CS315 Lab 5: Illumination 2


Highlights of this lab:

This lab extends your knowledge of basic illumination
  1. The Blinn Phong equation revisited
  2. Hemisphere lighting
  3. Distance and Positional Lights

Assignment:

After the lab lecture, you have approximately one week to:

Lab Notes

In last week's lab you saw these pictures. They show a full implementation of the Blinn-Phong reflection equation being applied in three different ways. The first is flat shading - one colour is used for one whole primitive (triangle). The second is Gouraud shading - reflection is only calculated at the vertices, and colours are interpolated. The last is Phong shading - the full lighting equation is performed per fragment in the fragment shader. This week you will see results that look like all three columns, but you will always be doing Gouraud shading. You will add the Blinn-Phong specular component to a vertex shader, which produces the whitish highlight you see. The smoothness or flatness you will observe will be created entirely in the model - either by using the same normal for all vertices of a primitive (flat-like results) or high resolution meshes (Phong-like results).

Flat Shading Gouraud Shading Phong Shading
Flat Shaded Low-tesselation torus Gouraud Shaded Low-tesselation torus Phong Shaded Low-tesselation torus
Flat Shaded Mid-tesselation torus Gouraud Shaded Mid-tesselation torus Phong Shaded Mid-tesselation torus
Flat Shaded High-tesselation torus Gouraud Shaded High-tesselation torus Phong Shaded High-tesselation torus
Figure 3:Torus at different resolutions lit with Blinn-Phong reflection and shaded with different shading models.

 

A. Blinn-Phong Equation Revisited

When you start to work with lighting, you move beyond color to normals, material properties and light properties. Normals describe what direction a surface is facing at a particular point. Material properties describe of what things are made of — or at least what they appear to be made of — by describing how they reflect light. Light properties describe the type and colour of the light interacting with the materials in the scene. Lights and materials can interact in many different ways. Describing these many different ways is one reason shaders are so important to modern 3D graphics APIs.

One common lighting model that relates geometry, materials and lights is the Blinn-Phong reflection model. It breaks lighting up into three simplified reflection components: diffuse, specular and ambient reflection. In this week's lab we will focus on specular reflection. The other two are left here for your reference.

Specular Reflection

Specular reflection represents the shine that you see on very smooth or polished surfaces. Phong specular reflection takes into account both the angle between your eye and the direction the light would be reflected. As your eye approaches the direction of reflection, the apparent brightness increases. It assumes that light will be scattered toward the mirror reflection direction. A special shininess parameter is used to control how tight this scattering is. The Blinn-Phong specular reflection is very similar to Phong, but it fixes some technical shortcomings having to do with backscatter (compare the curves you see if figure 5). Instead of using the reflection vector it uses a vector that is halfway between the light and the eye. This vector is then compared to the normal.

The Blinn-Phong specular component is calculated by these equations:

h = (e+l)/|(e+l)|
Is = ms Ls (h · n)s

Where:

Specular exponent
1 10 100
Phong Phong with low shine Phong with medium shine Phong with high shine
Blinn-Phong Blinn-Phong with low shine Blinn-Phong with medium shine Blinn-Phong with high shine
Figure 5: Phong vs Blinn-Phong With Varying Shininess Values.
Both the Phong and Blinn-Phong reflectance functions cause a highlight to appear around the direction of reflection. Blinn-Phong has a fix that allows a near-diffuse disctribution at low shininess. Notice that at shininess 1 the Phong highlight would be invisible past 90° from the reflection direction, but Blinn-Phong is visible well past that point. Blinn-Phong also appears slightly more diffuse at all shininess values than Phong.

 

Cross-section of Blinn-Phong specular lobe at various angles
Figure 6: Blinn-Phong at Varying Angles.
Diffuse Reflection

Diffuse reflection is the more or less uniform scattering of light that you see in matte or non-shiny materials, like paper. The intensity that you see depends solely on the position of the light and the direction the surface is facing. The Blinn-Phong model calculates it using the Lambertian reflectance equation:

Id = md Ld (l · n)

Where:

The dot product between l and n corresponds to the cosine of the angle between the two vectors. If they are the same, then the dot product is 1 and the diffuse reflection is brightest. As the angle increases toward 90° the dot product approaches 0, and the diffuse reflection gets dimmer. This change resembles the how a fixed width of light spreads out over a greater area when it hits a surface at different angles, as illustrated in Figure 4.

Demonstration of effect of same light striking flat surface at different angles.
Figure 4: The same width of light covers a larger area as its angle to the surface normal increases.
Ambient Reflection

Even if the light does not reach a point on the surface directly, it may reach it by reflecting off of other surfaces in the scene. Rather than compute all the complex interreflections, we approximate this with ambient reflection. The ambient reflection is a simple product of the ambient colors of both the light and material. Direction does not factor in. The ambient reflectance equation is then:

Ia = ma La

Where:

Putting Things Together
The illumination of an object, then, is the sum of each of these components.

