Radiosity CS5502 Fall 2006 (c) Chun-Fa Chang What is Radiosity - - PDF document

CS5502 Fall 2006 (c) Chun-Fa Chang

Radiosity

CS5502 Fall 2006 (c) Chun-Fa Chang

What is Radiosity

• Borrowed from

radiative heat transfer.

• Assuming diffuse

reflectance.

• View independent

solution.

CS5502 Fall 2006 (c) Chun-Fa Chang

Rendering Equation (Review)

• g() removed.
• ρ() is related to BRDF.

x d x x I x x x x x x x I

s

′ ′ ′ ′ ′ ′ ′ ′ ρ + ′ ε = ′

∫

) , ( ) , , ( ) , ( ) , (

CS5502 Fall 2006 (c) Chun-Fa Chang

Radiosity Equation – Single Patch

• Discrete form:
• Compared to Rendering Equation:

x d x x I x x x x x x x I

s

′ ′ ′ ′ ′ ′ ′ ′ ρ + ′ ε = ′

∫

) , ( ) , , ( ) , ( ) , (

∫

+ =

j ij j i i i

F B R E B

∑

+ =

j ij j i i i

F B R E B

CS5502 Fall 2006 (c) Chun-Fa Chang

Radiosity Equation – In Matrix Form

            =                         − − − − − − − −

n n nn n n n n n n n

E E E B B B F R F R F R F R F R F R F R F R M M L M L M M L L

2 1 2 1 2 1 2 2 22 2 1 1 12 1 11 1

1 1 1

                        +             =            

n nn n n n n n n n n n

B B B F R F R F R F R F R F R F R F R F R E E E B B B M L M L M M L L M M

2 1 2 1 2 2 22 2 21 2 1 1 12 1 11 1 2 1 2 1

∑

+ =

j ij j i i i

F B R E B

!

CS5502 Fall 2006 (c) Chun-Fa Chang

Form Factor Calculation

∫ ∫

′ − π θ θ =

Ai Aj i j i ij

dA dA x x j i A F

2

cos cos 1

CS5502 Fall 2006 (c) Chun-Fa Chang

Form Factor Calculation

• Analytical forms of form factors are

possible for simple shapes only.

• Form factor is reduced if a patch sees

the other patch partially.

• An approximation – Hemicube.
• One hemicube for each patch.

CS5502 Fall 2006 (c) Chun-Fa Chang

Hemicube

Patch i Hemicube Patch j

CS5502 Fall 2006 (c) Chun-Fa Chang

Solving the Linear Equation

• Direct method: Gaussian Elimination

O(n3)

• Iterative method: Gauss-Seidel or

Jacobi method O(n2)

CS5502 Fall 2006 (c) Chun-Fa Chang

Jacobi Iterations

• Take a initial guess {xi

0} , for i=1..n

• Each iteration produces better {xi

(k+1)}

from {xi

(k)}

ii k n n k i i k i

a x a x a E x E Ax

) ( 1 ) ( 1 1 ) 1 (

... − − − = =

+

CS5502 Fall 2006 (c) Chun-Fa Chang

Gauss-Seidel Variation

• New xi’s in iteration k+1 are used

whenever they are available.

• That is: xi

(k+1) uses x1 (k+1)… xi-1 (k+1)

and xi+1

(k)… xn (k)

Iteration k+1 Iteration k

CS5502 Fall 2006 (c) Chun-Fa Chang

Progressive Refinement

• Allowing the viewing of early incomplete

solution

• Start from the

patch with greatest unshot radiosity.

• Update receiving
• patches. Repeat.

CS5502 Fall 2006 (c) Chun-Fa Chang CS5502 Fall 2006 (c) Chun-Fa Chang

Artifacts

• Interpolation necessary to smooth out

the patches.

• Blocky shadow is still a problem.
• Meshing resolution is important to the

final quality.

CS5502 Fall 2006 (c) Chun-Fa Chang

Meshing

CS5502 Fall 2006 (c) Chun-Fa Chang

Adaptive Meshing

• Subdivide a patch if the radiosity

variation is large.

CS5502 Fall 2006 (c) Chun-Fa Chang

Advanced Techniques

• Discontinuity

Meshing.

• Hierarchical

Radiosity.

• See Watt’s

Section 11.7.2 for details.

CS5502 Fall 2006 (c) Chun-Fa Chang

For Further Information

• Watt’s book 10.3.2 and Chapter 11.

(Pharr’s book doesn’t cover radiosity because it

mainly uses Monte Carlo path tracing.)

• “Radiosity OverView Part 1”

SIGGRAPH 1993 Education Slide Set, by Stephen Spencer. (Link)