1. Week 8 - Friday

2.  What did we talk about last time?  Radiometry  Photometry  Colorimetry  Lighting with shader code  Ambient  Directional (diffuse and specular)  Point

6.  Adding a specular component to the diffuse shader requires incorporating the view vector  It will be included in the shader file and be set as a parameter in the C# code

7.  The camera location is added to the declarations  As are specular colors and a shininess parameter float4x4 World; float4x4 View; float4x4 Projection; float4x4 WorldInverseTranspose; float3 Camera; static const float PI = 3.14159265f; float4 AmbientColor = float4(1, 1, 1, 1); float AmbientIntensity = 0.1; float3 DiffuseLightDirection = float3(1, 1, 0); float4 DiffuseColor = float4(1, 1, 1, 1); float DiffuseIntensity = 0.7; float Shininess; float4 SpecularColor = float4(1, 1, 1, 1); float SpecularIntensity = 0.5; float4x4 World; float4x4 View; float4x4 Projection; float4x4 WorldInverseTranspose; float3 Camera; static const float PI = 3.14159265f; float4 AmbientColor = float4(1, 1, 1, 1); float AmbientIntensity = 0.1; float3 DiffuseLightDirection = float3(1, 1, 0); float4 DiffuseColor = float4(1, 1, 1, 1); float DiffuseIntensity = 0.7; float Shininess; float4 SpecularColor = float4(1, 1, 1, 1); float SpecularIntensity = 0.5;

8.  The output adds a normal so that the half vector can be computed in the pixel shader  A world position lets us compute the view vector to the camera struct VertexShaderInput { float4 Position : SV_POSITION; float3 Normal : NORMAL; }; struct VertexShaderOutput { float4 Position : SV_POSITION; float4 Color : COLOR; float3 Normal : NORMAL; float4 WorldPosition : POSITIONT; }; struct VertexShaderInput { float4 Position : SV_POSITION; float3 Normal : NORMAL; }; struct VertexShaderOutput { float4 Position : SV_POSITION; float4 Color : COLOR; float3 Normal : NORMAL; float4 WorldPosition : POSITIONT; };

9.  The same computations as the diffuse shader, but we store the normal and the transformed world position in the output VertexShaderOutput VertexShaderFunction(VertexShaderInput input) { VertexShaderOutput output; float4 worldPosition = mul(input.Position, World); output.WorldPosition = worldPosition; float4 viewPosition = mul(worldPosition, View); output.Position = mul(viewPosition, Projection); float3 normal = normalize(mul(input.Normal, (float3x3)WorldInverseTranspose)); float lightIntensity = dot(normal, normalize(DiffuseLightDirection)); output.Color = saturate(DiffuseColor * DiffuseIntensity * lightIntensity); output.Normal = normal; return output; } VertexShaderOutput VertexShaderFunction(VertexShaderInput input) { VertexShaderOutput output; float4 worldPosition = mul(input.Position, World); output.WorldPosition = worldPosition; float4 viewPosition = mul(worldPosition, View); output.Position = mul(viewPosition, Projection); float3 normal = normalize(mul(input.Normal, (float3x3)WorldInverseTranspose)); float lightIntensity = dot(normal, normalize(DiffuseLightDirection)); output.Color = saturate(DiffuseColor * DiffuseIntensity * lightIntensity); output.Normal = normal; return output; }

