Hi Joshua,
Sorry I haven't replied to you earlier. Once my email piles up, it takes
some time for me to go over it.
We basically have two translations. The one implemented by Pablo, and
used by Hugin, and the one implemented by Dev and I, which is not
directly available from Hugin.
I don't think we have this well documented, but let me try to explain
you how it works.
Any photo is mapped to the sphere, from the sphere, it is then remapped
to the corresponding output projection. This imposes a big limitation in
linear panoramas: they are not really linear, they are slices of the
sphere.
In a previous message I listed the order in which the remapping
happens. Remember, it is done backwards (any point of the output
projection is mapped back to each point in the source images.
In the panotools model (also used by Nona and Hugin), the center of a
photo is the center of the world, with X and Y in the usual
direction, and normalized according to their field of view and input
projection with respect to the area it would cover in the sphere.
I really don't know the way the Tr[XYZ] parameters work, but the code is
easy to read, and Pablo can probably answer any questions you have:
plane_transfer_from_camera is the inverse, if I remember correctly.
Some notes:
* mp->distance is a used to normalize the distances in the image (to a
unit sphere).
* the pointer variables are the outputs, and the non-pointers, the
inputs.
/** transfer a point from the master camera through a plane into camera
* at TrX, TrY, TrZ using the plane located at Te0 (yaw), Te1 (pitch)
*/
int plane_transfer_to_camera( double x_dest, double y_dest, double * x_src, double * y_src, void * params)
{
// params: distance, x1,y1,z1
double plane_coeff[4];
double p1[3];
double p2[3];
double intersection[3];
// compute ray of sight for the current pixel in
// the master panorama camera.
// camera point
p1[0] = p1[1] = p1[2] = 0;
// point on sphere.
cart_erect(x_dest, y_dest, &p2[0], mp->distance);
// compute plane description
cart_erect(DEG_TO_RAD(mp->test[0]), -DEG_TO_RAD(mp->test[1]),
&plane_coeff[0], 1.0);
// plane_coeff[0..2] is both the normal and a point
// on the plane.
plane_coeff[3] = - plane_coeff[0]*plane_coeff[0]
- plane_coeff[1]*plane_coeff[1]
- plane_coeff[2]*plane_coeff[2];
/*
printf("Plane: y:%f p:%f coefficients: %f %f %f %f, ray direction: %f %f %f\n",
mp->test[0], mp->test[1], plane_coeff[0], plane_coeff[1], plane_coeff[2], plane_coeff[3],
p2[0],p2[1],p2[2]);
*/
// perform intersection.
if (!line_plane_intersection(plane_coeff, p1, p2, &intersection[0])) {
// printf("No intersection found, %f %f %f\n", p2[0], p2[1], p2[2]);
return 0;
}
// compute ray leading to the camera.
intersection[0] -= mp->trans[0];
intersection[1] -= mp->trans[1];
intersection[2] -= mp->trans[2];
// transform into erect
erect_cart(&intersection[0], x_src, y_src, mp->distance);
/*
printf("pano->plane->cam(%.1f, %.1f, %.1f, y:%1f,p:%1f): %8.5f %8.5f -> %8.5f %8.5f %8.5f -> %8.5f %8.5f\n",
mp->trans[0], mp->trans[1], mp->trans[2], mp->test[0], mp->test[1],
x_dest, y_dest,
intersection[0], intersection[1], intersection[2],
*x_src, *y_src);
*/
return 1;
}
/** transfer a point from a camera centered at x1,y1,z1 into the camera at x2,y2,z2 */
int plane_transfer_from_camera( double x_dest, double y_dest, double * x_src, double * y_src, void * params)
{
double phi, theta;
double plane_coeff[4];
double p1[3];
double p2[3];
double intersection[3];
// params: MakeParams
// compute ray of sight for the current pixel in
// the master panorama camera.
// camera point
p1[0] = mp->trans[0];
p1[1] = mp->trans[1];
p1[2] = mp->trans[2];
// point on sphere (direction vector in camera coordinates)
cart_erect(x_dest, y_dest, &p2[0], mp->distance);
// add camera position to get point on ray
p2[0] += p1[0];
p2[1] += p1[1];
p2[2] += p1[2];
// compute plane description
cart_erect(DEG_TO_RAD(mp->test[0]), -DEG_TO_RAD(mp->test[1]),
&plane_coeff[0], 1.0);
// plane_coeff[0..2] is both the normal and a point
// on the plane.
plane_coeff[3] = - plane_coeff[0]*plane_coeff[0]
- plane_coeff[1]*plane_coeff[1]
- plane_coeff[2]*plane_coeff[2];
/*
printf("Plane: y:%f p:%f coefficients: %f %f %f %f, ray direction: %f %f %f\n",
mp->test[0], mp->test[1], plane_coeff[0], plane_coeff[1], plane_coeff[2], plane_coeff[3],
p2[0],p2[1],p2[2]);
*/
// compute intersection
if (!line_plane_intersection(plane_coeff, p1, p2, &intersection[0])) {
//printf("No intersection found, %f %f %f\n", p2[0], p2[1], p2[2]);
return 0;
}
// the intersection vector is the vector of the ray of sight from
// the master panorama camera.
// transform into erect
erect_cart(&intersection[0], x_src, y_src, mp->distance);
/*
printf("cam->plane->pano(%.1f, %.1f, %.1f, y:%1f,p:%1f): %8.5f %8.5f -> %8.5f %8.5f %8.5f -> %8.5f %8.5f\n",
mp->trans[0], mp->trans[1], mp->trans[2], mp->test[0], mp->test[1],
x_dest, y_dest,
intersection[0], intersection[1], intersection[2],
*x_src, *y_src);
*/
return 1;
}
Joshua Stults twisted the bytes to say:
Joshua> Hello Professor German,
Joshua> I am trying to learn more of the details of the Hugin software and saw
Joshua> your contributions on the mailing list about the new mosaic mode that
Joshua> includes translations (TrX, TrY, TrZ).
http://groups.google.com/group/hugin-ptx/browse_thread/thread/1de4517...
http://groups.google.com/group/hugin-ptx/browse_thread/thread/8b98de4...
Joshua> Is there a place that the coordinate system for these fits (all six
Joshua> degrees of freedom) is documented? I assume that it is a standard
Joshua> right-handed coordinate system (with yaw about y-axis, roll about
Joshua> z-axis, pitch about x-axis), but how is the positive direction
Joshua> defined? I am trying to use the fitted camera positions as a modeling
Joshua> aid. Thanks for any help / pointers you can provide.
Joshua> --
Joshua> Joshua Stults
Joshua> daytondiode.blogspot.com
--
--
Daniel M. German
http://turingmachine.org/
http://silvernegative.com/
dmg (at) uvic (dot) ca
replace (at) with @ and (dot) with .
