Re: [Plib-users] Shadow

[Steve B. <sjb...@ai...>]

Ran...@ma... wrote:

> Dredging up the stuff from a previous incarnation, the "hotspot" isn't
> an optical illusion, rather it is related to the amount of visible
> shadow (cast by protruding objects on the surface) relative to the
> amount of visible, directly illuminated surface.

I don't understand where this 'extra' light comes from.

Please explain how light rays that would need to travel through
the solid object casting the shadow somehow bend around that
object to land on the ground in the halo region.

I can't conceive of a mechanism that would do that other than
at a microscopic scale.

> You are right -- the
> hotspot will appear without any additional code if the surfaces do in
> fact have a vertical texture (that was what my former incarnation
> depended on).  In my mind I was imagining that the the surfaces we
> were talking about were textured with texture maps, rather than
> something with real vertical texture.

You have me *completely* confused - how does "texture" have anything to
do with it?

Let's talk about a simple case.  I have a 1' square chunk of metal.
I hold it 3 feet above the ground at midday.  This will cast a 1' shadow
(roughly) with a dark 'umbra' in the center and will fade out to bright
sunlight over an inch or two through the 'penumbra' part of the shadow.

The edge of the shadow isn't 'hard' because the sun isn't a point
light source - and from a spot on the ground just on the edge of the
shadow, you only see (say) half of the sun's disk (the other half
being occluded by the metal plate).

You claim that the region just outside the penumbra will actually be
brighter than normal sunlight?

If yes - how does this extra light get there from the sun?  What
         geometrical path does it take?
If no - then please explain what's wrong with my experiment?

> It isn't an optical illusion -- you can use the size and intensity of
> the hotspot to elicit information from aerial photography about the
> size of (for example) trees in a stand and their mean distance apart.

I don't see how...

Hmmm - I think that this 'halo' you are talking about is just the
penumbra of the shadow...but if so, your description is very confused.

But even so, I don't see how using the width of the penumbra allows
you to deduce the height of trees in a photo if you didn't know
where the camera was relative to those trees...and if you know that
information then you don't need the penumbra (or any other shadow
information) to tell you that.

For an infinite light source (and the sun is pretty close to being
infinitely far away for these purposes :-) - the width of the
penumbra as measured on the ground depends only on the distance
between the shadow caster and the surface you are casting onto.
Generally, that doesn't help you determine the size of something
in a photo though. The top of 5 meter tree will be twice as close
to the ground as a 10 meter tree and therefore have a half-sized
penumbra.  Unfortunately, in the photograph, the penumbra's width
is affected by visual perspective - just like the tree.

Hence the shadow from a 10 meter tree photographed from 100 meters
up will look EXACTLY the same as a 5 meter tree from 50 meters up.
So examining the penumbra gives you no extra information that the
size of the tree on the photograph doesn't provide.

> Real empirical science ... I can provide a few (old) references for
> those that are interested.

Yes please!

Anyway, if you are talking about rendering the penumbra of an
aircraft's shadow, that's an easy thing.  Unless the plane is
**HUGE** or very close to the ground, it'll appear to be
smaller than the sun's disk when seen from the ground and the
shadow will be all penumbra and no umbra.  In that case, you
can just model a fuzzy shadow polygon and make it less and
less opaque as the height of the plane above the terrain
increases.  You *might* want to add a more solid 'umbra'
at low altitudes - but frankly, I wouldn't bother.  Most
people don't notice all this fancy scientific shadow stuff
and will be perfectly happy to see a fuzzy outline at all
altitudes.  That has the (LARGE) benefit that you don't have
to be too specific about the exact shape of the shadow - so
it doesn't have to change shape as the aircraft changes
orientation.

Doing *true* shadows in a general situation is *still* a bitch
of a problem...

Consider a moment just before sunset.  The sun is on the horizon.
The plane is flying low over very flat terrain.

The shadow of the plane stretches all the way to the horizon.
Because the terrain undulates, you'd have to cut up the shadow
polygon to fit it to the terrain surface - in realtime - at full
frame rates!  That's one heck of a lot of math!

There are some algorithms to use multipass textures that are
rendered on-the-fly by rendering the scene from the perspective
of the light source.  This takes one full scene render for each
shadow caster.  However, you don't know what resolution that
texture needs to be.  From the perspective of the sun, your
texture will have a nice sharp edge and will look good.  But
when you apply that to the terrain, it'll be far to coarse
in resolution for some eyepoints (eg when you are looking at
90 degrees to the sun's direction vector and you are close
to the ground).

There are NO good algorithms for general shadow casting.

Fortunately, the pragmatist will realise that humans don't
care.  We like to have a shadow to give a feeling of
the height of the object above the ground (especially when
close to the ground)...but if it's just a fuzzy cross-shape
then that's "good enough".

-- 
Steve Baker   HomeEmail: <sjb...@ai...>
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