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== Week 4 - Jan 30 ==
=== This Week ===
* [http://msdn.microsoft.com/en-us/library/bb147178%28v=VS.85%29.aspx Mathematics of Lighting]
* Vertex Shaders
* Lighting in Vertex Shaders
** Lighting FormulasNotation**: G<sub>a</sub> - global ambient color**: C<sub>a</sub> - material ambient color**: C<sub>d</sub> - material diffuse color**: C<sub>s</sub> - material specular color**: L<sub>a<sub>i</sub></sub> - ambient color of light i**: L<sub>d<sub>i</sub></sub> - diffuse color of light i**: L<sub>s<sub>i</sub></sub> - specular color of light i**: L<sub>dir<sub>i</sub></sub> - direction vector of light i**: N - normal to the surface at the vertex*** [http://msdn.microsoft.com/en-us/library/bb172279%28v=VS.85%29.aspx Attenuation and Spotlight Factors]**** Atten<sub>i</sub> - attenuation of light i***: d<sub>i</sub> - distance from light i***:: d<sub>i</sub> = |L<sub>dir<sub>i</sub></sub>|***: a<sub>0</sub> - constant attenuation factor***: a<sub>1</sub> - linear attenuation factor***: a<sub>2</sub> - quadratic attenuation factor***: Atten<sub>i</sub> = 1/(a<sub>0</sub> + a<sub>1</sub> d<sub>i</sub> + a<sub>2</sub> d<sub>i</sub><sup>2</sup>)***: Atten<sub>i</sub> = [0, 1]**** Spot<sub>i</sub> - spot factor of light i***: Spot<sub>i</sub> = {[r<sub>i</sub> - cos(phi<sub>i</sub>/2)]/[cos(theta<sub>i</sub>/2) - cos(phi<sub>i</sub>/2)]}<sup>f<sub>i</sub></sup>***: r<sub>i</sub> - cosine of angle from axis of spotlight<sub>i</sub>***:: r<sub>i</sub> = norm(- light direction in camera space) . norm(L<sub>dir<sub>i</sub></sub>)***: phi<sub>i</sub> - penumbra (exterior cone) angle of spotlight<sub>i</sub>***: theta<sub>i</sub> - umbra (interior cone) angle of spotlight<sub>i</sub>***: f<sub>i</sub> - falloff factor of spotlight<sub>i</sub>** [http://en.wikipedia.org/wiki/Blinn%E2%80%93Phong_shading_model Blinn-Phong and Phong]**: V - viewpoint vector**:: V = norm(Camera<sub>position</sub> - Vertex<sub>position</sub>)** Phong - account accurately for position of viewer**: Specular reflectance = (R<sub>i</sub> . V)<sup>p<sub>i</sub></sup>**: R<sub>i</sub> - reflection vector**:: R<sub>i</sub> = 2 * (N . L<sub>dir<sub>i</sub></sub>) N - L<sub>dir<sub>i</sub></sub>**: p<sub>i</sub> - true specular power of light i**:** Blinn-Phong - use halfway vector instead of reflection vector - adjust power to compensate**: Specular reflectance = (N . H<sub>i</sub>)<sup>p'<sub>i</sub></sup>**: H<sub>i</sub> - halfway vector**:: H<sub>i</sub> = norm(V + L<sub>dir<sub>i</sub></sub>)**:: H<sub>i</sub> = norm([0,0,1] + L<sub>dir<sub>i</sub></sub>) - less computationally intensive - assumes that camera is at infinity along z axis**: p'<sub>i</sub> - adjusted specular power of light i**:* * [http://msdn.microsoft.com/en-us/library/bb172256%28v=VS.85%29.aspx Ambient]**: C<sub>a</sub> * ( G<sub>a</sub> + sum [L<sub>a<sub>i</sub></sub> * Atten<sub>i</sub> * Spot<sub>i</sub>] )** [http://msdn.microsoft.com/en-us/library/bb219656%28v=VS.85%29.aspx Diffuse]**: C<sub>d</sub> * sum [ L<sub>d<sub>i</sub></sub> * (N . L<sub>dir<sub>i</sub></sub>) * Atten<sub>i</sub> * Spot<sub>i</sub> ]** [http://msdn.microsoft.com/en-us/library/bb147399%28VS.85%29.aspx Specular]** : C<sub>s</sub> * sum [ L<sub>s<sub>i</sub></sub> * (N . H<sub>i</sub>)<sup>p'<sub>i</sub></sup> * Atten<sub>i</sub> * Spot<sub>i</sub> ] - Blinn-Phong**: C<sub>s</sub> * sum [ L<sub>s<sub>i</sub></sub> * (R<sub>i</sub> . V)<sup>p<sub>i</sub></sup> * Atten<sub>i</sub> * Spot<sub>i</sub> ] - Phong** [http://msdn.microsoft.com/en-us/library/ff471376%28v=vs.85%29.aspx HLSL Intrinsic Functions]*** [http://msdn.microsoft.com/en-us/library/bb509630%28v=vs.85%29.aspx normalize()] - normalize a vector*** [http://msdn.microsoft.com/en-us/library/bb509594%28v=vs.85%29.aspx dot(,)] - dot product of two vectors of any size*** saturate[http://msdn.microsoft.com/en-us/library/bb509617%28v=vs.85%29.aspx length()] - length of a vector*** length[http://msdn.microsoft.com/en-us/library/bb509645%28v=vs.85%29.aspx saturate()] - clamp scalar, vector, or matrix to [0, 1]
=== To Do ===
* reorganize framework code so that vertex shader receives product of world, view, and projection matrices
