AcceuilHome Intermediate projections between spherical and planar - ReProjector demo application ReProjector application

Have you ever seen an ugly partial panorama in planar projection (160 x 75) ?
Ugly wide planar projection: Belleville, Paris
Panorama was actually 179 x 75 as shown below in spherical projection:
Spherical partial 179: Belleville, Paris
As far as I remember this place, buildings in centre seem too near, on the contrary people and walls on left/right edges seem too far. This view doesn't give the feeling to see 180 in front of us. Panoramists are looking for intermediate projections, maybe like this:
Ellipso projection: Belleville, Paris
With vertical panoramas having high extend in vertical and low horizontal field of view, below is 81 x 95 , we like to try planar (pict #1) or mercator (pict #2) projection:
Planar: Ste Catherine, BrusselsMercator: Ste Catherine, Brussels
Planar (pict #1 above) seems too stretched in vertical. Mercator (pict #2 above) looks better but, as it's based on circular projection in horizontal axis, straight objects (streets, buildings) are not respected and being curved. Below, Mistery projection can keep a better geometry while reducing stretching in vertical:
Mistery projection: Ste Catherine, Brussels

Other projections may give a nicer look for entire picture on screen or for print

Here are some drawing to show where we go. An equirectangular picture is shown as a sphere, pixels coordinates are actually angles values. Planar, MiSpiro, Mistery are all projecting to a plan with less stretching for MiSpiro & Mistery by projecting from a more distant projection centre:
Drawing for Planar and Mistery
Ellipso with a zero eccentricity is a true circle (in green below): it's projecting original spherical coordinates to a spheroid with a larger radius. With a high eccentricity, we get an ellipse (in orange below): aspect around the centre stays constant while stretching on the edges decreases.
Drawing for Ellipso
To show more differences between these projections, lines were drawn on the equirectangular source (pict #1) to be projected as a regular square grid in planar projection (pict #2):
Spheric source with gridPlanar with square grid
MiSpiro (pict #1) was written to respect straight objects so the grid appears as rectangles with more compression when coming near edges, looking like "warping" in a picture editor. Mistery & Ellipso (pict #2) don't respect 100% the geometry of straight objects but allow better control of stretching on edges/corners.
MiSpiro: grid still rectangularMistery/Ellipso: grid no more rectangular

Ellipso projection - effect of parameters

Ellipso projection is more advanced with two parameters to control how picture is projected. As drawback, interface is more complex and user more hesitating to choose right parameters. Spherical (pict #1) makes scenery a bit "narrow" for this panorama 122 x 70, cars at bottom are stretched. Ellipso with a low radius and zero eccentricity (pict #2) widen the scenery aspect.
Spherical: Fontenoy, Paris Ellipso, low expand, zero eccentric
We can try to widen more the scenery aspect with a higher radius (pict #1), it's like opening more the spheroid to project to. But stretching becomes high on edges/corners. With a high eccentricity (pict #2) this stretching is reduced.
Ellipso, high expand, zero eccentric Ellipso, high expand, high eccentric

Make your opinion - ReProjector demo application ReProjector application

Some other pages about projections or changing the way to show panorama:
Squaring the circle in panorama
'Squeee' rectilinear panorama by Georges Lagarde
'Multiplane' projection examples by Georges Lagarde New projections in PTAssembler 4.5 by Max Lyons