I = Is + Id + Ia

A vertex shader that implements all of this is included in Demo 1. Its code is shown below. The new specular lighting code is highlighted for your convenience:
Multi-Light Shader with added Specular

//diffuse and ambient multi-light shader

//inputs
attribute vec4 vPosition;
attribute vec3 vNormal;

//outputs
varying vec4 color;

//structs
struct _light
{
    vec4 diffuse;
    vec4 ambient;
    vec4 specular;
vec4 position; }; struct _material { vec4 diffuse; vec4 ambient;
    vec4 specular;
    float shininess;
}; //constants const int n = 1; // number of lights //uniforms uniform mat4 p; // perspective matrix uniform mat4 mv; // modelview matrix uniform bool lighting; // to enable and disable lighting uniform vec4 uColor; // colour to use when lighting is disabled uniform _light light[n]; // properties for the n lights uniform _material material; // material properties //globals vec4 mvPosition; // unprojected vertex position vec3 N; // fixed surface normal //prototypes vec4 lightCalc(in _light light); void main() { //Transform the point mvPosition = mv*vPosition; //mvPosition is used often gl_Position = p*mvPosition; if (lighting == false) { color = uColor; } else { //Make sure the normal is actually unit length, //and isolate the important coordinates N = normalize((mv*vec4(vNormal,0.0)).xyz); //Combine colors from all lights color.rgb = vec3(0,0,0); for (int i = 0; i < n; i++) { color += lightCalc(light[i]); } color.a = 1.0; //Override alpha from light calculations } } vec4 lightCalc(in _light light) { //Set up light direction for positional lights vec3 L; //If the light position is a vector, use that as the direction if (light.position.w == 0.0) L = normalize(light.position.xyz); //Otherwise, the direction is a vector from the current vertex to the light else L = normalize(light.position.xyz - mvPosition.xyz);
  //Set up eye vector
  vec3 E = -normalize(mvPosition.xyz);

  //Set up Blinn half vector
  vec3 H = normalize(L+E); 

  //Calculate specular coefficient
  float Ks = pow(max(dot(N, H),0.0), material.shininess);
//Calculate diffuse coefficient float Kd = max(dot(L,N), 0.0); //Calculate colour for this light vec4 color = Ks * material.specular * light.specular + Kd * material.diffuse * light.diffuse + material.ambient * light.ambient; return color; }

Appropriate changes should be made to get and set the specular colour and shininess uniforms. The process is similar to what you observed with diffuse and ambient lighting.

 

Specifying Material Properties

Classic OpenGL has five material properties affect a material's illumination. They are introduced in the Blinn-Phong model section and implemented in the shaders in lab demo 2. They are explained below.

Diffuse and ambient properties:
The diffuse and ambient reflective material properties are a type of reflective effect that is independent of the viewpoint. Diffuse lighting describes how an object reflects a light that is shining on the object. That is, it is how the surface diffuses a direct light source. Ambient lighting describes how a surface reflects the ambient light available. The ambient light is the indirect lighting that is in a scene: the amount of light that is coming from all directions so that all surfaces are equally illuminated by it. Both properties are usually set to the similar colours, though the ambient colour is usually scaled down or darker than the diffuse colour.

Specular and shininess properties:
The specular and the shininess properties of the surface describe reflective effects that are affected by the position of the viewpoint. Specular light is reflected light from a surface that produces the reflective highlights in a surface. The shininess is a value that describes how focused the reflective properties are.

Emissive property:
Emissive light is the light that an object gives off by itself. Objects that represent a light source are typically the only objects that you give an emissive value. Lamps, fires, and lightning are all objects that give off their own light.
Choosing the Material Properties for an Object

The steps are as follows:

  1. Decide on the diffuse and ambient colors;
  2. Decide on the shininess of the object.
  3. Decide whether the object is giving off light. If it is, assign it the emissive properties

Seeing the effects of varying material properties may help you select the ones you want.

In this week's first demo, L5-1, specular, diffuse and ambient material properties have been implemented. They have been declared for you globally, given default values and sent to the shader. The program provides convenient colour pickers to allow you to select different specular and diffuse/ambient colours interactively. It also provides sliders to rotate the light about the Y-axis and change the shininess value. You should take some time to get familiar with the effects of the different properties.

Click here to view demo on its own.

 

Hemisphere Lighting

Specular lighting adds a lot to the diffuse and ambient lighting you learned last week. But there's more to add to diffuse lighting. The ambient components are a hack to simulate global illumination, and they do a pretty poor job. Unless you use textures, there's no detail to be seen in ambient light - only a flat silhouette. Hemisphere is a better looking hack that extends the light all around the object. Like diffuse/ambient it uses two light colours, but each is considered to be in opposite hemispheres shining down on the object. Toward the middle, their colours blend smoothly. These colours are intended to represent the sky and the ground, but many implementations allow you to specify the direction of the north pole, or top hemisphere, so it becomes simple to specify, directional, two colour global illumination.

This picture illustrates the intent:

Demonstration of effect of same light striking flat surface at different angles.
Figure 5: Hemisphere lighting's concept. Light falls on the object from two opposite hemispheres and blends across the object.

Downward facing normals are lit entierly by the bottom hemisphere. Upward facing normals are lit entirely by the upper hemisphere. Angled normals are linearly blended (or lerped) between the two based on their angle to the "north pole" or top direction.

