1. Fast Global-Illumination on Dynamic Height Fields
Derek Nowrouzezahrai
University of Toronto
John Snyder
Microsoft Research
Derek from UofT
Presenting my work  real-time GI for dynamic HF geometry
Collaboration  John Snyder  MSR

2. Related Work shadow map filtering [Reeves87; …]
light “bleeding” artifacts
small light sources
[Donnelly06]
 WEALTH OF WORK IN SHADOW MAP FILTERING TO APPROXIMATE SOFT SHADOWS
 AS WITH SHADOW MAPPING, ARBITRARILY COMPLEX GEOMETRY + REAL-TIME PERF.
 SUFFER FROM LIGHT-BLEEDING + OVER BLURRING.
 ARTIFACTS CAN BE MINIMIZED HEURISTICALLY.
CON: ONLY HANDLE APPROX. SMALL LIGHT SOURCES
ENV LIGHTING CAN BE APPROXIMATED WITH MANY LIGHT SOURCES

3. Related Work static geometry [Sloan02; Ng04; …]
dynamic geometry [Bunnell05, Ren06, Sloan07, Ritschel08]
 MOTIVATED BY GROWING LIT. IN PRT.
 STATIC CASE: DECOUPLE + PRECOMPUTE DIRECTIONAL LIGHTING SHADING POINTS
 CAN RELIGHT UNDER VARYING (TYPICALLY DISTANT) ILLUMINATION
DYNAMIC CASE:
REN ET AL. + SLOAN ET AL. APPROX. SCENE GEOM. AS SET OF SPHERES + ACCUMULATE OCCLUSION OVER SPHERES IN LOG SH SPACE
RITSCHEL ET AL. USE MANY INCOHERENT SHADOW MAPS TO APPROX GI EFFECTS IN DYNAMIC SCENES  SCALES WITH THE NUMBER OF INDIRECT AND DIRECT LIGHTS.

4. Related Work screen-space shading [Shanmugam07;Ritschel09…]
ignores view-occluded blockers
[Dimitrov08]
horizon mapping [Max88; …]
precomputation for hard shadows on static geometry
[Sloan&Cohen00]
 RECENTLY: IMAGE-SPACE SHADING FOR STATIC + DYNAMIC GEOMETRY.
 THESE TECHNIQUES USE: SCREEN-SPACE DEPTH, POSITION, NORMALS TO APPROX. THE A-&-D OCCLUSION VALUES
 NAMELY: DIMITROV ET AL. & RITSCHEL ET AL.: SAMPLE MANY DEPTHS AROUND EACH PIXEL IN FRAME BUFFER TO APPROXIMATE AO AND DO.
 NOT TEMPORALLY COHERENT: SINCE VIEW-OCCLUDED GEOMETRY DOES NOT CAST SHADOWS
 CAN’T HANDLE DISTANT EFFECTS DUE TO LOCAL VISIBILITY SHAMPLING
HORIZONG MAPPING: PRECOMPUTE MAX BLOCKING MANY AZIMUTHAL DIRECTIONS. HARD SHADOWS FOR FIXED GEOMETRY

5. Related Work fast soft-shadowing on dynamic height fields [SN08]
OUR PREVIOUS WORK: LAST EGSR
PRESENTED MULTI-RESOLUTION SAMPLING SCHEME
TABLE-BASED SH VISIBILITY SLICES

6. Goals all of [SN08] as well as dynamic indirect illumination
glossy effects (direct and indirect)
GOALS: ALL OF [SN08]:
REAL-TIME SHADOWS FROM SMALL AREA + ENV ANIMATING LIGHTING
DYNAMIC GEOMETRY
[CLICK]
NOW WITH GLOBAL ILLUMINATION
GLOSSY

7. Goals
HERE ILLUSTRATE THE DIFFERENCE B/W [SN08] & OUR RESULTS
[CLICK x2]
[SN08] Our results

8. Goals unified formulation for direct- and indirect-illumination
diffuse and glossy bounces
environmental + directional lighting
dynamic geometry (not precomputed)
real-time performance
simple implementation
limitation: geometry is a height field
applications:
terrain rendering (flight simulators, games, mapping/navigation)
data visualization
GOALS SUMMARY:
UNIFIED FORMULATION
DIRECTIONAL RESPONSE: CAST SHADOWS
DIFFUSE + GLOSSY INDIRECT
ENV + SMALL AREA SOURCES
DYNAMIC GEOMETRY
REAL-TIME
SIMPLE CODE: 1 SHADER < 150 LINES
[CLICK]
 MAIN LIMITATION: ONLY HANDLES H.F. GEOMETRY
POSSIBLE APPLICATIONS: TERRAIN RENDERING  FLIGHT SIM. + GAMES + MAPPING

