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Is there any practical difference? One option better than the other?

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There are differences.  Some differences are inherent in the format, other differences can happen between any file.

A lightprobe projection is the traditional projections used by Paul Debevec.  They are the result of taking a photograph of a scene in a mirror ball. It will wrap an image around the 360 view, however 180 degrees of the view will be distorted and the image will gather to a point.  There are less pixels around the edges to capture the outside 180 degrees. This is not a big deal when using the image for lighting.

A spherical projection is sometimes called equirectangular. Traditionally it is a 2:1 aspect ratio. I believe it is always the result of software stitching. It will wrap the image around and will only gather at the top and bottom.  This format will have better distribution of pixels for viewing directly.

There also are some very big differences in the absolute values of the pixels in the HDRI. Paul Debevec would set the value of his pixels so the actual value of the light is represented in the color channels.  I might call these calibrated probes.  In the render world, there are many "HDRI" images available.  Some are calibrated to actual values, some are set to values between 0 and others are set to relative floating point values.  So the strength of the light can very drastically from one HDRI to another. This can come into play when trying to balance artificial lights or sunlight with various HDRI files.  Just not that when changing HDRIs, other lights may also have to change.

Does this help?

Yes that answers my question. Basically spherical is better for a sky you could be looking at from any direction.

Yes.  Equilateral is better.  It will need to be very high in resolution, otherwise it will pixelate in the background and the reflections.  Sometimes a lower resolution HDRI is used for lighting and a high one for the view.  Wider camera lens will be more forgiving since they capture a wider arc of the background in the view.

One trick which is very effective is to use an spherical HDRI for the light and reflections, but use a planar image from the same image set for the background. Some services will distibute the speherical and planar background plates of the same scene. Here is an example: http://jeffpatton.net/2011/10/free-hdr-with-a-couple-of-backplates/

The set of skies I bought are 10,000 x 5,000. They didn't come with any background plates.

Will using a high resolution HDRI for lighting affect rendering speed?

The high resolution will not kill rendering speed, but will count against any memory limitations you have.  With the advent of 64-bit this has become much less of a problem.



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