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Determine which of the locations (A, B, C, D)

has the maximum and the minimum ambient occlusion:

Now I want to give you a quick survey, so that when you here the various names you have an idea what it is all about.

But first some important definitions and generalizations:

This general expression, where L is radiance, x is a location on a surface, n is the surface normal at that point, and ω are direction vectors,
can capture the surface properties of almost all materials; in
principle there is such a formula for every spectral band of interest
(e..g, R G B).

The simpler models of diffuse reflection, specular reflection, and Phong reflection are idealized special cases of a BRDF. (to learn more).

This is of mostly academic/theoretical use. It calculates the amount of reflected light in any direction given full knowledge of the BRDF of the surface and of the incoming light distribution. It serves as the most abstract formal expression of the non-perceptual aspect of rendering. All specific rendering algorithms can understood as finding (approximate) solutions to some parts of this equation.

The outgoing light (L_{o}) for a particular position and direction is the sum of the emitted light (L_{e}) and the reflected light. The reflected light is the sum of the incoming light (L_{i})
from all directions, multiplied by the surface reflection and cosine of incoming
angle. By connecting outward light to inward light, via an interaction
point, this equation stands for the whole 'light transport' — all the
movement of photons — in a scene. (to learn more).

## L = Path starting at a light source## D = Path makes a diffuse bounce## S = Path makes a specular (or refractive) bounce## E = Path hits (or starts at) the eye |

Symbolically, these are the paths that are being investigated:

(to learn more).

Symbolically, these are the paths that are being investigated:

(to learn more).

(to learn more).

(to learn more).

Symbolically, these are the paths that are being investigated:

(to learn more).

Symbolically, these are the paths that are being investigated:

(to learn more).

(to learn more).

(to lern more).

In the simplest case we assume all the surfaces are perfectly diffuse reflectors. Thus the apparent brightness of a surface is independent of viewer position.

However, large (flat) polygons can still have non-uniform brightness because of non-uniform illumination. We now consider indirect illumination by other illuminated and diffusely reflecting surfaces. For this, we break up large surfaces into small flat polygons (

Once all the patches have been assigned their brightness (color) values, we can render the scene from any viewpoint.

To calculate the amount of diffuse illumination that gets passed from
one patch to another, we need to know the **form factor** between them.

This **form factor** describes how well the two patches can see
one another (depends on distance, relative orientation, occluders between
them).

Once we have determined all these purely geometrical form factors,
we can set up a system of p linear equations in the radiosity of the
p patches.

Solving this system with a direct method (e.g. Gaussian elimination)
is not practical, if there are thousands or millions of patches.

But we can exploit the fact that most of the form factors are typically
zero, since many pairs of patches cannot send much light to each other.

Thus we can apply an **iterative approach**:

-- First consider only the **light directly emitted by the active light sources**.

-- Then add the light that results from only a **single reflection** on
any surface from the source lights.

-- Next add the light that has seen **two reflections**, and so on ...

-- The process is stopped locally whenever the additional contributions fall
below some desired level of accuracy.

Symbolically, these are the paths that are being investigated: ** L D* E**** **

(to learn more).

and of

The first pass is a radiosity-like algorithm that creates an approximate global illumination solution.

In the second pass this approximation is rendered using an optimized Monte Carlo ray tracer (statistical sampling).

This scheme works very well for modest scenes.

But for models with millions of polygons, procedural objects, and many glossy reflections, the rendering costs rise steeply,

mainly because storing illumination within a tessellated representation of the geometry uses too much memory.

Symbolically, these are the paths that are being investigated:

(to learn more).

Submit names of team members plus your plan (1 - 5 sentences) for the project by WED April 29, 2009.

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