Re: [Algorithms] Extracting Lights from a Dynamic SH Light Environment

[Willem de B. <wd...@mi...>]

Hi there -

Spherical harmonics are inherently very bad at representing directional lig=
hts.
When you visualise at the approximated radiance function you'll see horribl=
e
ringing artefacts.

Here's one thing I don't understand:

"But when we move closer to e.g. the red light, we're suddenly
extracting two red lights from the direction of the red light."

How is it possible to move 'closer' to a directional lightsource? Surely
this assumption of being able to move closer must have something to do
with you getting the maths mixed up?

One question to you though. Since you are trying to extract directional lig=
ht-
sources from an SH projection that you've generated from the directional
light sources yourself, is it not possible to retain these original lightso=
urces
instead of trying to extract them?
It would save you a great amount of hassle that way.

-----Original Message-----
From: gda...@li... [mailto:gdalgorithms-=
lis...@li...] On Behalf Of Martin Ecker
Sent: 01 March 2007 17:02
To: gda...@li...
Subject: [Algorithms] Extracting Lights from a Dynamic SH Light Environment

Hi,

I have a question about the mathematics involved in extracting
directional lights from a lighting environment represented in a
spherical harmonics basis.
We want to use this to light our in-game characters. Every couple of
frames the lights affecting a character in the scene are collected. They
are each projected into spherical harmonics (for this we simply treat
them all as directional lights, so the projection is simply
SH(normalized_direction) * intensity) and the resulting coefficients are
added up to create a low-frequency approximation of the lighting
environment around the character.

Now, we'd like to extract a few directional lights from that lighting
environment, which we use to do regular phong shading, and the remaining
light environment could be used in e.g. the vertex shader to do SH
diffuse lighting. Currently, we're doing this by determining the maximum
light intensity direction in SH, which will be the light direction
vector of our directional light. Now we evaluate our SH light
environment using that direction vector in order to get the light
intensity, i.e. intensity =3D Dot(light_environment_sh,
SH(normalized_light_direction)). So now that we have the direction
vector and intensity of our directional light, we extract it from the SH
light environment by projecting that directional light into the SH basis
and subtracting it from the light environment.

Apparently, somewhere along the line we're getting our math wrong,
because when we extract the first directional light it doesn't have the
expected intensity. As an example, imagine a character standing in
between two directional lights, a green light from the left and a red
light from the right. When we stand in the middle of the two lights
everything looks okay, i.e. the character is lit half green and half
red. But when we move closer to e.g. the red light, we're suddenly
extracting two red lights from the direction of the red light. When
extracting the first red light from such a lighting environment I would
expect most of the red intensity to go into that first red light and
then the second extracted light would have a kind of grayish ambient
color, which starts fading into green the closer we get to the green
light.

If anyone has done something similar, we'd appreciate any insights.

Also, does anyone know of any good tricks to get rid of or at least hide
the lighting discontinuities we get due to the sometimes harsh direction
changes of the extracted lights?

Thanks,
Martin Ecker



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