In [1] they describe a clever way of rendering the thickness of an object in a single pass. The method only correctly works for convex objects but this limitation isn’t that bad, the method can often be used to get the approximated thickness of concave objects as well. For example, [1] uses it to fake the light scattering in clouds rendered as billboards. The methods works like this:

The object is rendered and the distance from the near plane is saved in a color channel R. Also, the distance to the far plane is saved in channel G. By rendering with the blend color mode MIN, one will get the minimum distance from the near plane in R, and the minimum distance to the far plane in G. By using these two distances, one can easily calculate the thickness of the rendered object with the following formula (1-G) – R (if distance is scaled so one is the the distance between the clip planes). Alpha can be saved as well in the same render pass, by outputting it to the A channel. And selecting blend alpha mode ADD (color and alpha can have different modes). This will add up the alpha.

All this is done in only one pass. Just remember to clear to white before rendering.

The image below shows the thickness of the popular Hebe mesh rendered with this method. This model is not convex, and the problem areas are for example the arm holding the bowl. As one can see, the algorithm believes that the bowl and the shoulder are connected, and therefore believes that part of the object is the thickest.

[1] The Art and Technology of Whiteout
http://ati.amd.com/developer/gdc/2007/ArtAndTechnologyOfWhiteout(Siggraph07).pdf

In DirectX9, one can use instanced billboards to render lots of particles with good performance. Since we presume all particles to be billboards constructed from two triangles forming a quad, by using instancing, we can reuse this geometry data (only uv-coordinates needed) for each particle and therefore saving bandwidth. When rendering, two streams with different frequency should be used.  The quad-geometry data makes the first stream, the second stream consists of the per instance data that is unique for each particle. This instance data could be the position, rotation, color and more. The big drawback with this rendering approach is that it requires hardware instancing support, which means Shader Model 3.0. (or Shader Model 2.0 for ATI cards if using a trick described in the first source below).

This particle rendering approach described in details:
http://zeuxcg.blogspot.com/2007/09/particle-rendering-revisited.html

DirectX9 info about rendering multiple streams
http://msdn.microsoft.com/en-us/library/bb147299(VS.85).aspx

DirectX9 instancing info
http://msdn.microsoft.com/en-us/library/bb173349(VS.85).aspx

The aim with soft particles is to remove the ugly artifact that appears when the particle quad intersects the scene. There are a lot of different approaches to solve this, some more complicate than others. The simplest formula for soft particles is to just fade the particle if it’s getting to close to the scene. To do this, the scene without particles has to be rendered first and the depth saved in a texture. When drawing the particles, the depth of the particle will be compared to the scene depth. The alpha should be increased by a smooth fade by this depth difference. The formula below in HLSL is the simplest possible for soft particles, and works very well. Scene_depth is the sampled depth (in viewspace) of the scene in the direction of the current pixel. Particle_depth is the depth(in viewspace) of the current particle pixel. Scale is used to control the “softness” of the intersection between particles and scene:

fade = saturate((scene_depth – particle_depth) * scale);

NVIDIA [1] proposes a method that the following fade should be used instead of the linear one described above, to make the fade even smoother.

float Output = 0.5*pow(saturate(2*(( Input > 0.5) ? 1-Input : Input)), ContrastPower);
Output = ( Input > 0.5) ? 1-Output : Output;

Umenhoffer [2] proposes a method called spherical billboards to deal with these problems. In this method, the volume is approximated by a sphere. This method also deals with the near clipplane problem that particles will instantly disappear if they get to close to the camera.

There is also an idea [3] that the alpha channel can be used to represent the density of the particles. Although this method has the drawback that the textures might need to be redone by the artists.

The method by Microsoft [4] uses a combination of spherical billboards and a texture representation of the volume. But instead of using the alpha channel, they ray march the sphere and sample the density and volume from a 3D noise texture. The result can be seen in the image below.

The video below shows how soft shadows can increase realism in games using large particles. It’s originally an ad for Torque 3D engine.

[1] Soft Particles by NVIDIA
http://developer.download.nvidia.com/whitepapers/2007/SDK10/SoftParticles_hi.pdf

[2] Spherical Billboards and their Application to Rendering Explosions
http://www.iit.bme.hu/~szirmay/firesmoke.pdf

[3] A Gamasutra article about soft particles
http://www.gamasutra.com/view/feature/3680/a_more_accurate_volumetric_.php

[4] A DirectX 10 implementation of soft particles by Microsoft, called Volumetric Particles
http://msdn.microsoft.com/en-us/library/bb172449(VS.85).aspx

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This technique doesn’t actually invent something new. It’s just a combination of normal mapping and billboards to realistically lit particle systems. It has been used successfully in many games to fake volumetric smoke.

The movie below shows an example of a lot of particles, rendered as billboards that are normal mapped to look like spheres.

Lit smoke and Post-process system design (also in the book ShaderX 5)
http://www.gamedev.net/community/forums/topic.asp?topic_id=432218&whichpage=1?

A thesis that tried to implement this method (some interesting info, but results aren’t good enough)
http://epubl.ltu.se/1404-5494/2008/011/LTU-HIP-EX-08011-SE.pdf

Some discussion about normal mapped billboards
http://www.drone.org/tutorials/lighting_flat_objects.html