Real Time Rendering

1. Real Time Rendering Lighting and Reflectance Model

2. Light interaction. • Interaction • It depends on the physical characteristics of the light, the physical composition and characteristics fo the matter. • When light makes contact with material, three types of interactions may occur. • Light reflection, light absorption, light transmitted.

3. Light interaction. • Interaction. • Form. • Conservation of energy. • Majority of incident light. • Reflected light and Absorbed light. • Light is reflected towards the observer from all visible surface regines. • BRDF describes how much light is reflected when light makes with a certain material.

4. BRDF? • It is function that describes how light is reflected from a surface. • It is used to describe material properties. • Input value • Incoming and outgoing azimuth and elevation angles. • Wave length of the incoming light. • Presented with RGB color.

5. BRDF? • General functional notation. • Position-invariant BRDF in functional notation. λ : used to indicate that the BRDF depends on the wavelength under Consideration. θi, φi : represent the incoming light direction in spherical coordinates. θo, φo : represent the outgoing reflected direction in spherical coordinates u , v : represent the surface position parameterized in texture space.

6. BRDF? • Definition of BRDF • It is defined as the ratio of the quantity of reflected light in direction wo, to the amount of light that reaches the surface form direction wi. • wo is incoming light direction, wi is outgoing light direction.

7. BRDF? • Definition of BRDF • It is defined as the ratio of the quantity of reflected light in direction wo, to the amount of light that reaches the surface form direction wi. • Lo : quantity of light reflected from the surface in direction wo. • Ei : amount of light arriving from direction wi.

8. BRDF? • Definition of BRDF. • Incoming light projected onto the surface element. (similar to lambertian lighting)

9. BRDF? • Given a BRDF and an incoming radiance distribution (at Hemisphere) • The reflectance equation determines the outgoing radiance for a given viewing direction relative to the surface. • Single point light source

10. BRDF? • Important properties • Input and output angle can be switched. • Function value will be the same. • BRDF must be normalized. • Total outgoing energy must be less than or equal to incoming energy. • not include the scattering of light within the surface. • BSSRDF function describes this penomenas.

11. Phong Light Equation. • Phong Light • BRDF

12. Implementing BRDFs-Factorization • Idea • Map the incoming and outgoing directions to pixels on the texture. • BRDF function is separated in as few significant term as possible. • Direction vector can be interpolated linearly across the texture. • Convert a BRDF into a set of pairs of two-dimensional texture. • One texture is accessed by incoming direction. • The other is accessed by outgoing direction.

13. Implementing BRDFs-Factorization

14. Implementing BRDFs in Shaders. • Lambertian Model • Shader code PixelOut main(V2FI IN) { IN.LightVector=normalize(IN.LightVector); PixelOut Out; float4 DiffuseColor = float4(1.0f, 1.0f, 1.0f, 1.0f); Out.Color = DiffuseColor * max(dot(IN.LightVector,normalize(IN.Normal)), 0.0f); return Out; }

15. Implementing BRDFs in Shaders. • Lambertian Model

16. LIGHT N R=L+2S L+S=Ncosθ S=N(N×L)-L RESULT:R=2N(N×L)-L S R VIEWER L θ θ α V ( ) n = × R I K V I L S S Implementing BRDFs in Shaders. • Phong material. • Blinn-Phong material. Φ+ Ψ=(Φ- Ψ)+ θ 2 Ψ= θ H=L+V/|L+V| ( ) n = × H I K N I L S S

