cal/cal/vwparab.cal

{
        Generate rays for a parabolic view projection --
        i.e., a round image that when projected downwards
        in parallel onto a parabolic reflector results in
        a panoramic view from the paraboloid's focal point.

        The forward view direction corresponding to the top
        of the image is always +Y, and the up direction is
        always +Z.

        9/8/98 Greg Ward Larson

        Inputs:
                maxalt          : Maximum altitude (in degrees)
                x, y            = Image position, (0,0)->(1,0) is LL->LR

        Outputs:
                dx, dy, dz      = Direction vector for image point (x,y)

        Typical command line:
                cnt 1024 1024 | rcalc -e maxalt:25 \
                        -e 'x=($2+.5)/1024;y=1-($1+.5)/1024' -f vwparab.cal \
                        -e '$1=25.5;$2=12;$3=5;$4=dx;$5=dy;$6=dz' \
                        | rtrace @electric.opt -fac -x 1024 -y 1024 \
                                electric.oct > pan.pic
}
amax : PI/180*maxalt;
F0 : .5/cos(amax) - .5*tan(amax);       { dist. btwn. parabola and directrix }
xr = 2*x - 1;
yr = 2*y - 1;
r2 = xr*xr + yr*yr;
r = sqrt(r2);           { never actually needed }
z = r2/(4*F0) + F0;
zo = r2/(4*F0) - F0;
sin_alt = zo/z;
cos_alt = r/z;
dx = xr/z;              { same as xr/r*cos_alt }
dy = yr/z;              { same as yr/r*cos_alt }
dz = zo/z;              { same as sin_alt }
Revision:	1.1
Committed:	Sat Feb 22 02:07:21 2003 UTC (21 years, 2 months ago) by greg
Branch:	MAIN
CVS Tags:	rad3R7P2, rad3R7P1, rad3R5, rad3R6, rad3R6P1, rad3R8
Log Message:	Changes and check-in for 3.5 release Includes new source files and modifications not recorded for many years See ray/doc/notes/ReleaseNotes for notes between 3.1 and 3.5 release
#	Content
1	{
2	Generate rays for a parabolic view projection --
3	i.e., a round image that when projected downwards
4	in parallel onto a parabolic reflector results in
5	a panoramic view from the paraboloid's focal point.
6
7	The forward view direction corresponding to the top
8	of the image is always +Y, and the up direction is
9	always +Z.
10
11	9/8/98 Greg Ward Larson
12
13	Inputs:
14	maxalt : Maximum altitude (in degrees)
15	x, y = Image position, (0,0)->(1,0) is LL->LR
16
17	Outputs:
18	dx, dy, dz = Direction vector for image point (x,y)
19
20	Typical command line:
21	cnt 1024 1024 \| rcalc -e maxalt:25 \
22	-e 'x=($2+.5)/1024;y=1-($1+.5)/1024' -f vwparab.cal \
23	-e '$1=25.5;$2=12;$3=5;$4=dx;$5=dy;$6=dz' \
24	\| rtrace @electric.opt -fac -x 1024 -y 1024 \
25	electric.oct > pan.pic
26	}
27	amax : PI/180*maxalt;
28	F0 : .5/cos(amax) - .5*tan(amax); { dist. btwn. parabola and directrix }
29	xr = 2*x - 1;
30	yr = 2*y - 1;
31	r2 = xrxr + yryr;
32	r = sqrt(r2); { never actually needed }
33	z = r2/(4*F0) + F0;
34	zo = r2/(4*F0) - F0;
35	sin_alt = zo/z;
36	cos_alt = r/z;
37	dx = xr/z; { same as xr/r*cos_alt }
38	dy = yr/z; { same as yr/r*cos_alt }
39	dz = zo/z; { same as sin_alt }