Lecture 12: Monte Carlo Integration

Lecture 12:

Monte Carlo Integration

Computer Graphics and Imaging UC Berkeley CS184/284A

Reminder: Quadrature-Based Numerical Integration

f (x)

Zb f (x)dx = F (b) F (a)

a

x0 = a

x1 x1x2 xx12x3 xx23 x3

x4 = b

E.g. trapezoidal rule - estimate integral assuming function is piecewise linear

CS184/284A

Ren Ng

Multi-Dimensional Integrals (Rendering Examples)

2D Integral: Recall Antialiasing By Area Sampling

Point sampling

Area sampling

CS184/284A

Integrate over 2D area of pixel

Ren Ng

2D Integral: Irradiance from the Environment

Computing flux per unit area on surface, due to incoming

light froZm all directions.

E(p) = Li(p, !) cos d!

H2

Contribution to irradiance from light arriving

from direction !

Hemisphere: H2

d!

Light meter

CS184/284A

dA

Ren Ng

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