The proper equation for this is:

Color = a · TopColor + (1 - a) · BottomColor

Where:

a = 1.0 - (0.5 · sin(Θ)) for Θ ≤ 90°
a = (0.5 · sin(Θ)) for Θ > 90°

This can be simplified without too much error to:

a = 0.5 + (0.5 · cos(Θ))

Which replaces an expensive sin() with a cos() and saves a branch instruction. Remember, both paths through a branch are always executed in WebGL shader programs. Since this method of global illumination is already approximate, the error is mostly harmless. Here are the two curves overlaid on each other:

Demonstration of effect of same light striking flat surface at different angles.
Figure 6: Comparison of real vs. fake a calculation for hemisphere lighting.

The following shader implements hemisphere lighting. You will find it in L5-2.html:

Hemisphere Lighting Shader with Optional Diffuse Lighting Path

//hemisphere lighting shader with optional diffuse lighting path

//inputs
attribute vec4 vPosition;
attribute vec3 vNormal;

//outputs
varying vec4 color;

//structs
struct _light
{
    vec4 top;
    vec4 bottom;
    vec4 direction;
    bool hemisphere;  // to switch between hemisphere and directional lighting
};

struct _material
{
    vec4 diffuse;
};

//uniforms
uniform mat4 p;     // perspective matrix
uniform mat4 mv;    // modelview matrix


uniform _material material; // material properties
uniform _light light;		// light properties

//globals
vec4 mvPosition; // unprojected vertex position
vec3 N; // fixed surface normal

void main() 
{
  //Transform the point
  mvPosition = mv*vPosition;  //mvPosition is used often
  gl_Position = p*mvPosition; 

  //Make sure the normal is actually unit length, 
  //and isolate the important coordinates
  N = normalize((mv*vec4(vNormal,0.0)).xyz);
    
  //Clean up light direction
  vec3 L;
  L = normalize(light.direction.xyz);
  
  //Calculate cosine of angle between light direction and normal
  float costheta = dot(L,N);

  //Calculate appropriate lighting colour
  if (light.hemisphere == true) //hemisphere technique
  {
  	float a = 0.5+(0.5*costheta);
  	color = a * light.top * material.diffuse
  	      + (1.0-a)* light.bottom * material.diffuse;
  }
  else	//lambertian technique with pseudo-ambient
  {
  	float Kd = max(costheta, 0.0);
  	color = Kd * material.diffuse * light.top
               + material.diffuse * light.bottom;
  }

  color.a = 1.0; //Override alpha from light calculations
}

And here is Lab 5 Demo 2, L5-2, for you to experiment with:

Observe how much detail you can make out in the shadows with Hemisphere Lighting as compared with Lambertian Directional Lighting. Notice, also, that the latter is brighter - this is because the ambient and diffuse colours are added rather than linearly blended.

C. Distance and Positional Lights

In the real world a point light source, or positional light, will have less power to light an object the farther the two are apart. This is called attenuation. Because the light spreads out in an ever increasing sphere, the intensity of the light decreases in inverse proportion to the square of the distance. Classic OpenGL has three parameters to calculate the attenuation factor: constant, linear, and quadratic attenuation. These three factors are used as shown in this equation:

float attenuation = 1.0
if (/* light is positional */)
{
   float lightDistance = length(light.position.xyz - mvPosition.xyz);
   attenuation = 1.0/(constant + linear * lightDistance + quadratic * lightDistance^2);
}

This calculation is applied separately to the entire colour of each light - you multiply that light's colour by the attenuation, something like this

// where color is the color result for one light
// and attenuation is 1 for directional lights
color = attenuation * color;

Attenuation is not implemented in the shaders in this week's lab. This is left for you to do as an exercise.

 


Assignment

Before you begin, be sure you are using the Common folder from Lab5E.zip. This lab adds two important libraries - Apple's j3di.js, which provides an OBJ file loader, and East Desire's jscolor.js which provides the colour picker you see in the demos. They are in this folder for your convenience.

Remember to start Chrome like this on a Mac if you want to open local files (like Batman or your own OBJ):

open /Applications/Google\ Chrome.app --args --allow-file-access-from-files

Goals:

Instructions

  1. Study how the specular shader in the lab notes and example L5-1.html/L5-1.js works.
  2. Study how the simplified global hemisphere shader in the lab notes and example L5-2.html/L5-2.js works.
  3. L5E.html and L5E.js are a slightly modified version of L5-1.
  4. Move the global hemisphere shading code from L5-2.html's vertex shader to the one in L5E.html.
  5. Make the appropriate changes to L5E.js to use the modified shader and controls.
  6. Experiment with global light properties until you find a combination that fits your background. You might want to dim or disable the positional light while you do this.
  7. Experiment with material properties until you find a material you like. Set your material as the default and name it - your lab instructor will show you examples of materials they like in the L5-1 demo to help you get some ideas. Be sure to set specular color and shininess.
  8. Implement the attenuation calculation described in the lab notes, including constant, linear and quadratic factors.

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Deliverables


References