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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
** Notation**: 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/aa451203bb172279%28v=VS.85%29.aspx Lighting FormulasAttenuation and Spotlight Factors]*** Notation* Atten<sub>i</sub> - attenuation of light i***: d<sub>i</sub> - distance from light i***: G: d<sub>i</sub> = |L<sub>dir<sub>i</sub></sub>|***: a<sub>0</sub> - global ambient colorconstant attenuation factor***: Ca<sub>1</sub>- linear attenuation factor***: a<sub>2</sub> - material ambient colorquadratic attenuation factor***: CAtten<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> - material diffuse colorspot factor of light i***: CSpot<sub>i</sub> = {[r<sub>i</sub> - cos(phi<sub>i</sub>/2)]/[cos(theta<sub>si</sub> /2) - material specular colorcos(phi<sub>i</sub>/2)]}<sup>f<sub>i</sub></sup>***: Attenr<sub>i</sub> - attenuation 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>)***: Lphi<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>ai</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> - ambient color Vertex<sub>position</sub>)** Phong - account accurately for position of light 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>ddir<sub>i</sub></sub>) N - L<sub>dir<sub>i</sub></sub>**: p<sub>i</sub> - diffuse color 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>sdir<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 color 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> + Attensum [L<sub>a<sub>i</sub></sub> * sum[ LAtten<sub>ai</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>i</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
