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Real Time Rendering

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Real Time Rendering

Lighting and Reflectance Model

- 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.

- 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.

- Reflected light and Absorbed light.
- BRDF describes how much light is reflected when light makes with a certain material.

- Form.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

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

- 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

- 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.

- Phong Light
- BRDF

- 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.

- Map the incoming and outgoing directions to pixels on the texture.

- 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;

}

- Lambertian Model

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

- 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

- Phong and Blinn-Phong material.

- 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;

}

- Oren-Nayar Diffuse Relflection

- 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;

}

- Minnaert Reflection

- Specular and Metallic Reflection Models.
- Ward Reflection Model.
- Isotropic

- Ward Reflection Model.

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.

- Specular and Metallic Reflection Models.
- Ward Isotropic reflection model

- Specular and Metallic Reflection Models.
- Ward Reflection Model.
- Anisotropic
- Computationally convenient approximation.

- Ward Reflection Model.

- Specular and Metallic Reflection Models.
- Ward Reflection Model.
- Anisotropic

- Ward Reflection Model.

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;

}

- Specular and Metallic Reflection Models.
- Ward Anisotropic Reflection Model.

- 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;

}

- Specular and Metallic Reflection Models.
- Schlick Reflection Model.

- Specular and Metallic Reflection Models.
- Cook-Torrance Model.

- 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;

}

- Specular and Metallic Reflection Models.
- Cook-Torrance Model.

- Video