9. Summary of Main Ideas
approximate visibility & incident radiance w/ multi-resolution
compute visibility and radiance at discrete azimuthal directions
determine final spherical visibility and incident radiance
create height and shading pyramids
sample from pyramid levels
pre-filter data
 ROUGHLY DIVIDE INTO 3 MAIN IDEAS
 FIRSTLY: MULTI-RES SAMPLING APPROACH FOR CALC. HORIZON MAP AND INCIDENT RADIANCE
SECONDLY: ANALYTIC REPRESENTATION FOR VIS + INCIDENT RADIANCE PER AZIM DIR
THIRDLY: CONVERTING FROM SAMPLED ANALYTIC REPRESENTATION TO SH
 START WITH OUR MULTI-RES VIS & IR SAMPLING

10. Azimuthal Swaths [SN08] for smaller area (key) light sources:
restrict azimuthal extent and use m = 3
get sharper shadows
acts as a geometric mask
only sample where necessary
env lights and incident radiance:
complete swath and use m = 32
AS IN [SN08]
DISCRETE AZIM DIRECTIONS
RECONSTRUCT CONTINUOUS SPHERICAL Fn’s B/W THESE SAMPLES
[CLICK]
FOR SMALLER KEY LIGHTS: RESTRICT AZIM. EXTENT
GEOM MASK
ENV + INDIRECT LIGHT COMES FROM ALL AZIM. DIRECTIONS

11. Definitions and Notation
blocking angle: (t)
angle p makes at t along 
incident radiance: u(t)
incident radiance at t towards p along 
u(t)
(t)
 BASIC DEFINITIONS: H.F. = SCALAR FUNCTION OF 2 VARS, X + Y, DENOTE Z = F(X,Y)
 REPRESENT H.F. AS TABULATED UNIFORM GRID IN X + Y
3D SURFACE POINT P
BLOCKING ANGLE, \OMEGA(t) = ANGLE HORIZON MAKES ALONG AZIMUTHAL DIRECTION \PHI
INCIDENT RADIANCE U(t) ALONG AZIMUTHAL DIRECTION \PHI
REQUIRE: SAMPLE \OMEGA AND U ALONG \PHI TO DETERMINE VIS + IR
Sample  and u at all points t along direction .

12. Calculating the Max Blocking Angle
 NEED MAX BLOCKING ANGLE FOR VIS
 TRADITIONAL WAY OF DETERMINING: EXHAUSTIVELY SAMPLE H.F. ALONG \PHI, CALC. ANGLE MADE B/W P & SAMPLE POINT
 LIKE “WALKING” ALONG \PHI FOR ALL T
 AFTER EXHAUSTIVELY SAMPLING: KEEP MAX HEIGHT DIFFERENCE == MAX ANGLE

13. Calculating the Max Blocking Angle
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14. Calculating the Max Blocking Angle
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15. Calculating the Max Blocking Angle
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16. Calculating the Max Blocking Angle
[CLICK…]

17. Calculating the Max Blocking Angle
[CLICK…]

18. Calculating the Max Blocking Angle
[CLICK…]

19. Calculating the Max Blocking Angle
[CLICK…]

20. Calculating the Max Blocking Angle
[CLICK…]

21. Calculating the Max Blocking Angle
HAVE THE MAX ALONG \PHI

22. Calculating the Incident Radiance
Which points on the height field contribute indirect radiance?
FOR IR: NEED TO DETERMINE POINTS WHICH CONTRIBUTE INDIRECT P