10.  Here we finally have a real computation because we need to use the pixel normal (which is averaged from vertices) in combination with the view vector  The technique is the same float4 PixelShaderFunction(VertexShaderOutput input) : SV_Target { float3 light = normalize(DiffuseLightDirection); float3 normal = normalize(input.Normal); float3 reflect = normalize(2 * dot(light, normal) * normal – light); float3 view = normalize(input.WorldPosition - Camera); float dotProduct = dot(reflect, view); float4 specular = (8 + Shininess) / (8 * PI) * SpecularIntensity * SpecularColor * max(pow(dotProduct, Shininess), 0) * length(input.Color); return saturate(input.Color + AmbientColor * AmbientIntensity + specular); } float4 PixelShaderFunction(VertexShaderOutput input) : SV_Target { float3 light = normalize(DiffuseLightDirection); float3 normal = normalize(input.Normal); float3 reflect = normalize(2 * dot(light, normal) * normal – light); float3 view = normalize(input.WorldPosition - Camera); float dotProduct = dot(reflect, view); float4 specular = (8 + Shininess) / (8 * PI) * SpecularIntensity * SpecularColor * max(pow(dotProduct, Shininess), 0) * length(input.Color); return saturate(input.Color + AmbientColor * AmbientIntensity + specular); }

11.  Point lights model omni lights at a specific position  They generally attenuate (get dimmer) over a distance and have a maximum range  DirectX has a constant attenuation, linear attenuation, and a quadratic attenuation  You can choose attenuation levels through shaders  They are more computationally expensive than directional lights because a light vector has to be computed for every pixel  It is possible to implement point lights in a deferred shader, lighting only those pixels that actually get used

12.  We add light position float4x4 World; float4x4 View; float4x4 Projection; float4x4 WorldInverseTranspose; float3 LightPosition; float3 Camera; static const float PI = 3.14159265f; float4 AmbientColor = float4(1, 1, 1, 1); float AmbientIntensity = 0.1f; float LightRadius = 50; float4 DiffuseColor = float4(1, 1, 1, 1); float DiffuseIntensity = 0.7; float Shininess; float4 SpecularColor = float4(1, 1, 1, 1); float SpecularIntensity = 0.5f; float4x4 World; float4x4 View; float4x4 Projection; float4x4 WorldInverseTranspose; float3 LightPosition; float3 Camera; static const float PI = 3.14159265f; float4 AmbientColor = float4(1, 1, 1, 1); float AmbientIntensity = 0.1f; float LightRadius = 50; float4 DiffuseColor = float4(1, 1, 1, 1); float DiffuseIntensity = 0.7; float Shininess; float4 SpecularColor = float4(1, 1, 1, 1); float SpecularIntensity = 0.5f;

13.  We no longer need color in the output  We do need the vector to the camera from the location  We keep the world location at that fragment struct VertexShaderInput { float4 Position : SV_POSITION; float3 Normal : NORMAL; }; struct VertexShaderOutput { float4 Position : SV_POSITION; float4 WorldPosition : POSITIONT; float3 Normal : NORMAL; }; struct VertexShaderInput { float4 Position : SV_POSITION; float3 Normal : NORMAL; }; struct VertexShaderOutput { float4 Position : SV_POSITION; float4 WorldPosition : POSITIONT; float3 Normal : NORMAL; };

14.  We compute the normal and the world position VertexShaderOutput VertexShaderFunction(VertexShaderInput input) { VertexShaderOutput output; float4 worldPosition = mul(input.Position, World); output.WorldPosition = worldPosition; float4 viewPosition = mul(worldPosition, View); output.Position = mul(viewPosition, Projection); float3 normal = normalize(mul(input.Normal, (float3x3)WorldInverseTranspose)); output.Normal = normal; return output; } VertexShaderOutput VertexShaderFunction(VertexShaderInput input) { VertexShaderOutput output; float4 worldPosition = mul(input.Position, World); output.WorldPosition = worldPosition; float4 viewPosition = mul(worldPosition, View); output.Position = mul(viewPosition, Projection); float3 normal = normalize(mul(input.Normal, (float3x3)WorldInverseTranspose)); output.Normal = normal; return output; }