17. Implementing BRDFs in Shaders. • Phong and Blinn-Phong material.

18. Implementing BRDFs in Shaders. • Oren-Nayar Diffuse Relflection • Describe some rough surfaces such as dirt, clay, and some types of cloth exhibit a high degree of retro reflection PixelOut main(V2FI IN) { PixelOut Out; float3 N=normalize(IN.Normal); float3 L=normalize(IN.LightVector); float3 V=normalize(IN.ViewVector); float4 DiffuseColor = float4(0.7f, 0.8f, 0.7f, 1.0f); float VdotN = dot(N,V); float LdotN = dot(N,L); float Irradiance = max(LdotN,0.0f); float theta_r = acos(VdotN); float theta_i = acos(LdotN); float cos_phi_diff = dot( normalize(V-N*VdotN),normalize(L-N*LdotN)); float alpha = max(theta_i,theta_r); float beta = min(theta_i,theta_r); float roughness = 0; float A = 1.0f-0.5f*(roughness*roughness/roughness*roughness+0.3f); float B = 0.45f*(roughness*roughness/roughness*roughness+0.09f); float Oren_Nayer = (A+B*max(cos_phi_diff,0.0f)*sin(alpha)*tan(beta)); Out.Color = DiffuseColor * Oren_Nayer*Irradiance; return Out; }

19. Implementing BRDFs in Shaders. • Oren-Nayar Diffuse Relflection

20. Implementing BRDFs in Shaders. • Minnaert Reflection • Good for modeling the appearance of velvet. PixelOut main(V2FI IN) { PixelOut Out; float3 N=normalize(IN.Normal); float3 L=normalize(IN.LightVector); float3 V=normalize(IN.ViewVector); float4 DiffuseColor = float4(0.7f, 0.8f, 0.7f, 1.0f); float NdotL = dot(N,L); float NdotV = dot(N,V); float Irradiance = max(NdotL,0.0f); float Power = 0.75; float Minneart = pow(NdotL*NdotV,Power)*Irradiance; Out.Color = DiffuseColor * Minneart; return Out; }

21. Implementing BRDFs in Shaders. • Minnaert Reflection

22. Implementing BRDFs in Shaders. • Specular and Metallic Reflection Models. • Ward Reflection Model. • Isotropic PixelOut main(V2FI IN) { PixelOut Out; float3 N=normalize(IN.Normal); float3 L=normalize(IN.LightVector); float3 V=normalize(IN.ViewVector); float roughness = 0.35f; float roughness_2 = pow(roughness,2); float4 DiffuseColor = {0.2775f, 0.2775f, 0.2775f, 1.0f}; float4 SpecularColor = {0.773911f,0.773911f,0.773911f,1.0f}; float NdotV = dot(N,V); float NdotL = dot(N,L); float3 HalfVector = normalize((L+V)/2); float Irradiance = max(NdotL,0.0f); float r = acos(dot(N,HalfVector)); float tan2 = -pow(tan(r),2); float FirstTerm = exp(tan2/roughness_2)/(6.28*roughness_2); float SecondTerm = 1/sqrt(NdotL*NdotV); float Ward_Isotropic = FirstTerm * SecondTerm; Out.Color = (DiffuseColor+SpecularColor*Ward_Isotropic)*Irradiance; return Out; } α = standard deviation of the surface slope.

23. Implementing BRDFs in Shaders. • Specular and Metallic Reflection Models. • Ward Isotropic reflection model

24. Implementing BRDFs in Shaders. • Specular and Metallic Reflection Models. • Ward Reflection Model. • Anisotropic • Computationally convenient approximation.

