Multiplane Perspective in MathMap

Four rectilinear projections with carefully selected field-of-views to produce a 360° panorama without corners (almost). You have to view the original panorama to compare.

There are other "multiplane perspective" panoramas, loosely inspired by this paper.
Here is the script to be used in MathMap.

How to use this script

1. Load a suitable equirectangular image in Gimp (with four walls in a rectangle - this script does not cover trapezoidal rooms)
   
2. Open the MathMap plug-in
   
3. Copy & paste the code that you will find below
   
4. Select "Wrap" in the settings
   
5. In the User values, change lambda0 until a corner of the room in your panorama is at the border of the image.
   
6. Still in the User values, change t3 until the leftmost wall is exactly covered by
   the first rectilinear projection
   
7. Change t2 until the second leftmost wall is covered exactly by the second rectilinear
   projection
   
8. Finally, change t3 until the last corner of the room is split between the last two
   rectilinear projections
   
9. Change size (the vertical field of view) and yshift until the image looks fine
   
10. Press OK, wait, and save.

#####################################################
#    Four rectilinear projections covering 360°     #
#         Mathmap script by Seb Przd (2007)         #
#          http://flickr.com/photos/sbprzd          #
#            Licensed under the GPLv3               #
#####################################################
filter fourrectilinear (image in,float size: 1-2 (1),
float lambda0:-1-1 (0),float yshift:-1-1(0),float t3:
0-1(0.5),float t2:0-1(0.5),float t1:0-1(0.5))
il=0.01;ir=0.99;epsl=-100;epsr=100;iter=0;eps=1;while
(abs(eps)>0.0001)&&(iter<20) do xu=(il+ir)/2;tt1=tan(
pi/2-t1*pi)/2; tt3=tan(pi/2-t3*pi);yu=tt1+sqrt(xu*(1-
xu)+tt1^2); llmyy=tt3+sqrt(xu*(1-xu)+tt3^2);ll=llmyy+
yu;eps=tan(pi/2-t2*pi)-(-yu*llmyy+(1-xu)^2)/(ll*(1-xu
));if eps*epsl<0 then ir=xu;epsr=eps;else il=xu;epsl=
eps;end;iter=iter+1;end;l2=(1-xu)/(1+ll);l4=xu/(1+ll)
;l1=llmyy/(1+ll);l3=yu/(1+ll);xmvec=[-1,-1+l2+l4,0,l2
+l4,1]; xcvec=[-1+l4,-l3,l2,1-l1];lvec=[l1,l2,l3,l4];
lpv=[-3,-1,1,3]*pi/4+atan(l4,l1);xx=x*size;yy=y*size;
co=0; while co<=3 do xc=xcvec[co];xt=xx-xc*X;yt=yy-X*
yshift;if xx<=xmvec[co+1]*X&&xx>= xmvec[co]*X then lp
=lpv[co]; x0=xt;y0=yt;lc=lvec[co];end;co=co+1;end;rr=
sqrt(x0^2+y0^2);c=atan(rr/Y/2/lc);phi=asin(y0*sin(c)/
rr);in(xy:[atan(x0*tan(c),rr)*X/pi+lp*X/pi+lambda0*X,
phi*Y/(pi/2)]) end