Changes

** Notation**: G_a - global ambient color**: C_a - material ambient color**: C_d - material diffuse color**: C_s - material specular color**: L_{a_i} - ambient color of light i**: L_{d_i} - diffuse color of light i**: L_{s_i} - specular color of light i**: L_{dir_i} - 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] - note the corrections below*** Notation* Atten_i - attenuation of light i***: Gd_ai - global ambient colordistance from light i***: C: d_i = |L_{dir_ia} - material ambient color|***: Ca_d0 - material diffuse colorconstant attenuation factor***: Ca_s1 - material specular colorlinear attenuation factor***: Attena_i2 - quadratic attenuation of light ifactor****: Atten_i = 1/(a₀ + a₁ d_i + a₂ d_i²)****: Atten_i = [0, 1]****: dSpot_i - distance from spot factor of light i***: Spot_i = {[r_i - spot factor cos(phi_i/2)]/[cos(theta_i/2) - cos(phi_i/2)]}^f_i***: r_i - cosine of angle from axis of light spotlight_i***: : r_i = norm(- light direction in camera space) . norm(L_{adir_i})***: phi_i - ambient color penumbra (exterior cone) angle of light spotlight_i***: Ltheta_i - umbra (interior cone) angle of spotlight_di***: f_i - diffuse color falloff factor of light spotlight_i** [http://en.wikipedia.org/wiki/Blinn%E2%80%93Phong_shading_model Blinn-Phong and Phong]**: LV - viewpoint vector**:: V = norm(Camera_sposition- Vertex_iposition )** Phong - specular color account accurately for position of light viewer**: Specular reflectance = (R_i . V)^p_i**: R_i - reflection vector**: : R_i = 2 * (N . L_{dir_i}) N - L_{dir_i}**: p_i - direction vector true specular power of light i**:**: N Blinn-Phong - use halfway vector instead of reflection vector - normal adjust power to the surface at the vertexcompensate***: Specular reflectance = (N . H_i - halfway vector =)^p'_i****: = norm(norm(CameraH_positioni - Vertexhalfway vector**:: H_positioni) = norm(V + L_diri</sub>i</sub>)****: : H_i = norm([0,0,1] + L_diri</sub>i</sub>) - less computationally intensive - assumes that camera is at infinity along z axis**: p'_i - adjusted specular power of light i**:*** [http://msdn.microsoft.com/en-us/library/bb172256%28v=VS.85%29.aspx Ambient]***: C_a * ( G_a + sum [AttenL_{a_i} * LAtten_ai* Spot_i] )*** [http://msdn.microsoft.com/en-us/library/bb219656%28v=VS.85%29.aspx Diffuse]***: C_d * sum [ L_di</sub>i</sub> * (N . L_{dir_i}) * Atten_i) * AttenSpot_i ]*** [http://msdn.microsoft.com/en-us/library/bb147399%28VS.85%29.aspx Specular]***: C_s * sum [ L_si</sub>i</sub> * (N . H_i) ^p'_i * Atten_i * Spot_i ] - Blinn-Phong**: C_s * sum [ L_{s_i} * (R_i . V)^p_i * Atten_i * Spot_i ]- Phong