We should also assert that the pixels rendered on the poly implicitly represent volumes from the camera's perspective.

The idea is to take the drawn poly and define a pseudo volume around it. This volume is defined by the extents of the poly, extruded in the direction the camera is facing.

For the following example, the poly is extruded both towards and away from the camera by some distance D to define the volume.

The original poly defines the mirror-image plane P(mi) and the alpha channel in each pixel defines to what extent the sub-particle boundary B(sp) deviates from the P(mi). In practice the volume would be defined as the poly extruded away from the camera only to make full use of hardware clipping.

This is due to the fact that pixels that are rejected due to being occluded will never get calculated for the near region of the volume.

Fig 2.

Now for each pixel rendered in the particle, we have extents along all the view rays through those pixels that define the collision information necessary to remove the visual aliasing caused by a planar particle. There are at least two ways to consider the information provided by the alpha component of the texture:

1. As an average density of microscopic particles over the range from the front to back of the volume. I will call this method the average density method.
2. As relative the density that relates to the extent of the microscopic volume along the ray represented by the pixel. I will call this the density extent method.

In the shader we will need the depth of the environment at the given pixel. This could be passed in as texture information from a previous render-to-texture stage. I will call this EnvironmentDepth.

We will need the pixel position of the original poly that will define our mirror plane. This can be propagated from the vertex shader, and I will call it ParticleDepth.

We will also need a function to define the mapping from alpha value to real-world depth do define our deviation extent, I will call it DeviationExtent. The deviation extent will likely be constant across the whole poly and possibly the whole particle effect.

We will use the existing particle texture unmodified with its colour and alpha values as they were originally defined.

We will define a global opacity/transparency function that will be used to relate the maximum particle density and relates the actual colour transmission through the volume which I will call VolumeAlpha. This function is used to define the maximum transparency/opacity the extents of the volume will allow.