Parallel projection: projected landscape has constant scale with oblique but parallel coordinate system. Mathematically the projection is simpler but the actual reality is a little different.
Central projection: perspective projection is applied to the 3D coordinates of DEM, which produce the actual reality as human eye looks while closer objects have bigger scale and further objects have smaller scale.
Figure 6.9 shows the concept of the above two projections. Bird's eye view in parallel projection will be produced onto either vertical plane or perpendicular plane to the looking direction. Looking direction with the depression angle of 30~40 degree is widely used.
Mathematics of parallel projection with the depression angle of l and azimuth q measured from the north or Y axis, as shown in Figure 6.10 is as follows:
x = s (X cosq - Y cos q sin)
y = s (X sin q tanl + Y cosq tan l + Z)
in case of vertical plane
y = s (X sinq sinl + Y cos sinl + Z cosl )
in the case of perpendicular plane
where (x, y): coordinates in the projected plane
s = scale
q = azimuth
l = depression angle
Hidden points can be detected by checking whether yi is bigger or not than the current ymax among (i-l) points along a profile from i = 1 to i=n, as shown in Figure 6.11.