15.  Lots of junk in here float4 PixelShaderFunction(VertexShaderOutput input) : SV_Target { float3 normal = normalize(input.Normal); float3 lightDirection = LightPosition – (float3)input.WorldPosition; float intensity = pow(1.0f – saturate(length(lightDirection)/LightRadius), 2); lightDirection = normalize(lightDirection); //normalize after float3 view = normalize(Camera - (float3)input.WorldPosition); float diffuseColor = dot(normal, lightDirection); float3 reflect = normalize(2 * diffuseColor * normal – lightDirection); float dotProduct = dot(reflect, view); float specular = (8 + Shininess) / (8 * PI) * SpecularIntensity * SpecularColor * max(pow(dotProduct, Shininess), 0) * length(diffuseColor); return saturate(diffuseColor + AmbientColor * AmbientIntensity + specular); } float4 PixelShaderFunction(VertexShaderOutput input) : SV_Target { float3 normal = normalize(input.Normal); float3 lightDirection = LightPosition – (float3)input.WorldPosition; float intensity = pow(1.0f – saturate(length(lightDirection)/LightRadius), 2); lightDirection = normalize(lightDirection); //normalize after float3 view = normalize(Camera - (float3)input.WorldPosition); float diffuseColor = dot(normal, lightDirection); float3 reflect = normalize(2 * diffuseColor * normal – lightDirection); float dotProduct = dot(reflect, view); float specular = (8 + Shininess) / (8 * PI) * SpecularIntensity * SpecularColor * max(pow(dotProduct, Shininess), 0) * length(diffuseColor); return saturate(diffuseColor + AmbientColor * AmbientIntensity + specular); }

18.  The bidirectional reflectance distribution function is a function that describes the difference between outgoing radiance and incoming irradiance  This function changes based on:  Wavelength  Angle of light to surface  Angle of viewer from surface  For point or directional lights, we do not need differentials and can write the BRDF:

19.  We've been talking about lighting models  Lambertian, specular, etc.  A BRDF is an attempt to model physics slightly better  A big difference is that different wavelengths are absorbed and reflected different by different materials  Rendering models in real time with (more) accurate BRDFs is still an open research problem

20.  They also have global lighting (shadows and reflections)  Taken from www.kevinbeason.comwww.kevinbeason.com

21.  The BRDF is supposed to account for all the light interactions we discussed in Chapter 5 (reflection and refraction)  We can see the similarity to the lighting equation from Chapter 5, now with a BRDF:

22.  If the subsurface scattering effects are great, the size of the pixel may matter  Then, a bidirectional surface scattering reflectance distribution function (BSSRDF) is needed  Or if the surface characteristics change in different areas, you need a spatially varying BRDF  And so on…

23.  Helmholtz reciprocity:  f(l,v) = f(v,l)  Conservation of energy:  Outgoing energy cannot be greater than incoming energy  The simplest BRDF is Lambertian shading  We assume that energy is scattered equally in all directions  Integrating over the hemisphere gives a factor of π  Dividing by π gives us exactly what we saw before:

25.  We'll start with our specular shader for directional light and add textures to it

26.  The texture for the ship is below:

27.  We add a texture variable called ModelTexture  We also add a SamplerState structure that specifies how to filter the texture Texture2D ModelTexture; SamplerState ModelTextureSampler { Filter = MIN_MAG_MIP_LINEAR; AddressU = Clamp; AddressV = Clamp; }; Texture2D ModelTexture; SamplerState ModelTextureSampler { Filter = MIN_MAG_MIP_LINEAR; AddressU = Clamp; AddressV = Clamp; };

28.  We add a texture coordinate to the input and the output of the vertex shader struct VertexShaderInput { float4 Position : SV_POSITION; float3 Normal : NORMAL; float2 Texture : TEXCOORD; }; struct VertexShaderOutput { float4 Position : SV_POSITION; float4 Color : COLOR; float3 Normal : NORMAL; float4 WorldPosition : POSITIONT; float2 Texture : TEXCOORD; }; struct VertexShaderInput { float4 Position : SV_POSITION; float3 Normal : NORMAL; float2 Texture : TEXCOORD; }; struct VertexShaderOutput { float4 Position : SV_POSITION; float4 Color : COLOR; float3 Normal : NORMAL; float4 WorldPosition : POSITIONT; float2 Texture : TEXCOORD; };

