Databases and Systems

135
which is a cut at an arbitrary orientation through the voxel model. The viewing
coordinates define this section, how it is displayed on the screen and the transform
from screen to model coordinates for mapping data or DB query.
To define the sectioning plane two angles are required to define the viewing
direction and a perpendicular distance from a fixed point will define the section. For
the viewing angles we define pitch as the angle by which the view is tilted away from
the vertical, and yaw as the rotation of that view around the vertical. These two
angles are the usual spherical coordinates, and and define the normal to the
viewing plane. The other parameters that define the plane are the fixed point f and
distance d.
The transformation from the image coordinate r = (x,y,z) T to section coordinate r’
= (x’,y’,z’) T is given by
r’ =R(r - f), with z’ = d,
and the rotation matrix R is defined in terms of rotation by the three Eulerian angles
(xsi, eta, zeta) [18] by
The two Eulerian angles and are equal to pitch and yaw respectively and with the
fixed point and distance determine the section plane.
To determine the transform from screen to voxel coordinates the third Euler angle
must be fixed. The choice of this angle depends on how the user wishes to view the