25. Implementing BRDFs in Shaders. • Specular and Metallic Reflection Models. • Ward Reflection Model. • Anisotropic PixelOut main(V2FI IN) { PixelOut OutPixel; float3 PixelToEye = normalize(IN.ViewVector); float3 NewNormal = normalize(IN.Normal); float3 HalfVector = normalize(IN.LightVector + PixelToEye); //First Term float CosTheta = dot(NewNormal, IN.LightVector); float CosDelta = dot(NewNormal, PixelToEye); float4 FirstTerm = 1.0f / sqrt(CosTheta * CosDelta); float2 Roughness = {0.9f, 0.1f}; //Second Term float4 SecondTerm = 1.0f / (12.56 * Roughness.x * Roughness.y); //Third Term float3 Direction = {0.0f, 0.0f, 1.0}; float3 X = normalize(cross(NewNormal, Direction)); float3 Y = normalize(cross(NewNormal, X)); float HdotX = dot(HalfVector, X); float HdotY = dot(HalfVector, Y); float HdotN = dot(HalfVector, NewNormal); float A = -2.0f * (pow((HdotX / Roughness.x), 2) + pow((HdotY / Roughness.y), 2)); float B = 1.0f + HdotN; float4 ThirdTerm = exp(A / B); float4 Irradiance = max(0.0f, CosTheta); float4 DiffuseColor = {0.2775f, 0.2775f, 0.2775f, 1.0f}; float4 SpecularColor = {0.773911f,0.773911f,0.773911f,1.0f}; float4 SpecularTerm = SpecularColor * FirstTerm * SecondTerm * ThirdTerm; OutPixel.Color = (DiffuseColor + SpecularTerm) * Irradiance; return OutPixel; }

26. Implementing BRDFs in Shaders. • Specular and Metallic Reflection Models. • Ward Anisotropic Reflection Model.

27. Implementing BRDFs in Shaders. • Specular and Metallic Reflection Models. • Schlick Reflection Model. PixelOut main(V2FI IN) { PixelOut Out; float3 N=normalize(IN.Normal); float3 L=normalize(IN.LightVector); float3 V=normalize(IN.ViewVector); float4 DiffuseColor = {0.75164f, 0.60648f, 0.22648f, 1.0f}; float4 SpecularColor = {0.628281f,0.555802f,0.366065f,10.0f}; float3 Reflection = normalize(2.0f * N * dot(N,L)-L); float RdotV = max(dot(Reflection.xyz,V),0.0); float SchlickTerm = RdotV / (SpecularColor.w - (SpecularColor.w * RdotV) + RdotV); float4 Diffuse = DiffuseColor * max(0.0f, dot(L,N)); float4 Specular = SpecularColor * SchlickTerm; Out.Color = Diffuse + Specular; return Out; }

28. Implementing BRDFs in Shaders. • Specular and Metallic Reflection Models. • Schlick Reflection Model.

29. Implementing BRDFs in Shaders. • Specular and Metallic Reflection Models. • Cook-Torrance Model.

30. Implementing BRDFs in Shaders. • Specular and Metallic Reflection Models. • Cook-Torrance Model. PS_OUTPUT OutPixel; float3 PixelToEye = normalize(In.ViewVector); float3 NewNormal = normalize(In.Normal); float3 LightVector = normalize(In.LightVector); float3 HalfVector = normalize(LightVector + PixelToEye); float NdotH = max(0.0f, dot(NewNormal, HalfVector)); float3 RoughnessParams = {0.5f, 0.5f, 0.5f}; //Start the "D" term, use Blinn Gaussian float Alpha = acos(NdotH); float C = RoughnessParams.x; float m = RoughnessParams.y; float D = C * exp(-(pow(Alpha / m, 2.0f))); //Start the "G" term float NdotV = dot(NewNormal, PixelToEye); float VdotH = dot(HalfVector, PixelToEye); float NdotL = dot(LightVector, NewNormal); float G1 = 2 * NdotH * NdotV / NdotH; float G2 = 2 * NdotH * NdotL / NdotH; float G = min(1.0f, max(0.0f, min(G1, G2))); //Start the fresnel term. Use the approximation from //http://developer.nvidia.com/docs/IO/3035/ATT/FresnelReflection.pdf float R0 = RoughnessParams.z; float F = R0 + (1.0f - R0) * pow(1.0f - NdotL, 5.0); float4 DiffuseColor = {1.0f, 1.0f, 1.0f, 1.0f}; OutPixel.Color = DiffuseColor * F * D * G / (NdotL * NdotV); return OutPixel; }

31. Implementing BRDFs in Shaders. • Specular and Metallic Reflection Models. • Cook-Torrance Model.

32. Implementing BRDFs in Shaders. • Video