16-global_illumination.md

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Global Illumination

Local vs. Global Illumination

• OpenGL uses the Phong Model which is a local illumination model
  • It is very simplified
  • Doesn't cater for bouncing light
  • Uses basic light sources
  • Difficult to get reflections, shadows
  • Performance-heavy to simulate Global Illumination techniques
  • Also cannot be approximated well
• Global Illumination models are more sophisticated
  • Ray Tracing — good for rendering reflections & transparency
  • Radiosity — good for diffuse surfaces

Ray Tracing

• Logical extension to rendering with a local lighting model
• Works on a pixel-by-pixel basis
• Based on observation that the only light rays that matter are those that enter the lens of the synthetic camera
• So, reverse the direction of the rays and consider only those rays that start at the center of projection — these are cast rays
• At least one ray is assigned through each pixel
• Each ray cast either:
  • Intersects a light source
  • Goes to infinity without striking anything
• If we compute the shade at the point of intersection, using the Phong Model, we would produce the same image as would our local renderer
• How rays enter the lens:
  • Directly from the source
  • From interaction with a surface visible to the camera
  • After multiple reflections from surfaces
  • After transmission through one or more surfaces
• Rather than immediately applying our reflection model, we first check whether the point of intersection between the cast ray and the surface is illuminated — shadow rays are computed from the point on the surface to each source

Shadow Rays

• If a shadow ray intersects a surface before it meets the source, the light is blocked from reaching the point under consideration, and this point is in shadow (at least from the source) — as such, no lighting calculation is needed
• For highly reflective surfaces, we can follow the shadow ray as it bounces from surface to surface, until it either goes off to infinity or intersects a source
• If all surfaces are opaque, we do not consider light scattered from surface to surface
• Such calculations are done recursively and take into account any absorption of light at surfaces
• Ray tracing is particularly good at handling surfaces that both reflect and transmit light through refraction
• Usinng our basic paradigm, we follow a cast ray to a surface with the property that if a ray from a source strikes a point, then the light from the source is partially absorbed and some of this light contributes to the diffuse reflection term
• The rest of the incoming light is divided between a transmitted ray and a reflected ray
• If a light source is visible at the intersection point, we need to to:
  • Compute the contribution from the light source at the point, using our standard reflection model
  • Cast a ray in the direction of a perfect reflection
  • Cast a ray in the direction of the transmitted ray

Simple Ray Tracer

color c trace(point p, vector d, int step) {
	color local, reflected, transmitted;
	point q;
	normal n;
	
	if (step > max) return (background_color);
	q = intersect(p, d, status);
	if (status == light_source) return (light_source_color);
	if (status == no_intersection) return (background_color);
	
	n = normal(q);
	r = reflect(q, n);
	t = transmit(q, n);
	local = phone(q, n, r);
	
	reflected = trace(q, r, step+1);
	transmitted = trace(q, t, step+1);
	
	return (local + reflected + transmitted);
}

Radiosity

• Radiosity — the amount of light leaving a surface
• Technique involves calculating the radiosity of surfaces in a scene and reflecting the light accordingly based on the laws of energy conservation
• Primarily addresses diffuse lighting — specular effects need to be handled by another method
• It is a global illumination model because it models the effect of light energy being bounced around between objects in the scene
• Two important features of this approach:
  • Light sources are treated no differently from any other surface
  • Radiosity equations are solved once before the scene is rendered, so the scene can be viewed from anywhere without re-computation
• Radiosity is made up of two components:
  • the light reaching it from other surfaces and scattered by it (Form Factor)
  • the light which it generates directly (usually light sources)
• Radiosity_i = Emission_i + Reflectivity_i × ∫(Radiosity_j × FormFactor_j)
  • i and j are two surfaces
• It is impractical to calculate radiosity at every point — instead, a surface is divided into patches
  • Each patch is assumed to be energetically uniform
  • Each patch is shaded using Gouraud-shade triangles
  • A good estimate of radiosity is at the center of the patch, then interpolated with the triangles
  • An advantage of this method: we can have lights of any shape built from patches, not just point sources
  • The radiosity of any patch depends on the radiosity of every other patch

Radiosity Equations

• A_i is the area of the patch i
• B_i is the radiosity of the patch i
• E_i is the generated energy per unit area per time (light source only)
• R_i is the reflection coefficient, the fraction of the incident energy that is reflected
• F_ij is the fraction of the energy which leaves patch j and reaches patch i (the form factor)
• ∫_j F_ij × B_j × d × A_j is the total amount of energy reaching patch i
• But some of this is absorbed and the rest is reflected, so we multiply by R_i
• Finally, we get: B_i × d × A_i = E_i × d × A_i + R_i ∫_j F_ij × B_j × d × A_j as the general radiosity equation

How to use Radiosity

1. Divide the scene into a mesh of patches
2. Compute the form factors
3. Solve the radiosity equations
4. Place the viewer in the scene and render conventionally

Progressive Radiosity

• The major problem of this approach is the
  • O(N^2) cost of calculating all the form factors
  • O(N^2) cost of storing them
• Progressive radiosity does this in O(N)
  • Instead of working on solutions to all patches simultaneously, the effects of one specific patch on all the others are calculated in full — then looped over all patches, accumulating contributions
  • If we iterate this process "forever" we arrive at the same solutions as we did calculating it in the original way
• "Important" surfaces can be processed first (e.g. light sources)
  • This is sometimes called the shooting variant, because the energy from one patch is shot out to all the others
• When working iteratively, we have to be careful not to count energies more than once — we initialise all radiosities to zero, except for those of the light source patches
• Radiosity cannot handle highlights so it is often combined with Ray Tracing or Light Map techniques (which are visually important)