Cg Programming/Unity/Specular Highlights

“Apollo the Lute Player” (Badminton House version) by Michelangelo Merisi da Caravaggio, ca. 1596.

This tutorial covers per-vertex lighting (also known as Gouraud shading) using the Phong reflection model.

It extends the shader code in Section “Diffuse Reflection” by two additional terms: ambient lighting and specular reflection. Together, the three terms constitute the Phong reflection model. If you haven't read Section “Diffuse Reflection”, this would be a very good opportunity to read it.

Ambient Light

Consider the painting by Caravaggio to the left. While large parts of the white shirt are in shadows, no part of it is completely black. Apparently there is always some light being reflected from walls and other objects to illuminate everything in the scene — at least to a certain degree. In the Phong reflection model, this effect is taken into account by ambient lighting, which depends on a general ambient light intensity $I_{\text{ambient light}}$ and the material color $k_{\text{diffuse}}$ for diffuse reflection. In an equation for the intensity of ambient lighting $I_{\text{ambient}}$ :

$I_{\text{ambient}}=I_{\text{ambient light}}\,k_{\text{diffuse}}$

Analogously to the equation for diffuse reflection in Section “Diffuse Reflection”, this equation can also be interpreted as a vector equation for the red, green, and blue components of light.

In Unity, a uniform ambient light is specified by choosing Window > Rendering > Lighting Settings from the main menu, setting Scene > Environment Lighting > Source to Color and specifying the Ambient Color. In a Cg shader in Unity, this color is then available as UNITY_LIGHTMODEL_AMBIENT, which is one of the pre-defined uniforms mentioned in Section “Shading in World Space”. (If you choose Gradient instead of Color then UNITY_LIGHTMODEL_AMBIENT and unity_AmbientSky specify the Sky Color, while the Equator Color and the Ground Color are specified by unity_AmbientEquator and unity_AmbientGround.)

Specular Highlights

If you have a closer look at Caravaggio's painting, you will see several specular highlights: on the nose, on the hair, on the lips, on the lute, on the violin, on the bow, on the fruits, etc. The Phong reflection model includes a specular reflection term that can simulate such highlights on shiny surfaces; it even includes a parameter $n_{\text{shininess}}$ to specify a shininess of the material. The shininess specifies how small the highlights are: the shinier, the smaller the highlights.

A perfectly shiny surface will reflect light from the light source only in the geometrically reflected direction R. For less than perfectly shiny surfaces, light is reflected to directions around R: the smaller the shininess, the wider the spreading. Mathematically, the normalized reflected direction R is defined by:

$\mathbf {R} =2\mathbf {N} (\mathbf {N} \cdot \mathbf {L} )-\mathbf {L}$

for a normalized surface normal vector N and a normalized direction to the light source L. In Cg, the function float3 reflect(float3 I, float3 N) (or float4 reflect(float4 I, float4 N)) computes the same reflected vector but for the direction I from the light source to the point on the surface. Thus, we have to negate our direction L to use this function.

The specular reflection term computes the specular reflection in the direction of the viewer V. As discussed above, the intensity should be large if V is close to R, where “closeness” is parametrized by the shininess $n_{\text{shininess}}$ . In the Phong reflection model, the cosine of the angle between R and V to the $n_{\text{shininess}}$ -th power is used to generate highlights of different shininess. Similarly to the case of the diffuse reflection, we should clamp negative cosines to 0. Furthermore, the specular term requires a material color $k_{\text{specular}}$ for the specular reflection, which is usually just white such that all highlights have the color of the incoming light $I_{\text{incoming}}$ . For example, all highlights in Caravaggio's painting are white. The specular term of the Phong reflection model is then:

$I_{\text{specular}}=I_{\text{incoming}}\,k_{\text{specular}}\max(0,\mathbf {R} \cdot \mathbf {V} )^{n_{\text{shininess}}}$

Analogously to the case of the diffuse reflection, the specular term should be ignored if the light source is on the “wrong” side of the surface; i.e., if the dot product N·L is negative.

