h,
though, I start to see nonlinearities in the output from ARToolKit.

Before I dig any further, could one of you kind souls tell me if I am
somehow confused about these ideal camera parameters, or am missing
something obvious?

Thanks,
						Konrad Schroder
						perseant@h .......

From:	Konrad Schroder <perseant@h .......>	Received:	Sep 25, 2003
To	artoolkit@h ..................
Subject:	Camera parameters for "ideal" camera?
Hello, Recently I've been looking into an error characterization of the ARToolKit, using OpenGL to render images of markers into a framebuffer, which is then fed back into ARToolKit as if the framebuffer had come from an ideal camera. If I understand the meanings of the camera parameters correctly, a rectangular viewport with dimensions (w,h) subtending theta degrees horizontally, e.g., the viewpoint given by double w, h, theta; glViewport(0, 0, (GLsizei) w, (GLsizei) h); glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluPerspective(theta, w / h, 1.0, 100.0); should have a corresponding intrinsic camera matrix as follows: {{ a, 0.0, w / 2.0}, { 0.0, a, h / 2.0}, { 0.0, 0.0, 1.0 }} where a = (w / 2.0) * tan((M_PI * theta / 180.0) / 2.0). Distortion parameters are {0.0, 0.0, 1.0, 1.0}. (I've arbitrarily chosen a focal distance of 1.0.) Now, if my windows are square (w = h), this is great: the outputs more or less match the inputs, up to a linear scale and offset. When w != h, though, I start to see nonlinearities in the output from ARToolKit. Before I dig any further, could one of you kind souls tell me if I am somehow confused about these ideal camera parameters, or am missing something obvious? Thanks, Konrad Schroder perseant@h .......