I'm trying to understand the math behind 3d perspective clipping algorithm
dixit:
We need four constant to express the equations of the four side planes. These are the slopes of the planes in relation to the z-axis. Figure 6.27 shows a vertical cross section through the frustrum and will help in determing the slopes for the top and bottom planes. A similar situation exists for the left and right planes:
slope of the right plane: $S_R=1/2*(wxh-wxl)/(d+wzl)$
slope of the left plane: $S_L=-1/2*(wxh-wxl)/(d+wzl)$
slope of the top plane: $S_T=1/2*(wyh-wyl)/(d+wzl)$
slope of the bottom plane: $S_B=-1/2*(wyh-wyl)/(d+wzl)$
With these constants the equations of the planes are:
$$ L: x = wxl + S_L(z-wzl) \\ R: x = wxh + S_R(z-wzl) \\ B: y = wyl + S_B(z-wzl) \\ T: y = wyh + S_T(z-wzl) \\ N: z = wzl \\ F: z = wzh $$
I don't understand how the slope of each planes has been calculated, also the respectives equations of the planes looks like the equation of the line