Time-Dependent Photon Mapping

Mike Cammarano

Henrik Wann Jensen

EGWR ‘02

Standard Photon Map

Two-pass algorithm:

1. Photon trace

2. Rendering

First Pass - Photon Trace

For 100 photons emitted from 100W source, each photon initially carries 1W.

Propagate this radiant flux through scene using MC methods.

Estimating incident flux

• At any patch of surface, we can estimate the incident flux:

Just average the contributions of all the photons that hit the patch.

A Photon

• For each surface interaction, we store:

struct photon {

float x,y,z; // position

char power[4]; // power (RGBE)

char phi, theta; // incident direction

short flag;

}

Photon Storage

Store this information about surface

interactions in photon map (kd-tree)

Photon storage is decoupled from geometry

Second Pass - Rendering

• Estimate flux incident at a surface point based on nearby photons.

Radiance Estimate

Expand ball until it contains some reasonable number of photons.

Use intersection with plane to estimate area of surface patch.

Radiance Estimate

What About Motion?

One Approach

• Render lots of intermediate frames independent of one another.

Average Intermediate Frames

Expensive

• Only some areas need to be densely sampled in time.

• Need MANY intermediate frames to get smooth results.

Adaptive Sampling

• Want to sample densely in time only for the pixels that need it.

• Easy with ray tracing. Can trace each ray for a different time in the interval. [Cook84]

Photon Map

• We can’t rebuild the photon map for every eye-ray with a different time!

• We would like to do DRT with photons, too.

• Given rays sampling various times and photons representing lighting at various times, how do we match them up?

Photons distributed in time

t=0.0 t=0.5 t=1.0

Energy

Radiant Flux Radiant Energy

Time-Dep. Radiance Estimate

Static surface, no occlusion

Photons in time

• Want average radiance ( ∫ … dt )

Time distribution

Average over time

Case 1

For stationary surfaces with unobstructed visibility through the entire view interval, we can ignore time distribution of photons.

Plane Moving Down

t=0.0

t=0.5

t=1.0

Photon Visualization

t=0.0

t=0.5

t=1.0

A Trickier Case

t=0.0

t=0.5

t=1.0

Average of independent frames Distributed photon times

Examples

Problem

• A given patch of surface is only visible through a particular pixel for a small portion of the total time interval.

• It’s brightness during that visible interval should depend only on the photons reaching it during that narrow window of time – not the “average” over all times.

Distribution in Time

Uncounted!

Narrow Window in Time

• Integrate over small visible interval.

Comparison

Performance

• Path tracing 9+ hrs

• Average of independent frames 47 sec

• TDPM 43 sec

• Our worst case: we get essentially no benefit from adaptive sampling – doesn’t cost much to oversample blue background.

• Try it in front of ~107 polygon forest …

Summary of Method

IF ray-path from eye is unaffected by motion:Can integrate over entire time interval – Δt = 1.(Use all the spatially nearby photons in the estimate)

ELSEIntegrate over shorter visible interval.Can use several criteria for choosing Δt adaptively:

1. Δt < user-specified MaxΔt

2. Δt chosen to use only k-nearest-photons-in-time

3. Δt < time spanned by the photons

Truck Scene

Effect

Comparison

Average of 9 frames - 316 seconds

Comparison

Our method – 72 seconds

Comparison

Ignoring case for eye-paths with movement

Conclusion

• Can incorporate correct global illumination via photon mapping in a ray-tracer that adaptively samples in time.

• Computing photon map with time-dependence requires little or no added cost beyond photon mapping for the corresponding still scene.

• Better performance than alternative methods for animated global illumination.