/*
 * This is the basic pinhole projection model with distortion correction
 */

x : tan(m_view - c_view)$
y : tan(c_nick - m_nick)$ 
x_rot : y * sin(c_tilt) + x * cos(c_tilt)$
y_rot : y * cos(c_tilt) - x * sin(c_tilt)$
d : x_rot ^ 2 + y_rot ^ 2$
dist_fact : d ^ 2 * k1 + d * k0$
x_dist : x_rot * (1 + dist_fact) * scale$
y_dist : y_rot * (1 + dist_fact) * scale$

/*
 * Some mangling for C code generation
 */

x_expand : trigexpand(x_dist)$
y_expand : trigexpand(y_dist)$

args: "(double c_view, double c_nick, double c_tilt, double scale, double k0, double k1, double m_view, double m_nick)"$

printfunc(name, expression) := sprint("double ProjectionRectilinear::", name, args, "{ return ", string(subst(pow, "^", expression)), ";}", "
")$

printfunc("mac_x", x_expand)$
printfunc("mac_y", y_expand)$

printfunc("mac_x_dc_view", diff(x_expand, c_view))$
printfunc("mac_x_dc_nick", diff(x_expand, c_nick))$
printfunc("mac_x_dc_tilt", diff(x_expand, c_tilt))$
printfunc("mac_x_dscale", diff(x_expand, scale))$
printfunc("mac_x_dk0", diff(x_expand, k0))$
printfunc("mac_x_dk1", diff(x_expand, k1))$
printfunc("mac_y_dc_view", diff(y_expand, c_view))$
printfunc("mac_y_dc_nick", diff(y_expand, c_nick))$
printfunc("mac_y_dc_tilt", diff(y_expand, c_tilt))$
printfunc("mac_y_dscale", diff(y_expand, scale))$
printfunc("mac_y_dk0", diff(y_expand, k0))$
printfunc("mac_y_dk1", diff(y_expand, k1))$