# How to choose the Light Size in World Space for Shadow Mapping and Percentage Closer Filtering?

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Hi computer graphics and math people :-)

Short question: How to let an artist choose a meaningful light size in world space for shadow maps filtered by percentage closer filtering (PCF) and is it possible to use the same technique to support spot and directional light sources?

Longer question: I have implemented shadow mapping and filter the edges by applying percentage closer filtering (PCF). The filter kernel is a Poisson-disk in contrast to a regular, rectangular filter kernel. You can think of a Poisson-disk as sample positions more or less randomly distributed inside the unit circle. So the size of the filter region is simply a factor multiplied to each of the 2D sample positions of the kernel (Poisson-disk).

I can adjust the radius/factor for the Poisson-disk and change the size of the penumbra at runtime for either a spot light (perspective frustum) or directional light (orhtographic frustum). This works great but the values for the parameter does not really make any sense which is fine for small 3d samples or even games where one can invest some time to adjust the value empirically. What I want is a parameter called "LightSize" that has an actual meaning in world space. A large scene, for example, with a building that is 100 units long the LightSize has to be larger than in a scene with a close-up of a book shelf to result in the same smooth shadows. On the other hand a fixed LightSize would result in extremely smooth shadows on the shelf and quite hard shadows outside the building. This question is not about soft shadows, contact hardening etc. so ignore physically accurate blocker-receiver estimations ;-)

Oh and take a look at my awesome MS Paint illustrations:

Idea 1: If I use the LightSize directly as the filter-size, a factor of 0.5 would result in a Poisson-disk of the diagonal 1.0 and a radius 0.5. Since texture coordinates are in the range [0,1] this leads to a filter size that evaluates the whole texture for each fragment: imagine a fragment in the center of the shadow map, this fragment would fetch neighboring texels that are distributed inside the whole area of the texture. This would of course yield extremely large penumbra, but let's call this the "maximum". A penumbra factor of 0.05 for example would result in a diagonal of 0.1 so that each fragment would evaluate about 10% of its neighboring texels (ignore the circle etc. just think in 2d from a side view). This approach works but when the angle of a spotlight becomes larger or the frustum of a directional light changes its size, the penumbra changes its width because the LightSize defines the penumbra in texture space (UV space). The penumbra should stay the same independent of the size of the near plane. Imagine a fitted orthographic frustum. When the camera rotates the fitted frustum changes in size and so does the size of the penumbra, which is wrong.

Idea 2: Divide the LightSize by the size of the near plane in world space. This works great for orthographic projections because when the size of the frustum becomes larger, the LightSize is divided by a larger value so that the penumbra stays the same in world space. Unfortunately this doesn't work for a perspective frustum because the distance of the near plane leads to a changing size of the near plane so that the penumbra size is now dependent on the near plane distance which is anoying and wrong.

It feels like there has to be a way so that the artist can choose a meaningful light size in world space. I know that PCF is only a (quite bad) approximation of a physically plausible light source, but imagine the following:
When the light source is sampled multiple times by using a Poisson-disk in world space one can create physically accurate shadows by rendering a hard shadow for each sample position. This works for spot lights. The situation is different for directional lights. One can use an "angle in the origin of the directional light" and render multiple hard shadows for each slightly rotated frustum. This does not make any physically sense at all in the real world, but directional lights do not exist, so... by the way the sampling of a light source is often referred to as multi-view soft shadows (MVSS).

Do you have any suggestions? Could it be that spot and directional lights have to be handled differently and PCF does not allow me to use a meaningful real world light size for a perspective frustum?

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