Shader Code

The shader code for the ambient lighting is straightforward with a component-wise vector-vector product:

            float3 ambientLighting = 
               UNITY_LIGHTMODEL_AMBIENT.rgb * _Color.rgb;

For the implementation of the specular reflection, we require the direction to the viewer in world space, which we can compute as the difference between the camera position and the vertex position (both in world space). The camera position in world space is provided by Unity in the uniform _WorldSpaceCameraPos; the vertex position can be transformed to world space as discussed in Section “Diffuse Reflection”. The equation of the specular term in world space could then be implemented like this:

            float3 viewDirection = normalize(_WorldSpaceCameraPos 
               - mul(modelMatrix, input.vertex).xyz);

            float3 specularReflection;
            if (dot(normalDirection, lightDirection) < 0.0) 
               // light source on the wrong side?
            {
               specularReflection = float3(0.0, 0.0, 0.0); 
                  // no specular reflection
            }
            else // light source on the right side
            {
               specularReflection = attenuation * _LightColor0.rgb 
                  * _SpecColor.rgb * pow(max(0.0, dot(
                  reflect(-lightDirection, normalDirection), 
                  viewDirection)), _Shininess);
            }

This code snippet uses the same variables as the shader code in Section “Diffuse Reflection” and additionally the user-specified properties _SpecColor and _Shininess. (The names were specifically chosen such that the fallback shader can access them; see the discussion in Section “Diffuse Reflection”.) pow(a, b) computes $a^{b}$ .

If the ambient lighting is added to the first pass (we only need it once) and the specular reflection is added to both passes of the full shader of Section “Diffuse Reflection”, it looks like this:

Shader "Cg per-vertex lighting" {
   Properties {
      _Color ("Diffuse Material Color", Color) = (1,1,1,1) 
      _SpecColor ("Specular Material Color", Color) = (1,1,1,1) 
      _Shininess ("Shininess", Float) = 10
   }
   SubShader {
      Pass {	
         Tags { "LightMode" = "ForwardBase" } 
            // pass for ambient light and first light source
 
         CGPROGRAM
 
         #pragma vertex vert  
         #pragma fragment frag 
 
         #include "UnityCG.cginc"
         uniform float4 _LightColor0; 
            // color of light source (from "Lighting.cginc")
 
         // User-specified properties
         uniform float4 _Color; 
         uniform float4 _SpecColor; 
         uniform float _Shininess;
 
         struct vertexInput {
            float4 vertex : POSITION;
            float3 normal : NORMAL;
         };
         struct vertexOutput {
            float4 pos : SV_POSITION;
            float4 col : COLOR;
         };
 
         vertexOutput vert(vertexInput input) 
         {
            vertexOutput output;
 
            float4x4 modelMatrix = unity_ObjectToWorld;
            float3x3 modelMatrixInverse = unity_WorldToObject;
            float3 normalDirection = normalize(
               mul(input.normal, modelMatrixInverse));
            float3 viewDirection = normalize(_WorldSpaceCameraPos 
               - mul(modelMatrix, input.vertex).xyz);
            float3 lightDirection;
            float attenuation;
 
            if (0.0 == _WorldSpaceLightPos0.w) // directional light?
            {
               attenuation = 1.0; // no attenuation
               lightDirection = normalize(_WorldSpaceLightPos0.xyz);
            } 
            else // point or spot light
            {
               float3 vertexToLightSource = _WorldSpaceLightPos0.xyz
                  - mul(modelMatrix, input.vertex).xyz;
               float distance = length(vertexToLightSource);
               attenuation = 1.0 / distance; // linear attenuation 
               lightDirection = normalize(vertexToLightSource);
            }
 
            float3 ambientLighting = 
               UNITY_LIGHTMODEL_AMBIENT.rgb * _Color.rgb;
 
            float3 diffuseReflection = 
               attenuation * _LightColor0.rgb * _Color.rgb
               * max(0.0, dot(normalDirection, lightDirection));
 
