1	Global Illumination
2	Lighting Simulation The Rendering Equation Challenges Primitives complex: lights, materials, shapes Exponential number of paths, dense coupling How to solve it? Radiosity Finite element Ray Tracing Monte Carlo
3	Lighting Example: Cornell Box
4	Lighting Example: Diffuse Reflection
5	Lighting Example: Shadows
6	Lighting Example: Soft Shadows
7	Radiosity: Cornell Experment
8	Early Radiosity
9	Very Early Radiosity
10	Lighting Effects
11	Caustics
12	Complex Indirect Illumination
13	Measuring things Flux (Power): rate at which light energy is emitted Measured in? Solid angle: 3D generalization of angle Measured in? Intensity: Flux per solid angle Measured in?
14	Radiance Radiance: intensity per unit foreshortened area Foreshortened area found by multiplying the area by cos(q) Think of the projection of the area onto the plane perpendicular to the direction of radiation Properties of radiance: Remains constant along a ray The response of a sensor is proportional to the incident radiance
15	Irradiance Irradiance: flux per unit area
16	Example: Point Light Sources Energy distribution has an irritating singularity The flux in some small differential solid angle is Assume isotropic light source Then irradiance at a point on a unit sphere is:
17	Point Source Irradiance Irradiance on a small surface from a point light
18	BRDF’s Bidirectional Reflection Distribution Function How much light is reflected in direction w_o from direction w_i? Two main properties: Reciprocity: Energy preservation:
19	The Reflection Equation How much light reflects in some given direction? Take light coming from all incoming directions, multiply it by the BRDF, multiply by cos(q)
20	Aside: Delta Functions The Dirac delta function is defined as follows:
21	BRDF Example: Mirror Mirror reflection, so: Also, since no light is absorbed: Mirror’s BRDF uses delta functions to enforce this:
22	Diffuse Reflection Light is equally likely to be scattered in any direction, regardless of the incident direction The BRDF is a constant!
23	Indirect Illumination Radiance is invariant along a ray The radiance at x’ due to the radiance from x is is a boolean visibility function
24	So… Close… Hemispherical integral bad. Surface integral good. Relationship between solid angle and projected surface area: So define G: Change variables in the reflection equation:
25	The Rendering Equation Incorporate emission: This completely captures all light transport in a scene Is this true? Global illumination = solve the rendering equation But it’s too hard!
26	The Radiosity Equation Assume all surfaces are diffuse BRDF is a constant, we can pull it out of the integral
27	Solving the radiosity equation Radiosity solutions are view-independent! This is actually a tractable problem! Bounce light around in the scene, absorbing some and reflecting some, until everything settles down What’s that called?
28	The Radiosity Equation We can’t compute integrals, but that’s OK Cut up the scene into little “patches” Sum the light contribution over all patches: : the fraction of energy leaving patch j that arrives at patch i. Called the form factor between the two patches
29	Form Factor Facts Reciprocity relationship between form factors: Simplify the summation: this is pretty simple, considering the rendering equation Rearrange terms:
30	Wait A Minute… This looks suspiciously like a system of equations! This is Ye Olde Huge Matrixe! Solve it using numerical techniques
31	Finding Form Factors The form factor between two tiny surface patches is: is the binary visibility function So the true form factor is:
32	Nusselt’s Method Project the visible areas of A_j onto a unit hemisphere centered at dA_i, and then onto the base The ratio of this projected area to the area of the base circle is the form factor
33	Hemicubes Approximate the hemisphere:
34	Hemicubes Each small hemicube cell has a precomputed delta form factor: We can render the scene using normal Z-buffer scan conversion onto the faces of the hemicube!
35	Progressive Refinement Radiosity solving is really slow Display a reasonable picture while solving The approach so far: estimate the radiosity of patch I based on the estimates of all other patch radiosities: This is called gathering Poor intermediate results Why?
36	Shooting Instead of gathering light, we can shoot the light energy stored at each patch to every other patch: This requires knowing all the form factors at once That’s bad Rewrite the equation as: Choose the patch with maximum stored energy Starting with the light sources
37	Intermediate Results Display the latest radiosity values at each patch Use ambient to make up the difference Set initial radiosities to the emission Compute an average diffuse reflectivity for the scene
38	Intermediate Results Compute an overall reflection factor Take into account all paths which energy can take Weight the unshot radiosity by the ratio of the patch’s area to the total area:
39	Shooting Without Ambient
40	Shooting With Ambient
41	The Cornell Box
42	Aliasing in Radiosity
43	Non-Axis Aligned Meshes
44	More Discontinuity Meshing
45	Engine Room
46	Indoor Lighting
47	Architectural Design
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