Fragment lighting is a DMP extension to the standard OpenGL pipeline with which applications can calculate object lighting for each rendered pixel instead of just per vertex. The fragment lighting algorithm furthermore supports the shading models Blinn-Phong, Cook-Terrance, Ward, and microfacet-based BRDF-models. While the lighting calculations take place in a very localized position of the pixel processing pipeline, the feature interacts with different other pipeline stages.
Overview #
In general, lighting is calculated at a particular point in space X by determining the angles (i.e. dot products) between different vectors:
- The face normal vector N, which points from X to the direction perpendicular to the lighted object
- The tangent vector T, which points from X to a direction which is tangential to the lighted object
- The bitangent vector B, which points to a tangential direction such that it is orthogonal to both N and T
- The view vector V, which points from X “into the camera”
- The light vector L, which points from X to the light source (note that lighting is always evaluated separately for each light source; the results for multiple light sources can simply be added to each other)
For example, in the Blinn-Phong shading model the dot product of L and N determined the intensity of a lighting type called diffuse lighting. More generally, the dot products between these vectors (from now on simply referred to as “dot products”) are combined to a lighting equation, which is evaluated once per light source at each considered point in space.
Before pixel shaders were common, the lighting equation was only considered at each vertex, and the output color was then interpolated across the triangle. To achieve higher visual quality, pixel shaders can be used nowadays to evaluate the lighting equation at each pixel. The PICA200 does not have a programmable pixel shader, but has a fixed-function pipeline stage to achieve the same quality.
In any case, per-pixel lighting requires to somehow obtain a normal vector for each pixel. Theoretically, the vertex shader could output one normal vector per vertex, and per-pixel normals could then be obtained by interpolating these vectors in a specific way. This, however, is very inefficient, which is why vertex shaders on the PICA200 instead output mathematical objects called quaternions: Quaternions can be computed from normal/tangent vectors, and vice versa, so no information is lost by doing so. However, quaternion interpolation is a lot faster (see the “Kuijk and Blake” source below), and so the GPU can compute per-pixel normals simply using the interpolated quaternion. This is just the general idea, and the dirty mathematical details are explained below.
In addition to allowing per-pixel calculations, the lighting equation used in the PICA200 involves using the dot products as indices into configurable lookup tables. A good example of why this is useful is cell-shading, which can be achieved simply by setting adjacent lookup table values to the same color.
Quaternions as Shader Outputs #
The shaders are usually the point where normal and tangent vector information flows in. Usually, the source vertex data will include normal vectors for each vertex. This need not be the case though; one could also just input raw vertex positions, and have a geometry shader automatically calculate normal vector information.
In any case: There is no vertex output attribute semantic for normal or tangent vectors. To use fragment lighting, the shader must actually output an attribute with the quaternion semantic. So some sort of conversion needs to happen from normal and tangent vectors to quaternions. This can be done using the surface-local matrix.
Quaternion Interpolation #
Quaternion interpolation needs to happen to obtain a per-fragment quaternion, from which in turn per-fragment normals and tangent vectors can be computed. It is unknown how quaternions are interpolated on the PICA200. The architecture suggests that plain linear interpolation is used, but there are also more sophisticated algorithms like Slerp and Nlerp.
Quaternions and Normal/Tangent Vectors #
Quaternions describe a transformation from surface-local space to eye space. In surface-local space, by definition (and up to permutation) the normal vector is (0,0,1), the tangent vector is (1,0,0), and the bitangent vector is (0,1,0).
Alternatively, one may consider quaternions a transformation from eye space to surface-local space.
Fragment Lighting Equation #
There are two lighting equations: One for the primary color and one for the secondary color. Both of them are given in section 3.2.2 of the “Kazakov and Ohbuchi” source below. In addition, the fragment lighting can be set up to write to the alpha channel of the primary or secondary color depending on a selectable angle and a LUT. The equations used can be found here: 🔗 http://mathb.in/26766
Some common setups include:
| Model | LutD0 | LutD1 | ReflectionLuts | Geometry factors | SpotlightLut |
|---|---|---|---|---|---|
| Blinn-Phong | Input: N dot H, Contents: x^s | – | – | Disabled | Spotlight setup or no-op |
| Cook-Torrance | – | Input: N dot H, D(x) | Input: V dot H, Contents: F(x) | Enabled | Spotlight setup or no-op |
| Schlick-like | – | Input: N dot H, Contents: Schlick Z(x) | Input: V dot H, Contents: F(x) | Enabled | Input: cos phi_i, Contents: Schlick A(x) |
| Subsurface scattering (not entirely sure) | – | Input: N dot V, Contents: Transmittance by angle | Input: L dot N, Contents: Reflectance by angle | Disabled | Spotlight setup or no-op |
s is the specularity factor for Blinn-Phong.
Spotlight setup means input -L dot P and contents spotlight falloff.
F and D can be found in 🔗 http://inst.cs.berkeley.edu/~cs294-13/fa09/lectures/cookpaper.pdf
Schlick Z and Schlick A are defined in 🔗 http://www.cs.virginia.edu/~jdl/bib/appearance/analytic%20models/schlick94b.pdf .
The Fresnel LUT can be used to, for example, blend two colours according to how oblique the view angle is, or to simply additively blend white onto fragments with an exponential falloff, resulting in rim lighting.
Fragment Lighting Output #
The fragment lighting results are accessible as two inputs to the texture combiners (one for the primary color, one for the secondary color).
Resources #
This wiki page can only give a short overview of the fragment lighting feature. Luckily, there is a plethora of public literature available which describes the feature in more detail:
- Everitt - “Per-Pixel Lighting”: A presentation given at the Game Developers Conference 2001 about per-pixel lighting. It doesn’t have anything to do with the PICA200 algorithm, but explains the core ideas very well (especially the concepts of surface-local space and how it relates to other coordinate systems).
- Kazakov and Ohbuchi - “Primitive Processing and Advanced Shading Architecture for Embedded Space”: Provides a general overview over the fragment lighting algorithm used by the PICA200 and provides explicit formulas for the primary and secondary lighting output. NOTE: There exist both a scientific publication and a short presentation with this title. Both are useful, but the former goes into much greater detail.
- Ohbuchi and Unno - “A Real-Time Configurable Shader Based on Lookup Tables”: Provides a very detailed explanantion of the fragment lighting implementation
- Kuijk and Blake - “Faster Phong Shading via Angular Interpolation”: Explains in greater detail how quaternions can be used to encode information about normals and tangents (and how quaternions are easier to interpolate than vectors).