            float3 specularReflection;
            if (dot(normalDirection, lightDirection) < 0.0) 
               // light source on the wrong side?
            {
               specularReflection = float3(0.0, 0.0, 0.0); 
                  // no specular reflection
            }
            else // light source on the right side
            {
               specularReflection = attenuation * _LightColor0.rgb 
                  * _SpecColor.rgb * pow(max(0.0, dot(
                  reflect(-lightDirection, normalDirection), 
                  viewDirection)), _Shininess);
            }
 
            output.col = float4(ambientLighting + diffuseReflection 
               + specularReflection, 1.0);
            output.pos = UnityObjectToClipPos(input.vertex);
            return output;
         }
 
         float4 frag(vertexOutput input) : COLOR
         {
            return input.col;
         }
 
         ENDCG
      }
 
      Pass {	
         Tags { "LightMode" = "ForwardAdd" } 
            // pass for additional light sources
         Blend One One // additive blending 
 
         CGPROGRAM
 
         #pragma vertex vert  
         #pragma fragment frag 
 
         #include "UnityCG.cginc"
         uniform float4 _LightColor0; 
            // color of light source (from "Lighting.cginc")
 
         // User-specified properties
         uniform float4 _Color; 
         uniform float4 _SpecColor; 
         uniform float _Shininess;
 
         struct vertexInput {
            float4 vertex : POSITION;
            float3 normal : NORMAL;
         };
         struct vertexOutput {
            float4 pos : SV_POSITION;
            float4 col : COLOR;
         };
 
         vertexOutput vert(vertexInput input) 
         {
            vertexOutput output;
 
            float4x4 modelMatrix = unity_ObjectToWorld;
            float3x3 modelMatrixInverse = unity_WorldToObject;
            float3 normalDirection = normalize(
               mul(input.normal, modelMatrixInverse));
            float3 viewDirection = normalize(_WorldSpaceCameraPos 
               - mul(modelMatrix, input.vertex).xyz);
            float3 lightDirection;
            float attenuation;
 
            if (0.0 == _WorldSpaceLightPos0.w) // directional light?
            {
               attenuation = 1.0; // no attenuation
               lightDirection = normalize(_WorldSpaceLightPos0.xyz);
            } 
            else // point or spot light
            {
               float3 vertexToLightSource = _WorldSpaceLightPos0.xyz
                  - mul(modelMatrix, input.vertex).xyz;
               float distance = length(vertexToLightSource);
               attenuation = 1.0 / distance; // linear attenuation 
               lightDirection = normalize(vertexToLightSource);
            }
 
            float3 diffuseReflection = 
               attenuation * _LightColor0.rgb * _Color.rgb
               * max(0.0, dot(normalDirection, lightDirection));
 
            float3 specularReflection;
            if (dot(normalDirection, lightDirection) < 0.0) 
               // light source on the wrong side?
            {
               specularReflection = float3(0.0, 0.0, 0.0); 
                  // no specular reflection
            }
            else // light source on the right side
            {
               specularReflection = attenuation * _LightColor0.rgb 
                  * _SpecColor.rgb * pow(max(0.0, dot(
                  reflect(-lightDirection, normalDirection), 
                  viewDirection)), _Shininess);
            }
 
            output.col = float4(diffuseReflection 
               + specularReflection, 1.0);
               // no ambient contribution in this pass
            output.pos = UnityObjectToClipPos(input.vertex);
            return output;
         }
 
         float4 frag(vertexOutput input) : COLOR
         {
            return input.col;
         }
 
         ENDCG
      }
   }
   Fallback "Specular"
}

Summary

Congratulations, you just learned how to implement the Phong reflection model. In particular, we have seen:

What the ambient lighting in the Phong reflection model is.
What the specular reflection term in the Phong reflection model is.
How these terms can be implemented in Cg in Unity.

Ambient Light

Specular Highlights

Shader Code

Summary

Further reading