29.  Almost nothing changes here except that we copy the input texture coordinate into the output VertexShaderOutput VertexShaderFunction(VertexShaderInput input) { VertexShaderOutput output; float4 worldPosition = mul(input.Position, World); output.WorldPosition = worldPosition; float4 viewPosition = mul(worldPosition, View); output.Position = mul(viewPosition, Projection); float3 normal = normalize(mul(input.Normal, (float3x3)WorldInverseTranspose)); float lightIntensity = dot(normal, normalize(DiffuseLightDirection)); output.Color = saturate(DiffuseColor * DiffuseIntensity * lightIntensity); output.Normal = normal; output.Texture = input.Texture; return output; } VertexShaderOutput VertexShaderFunction(VertexShaderInput input) { VertexShaderOutput output; float4 worldPosition = mul(input.Position, World); output.WorldPosition = worldPosition; float4 viewPosition = mul(worldPosition, View); output.Position = mul(viewPosition, Projection); float3 normal = normalize(mul(input.Normal, (float3x3)WorldInverseTranspose)); float lightIntensity = dot(normal, normalize(DiffuseLightDirection)); output.Color = saturate(DiffuseColor * DiffuseIntensity * lightIntensity); output.Normal = normal; output.Texture = input.Texture; return output; }

30.  We have to pull the color from the texture and set its alpha to 1  Then scale the components of the color by the texture color float4 PixelShaderFunction(VertexShaderOutput input) : SV_Target { float3 light = normalize(DiffuseLightDirection); float3 normal = normalize(input.Normal); float3 reflect = normalize(2 * dot(light, normal) * normal – light); float3 view = normalize(input.WorldPosition - Camera); float dotProduct = dot(reflect, view); float4 specular = (8 + Shininess) / (8 * PI) * SpecularIntensity * SpecularColor * max(pow(dotProduct, Shininess), 0) * length(input.Color); float4 textureColor = ModelTexture.Sample(ModelTextureSampler, input.Texture); textureColor.a = 1; return saturate(textureColor * input.Color + AmbientColor * AmbientIntensity + specular); } float4 PixelShaderFunction(VertexShaderOutput input) : SV_Target { float3 light = normalize(DiffuseLightDirection); float3 normal = normalize(input.Normal); float3 reflect = normalize(2 * dot(light, normal) * normal – light); float3 view = normalize(input.WorldPosition - Camera); float dotProduct = dot(reflect, view); float4 specular = (8 + Shininess) / (8 * PI) * SpecularIntensity * SpecularColor * max(pow(dotProduct, Shininess), 0) * length(input.Color); float4 textureColor = ModelTexture.Sample(ModelTextureSampler, input.Texture); textureColor.a = 1; return saturate(textureColor * input.Color + AmbientColor * AmbientIntensity + specular); }

31.  To use a texture, we naturally have to load a texture  We have to set the texture, but as a resource, not as a value texture = Content.Load (" ShipTexture "); effect.Parameters["ModelTexture"].SetResource ( shipTexture); effect.Parameters["ModelTexture"].SetResource ( shipTexture);

32.  It's easiest to do bump mapping in SharpDX using a normal map  Of course, a normal map is hard to create by hand  What's more common is to create a height map and then use a tool for creating a normal map from it  xNormal is a free utility to do this  http://www.xnormal.net/Downloads.aspx

33.  The conversion from a grayscale height map to a normal map looks like this

34.  We have a normal to a surface, but there are also tangent directions  We call these the tangent and the binormal  Apparently serious mathematicians think it should be called the bitangent  The binormal is tangent to the surface and orthogonal to the other tangent  We distort the normal with weighted sums of the tangent and binormal (stored in our normal map) Normal Tangent Binormal

36.  Choosing BRDFs  Implementing BRDFs  Image-based approaches to sampling BRDFs

37.  Finish reading Chapter 7  Finish Project 2  Due tonight by midnight