23. Calculating the Incident Radiance
Which points on the height field contribute indirect radiance?
[CLICK…]

24. Calculating the Incident Radiance
Which points on the height field contribute indirect radiance?
[CLICK…]

25. Calculating the Incident Radiance
Which points on the height field contribute indirect radiance?
[CLICK…]

26. Calculating the Incident Radiance
Which points on the height field contribute indirect radiance?
[CLICK…]

27. Calculating the Incident Radiance
Which points on the height field contribute indirect radiance?
[CLICK…]

28. Calculating the Incident Radiance
Which points on the height field contribute indirect radiance?
[CLICK…]

29. Calculating the Incident Radiance
Which points on the height field contribute indirect radiance?
[CLICK…]

30. Calculating the Incident Radiance
Which points on the height field contribute indirect radiance?
[CLICK…]

31. Calculating the Incident Radiance
Which points on the height field contribute indirect radiance?
[CLICK…]

32. Calculating the Incident Radiance
Which points on the height field contribute indirect radiance?
[CLICK]
ONLY POINTS W/ MONOTONICALLY INCREASING BLOCKING ANGLES CONTRIBUTE INDIRECT LIGHT
CALLED CASTING SET T
The set of points with monotonically increasing blocking angles.
We call this the casting set.

33. Brute Force Sampling – Pitfall…
PROBLEM WITH BRUTE FORCE SAMPLING: [CLICK]
UNEVEN OR INSUFFICIENT SAMPLING LEADS TO ALIASING
“W/O KNOWING ANYTHING SPECIFIC ABOUT THE HF, WE BASICALLY NEED A CONSTANT # OF SAMPLES PER UNIT DISTANCE”
SOLVE BY:
PRE-FILTERING DATA
USE MULTI-SCALE SAMPLING
Problem: aliasing – need many samples in t.
Solution: prefilter data, apply multi-scale sampling.

34. Multi-Resolution Height Sampling
height pyramid level i
sampling distance for level i
Sample coarser levels further from x. fi
fi-1
fi-2
fi-3 τ i
i-1
i-2
i-3
DEFINE A MULTI-RES BLOCKING ANGLE, \OMEGA_i
 F_i == SUCCESSIVELY PRE-FILTERED VERSIONS OF ORIGINAL H.F.
STORED IN PYRAMID == A STACK AFTER UPSAMPLING
\TAU_i == MULTI-RES SAMPLING DISTANCE
[CLICK]
 AS WE MOVE ALONG LARGER DISTANCES IN THE DIRECTION \PHI, WE SAMPLE FROM COARSER LEVEL IN PYRAMID

35. Multi-Resolution Radiance Sampling
multi-scale incident radiance samples
radiance pyramid (for the previous bounce)
blocking angle at
Sample coarser levels further from x. ui
ui-1
ui-2
ui-3 τ i
i-1
i-2
i-3
 U_i == SUCCESSIVELY PRE-FILTERED VERSIONS OF PREVIOUS BOUNCE’S SHADING
STORED IN PYRAMID == A STACK AFTER UPSAMPLING
[CLICK]
AS WE MOVE ALONG LARGER DISTANCES IN THE DIRECTION \PHI, WE SAMPLE FROM COARSER LEVEL IN PYRAMID

36. Summary of Main Ideas
approximate visibility & incident radiance w/ multi-resolution
compute visibility and radiance at discrete azimuthal directions
determine final spherical visibility and incident radiance
analytic visibility and incident radiance
use normalized Legendre polynomials (NLPs)
NEXT: ANALYTIC REPRESENTATION FOR VIS + INCIDENT RADIANCE PER AZIM DIR

37. Analytic Occlusion Elevation Function
we start with the binary occlusion function: σ 1
and represent it analytically in the Normalized Legendre Polynomial (NLP) basis:
START W/: BINARY OCCLUSION Fn
\OMEGA = \SIGMA
AND REPRESENT IT IN THE N.L.P. BASIS W/ THE FOLLOWING ANALYTIC FORM
[CLICK]
MOTIVATION BEHIND N.L.P.: n-TH ORDER N.L.P. CAPTURES ALL ELEV. VARIATION OF n-TH ORDER SH

38. Analytic Visibility and IR
can represent visibility and incident radiance in NLP with 1
max - =
v ()
max 1
visibility  binary function with 1 transition from 0 to max as  increases
u ()
incident radiance  piece-wise constant, RGB function of elevation + =
NOW THE N.L.P. PROJECTION OF VIS & IR CAN BE EASILY COMPUTED W/ OCCLUSION Fn’s
[CLICK]
[EXPLAIN]

39. Summary of Main Ideas
approximate visibility & incident radiance w/ multi-resolution
compute visibility and radiance at discrete azimuthal directions
determine final spherical visibility and incident radiance
NLPSH blending & projection
fast shading pipeline
LASTLY: CONVERTING FROM SAMPLED ANALYTIC REPRESENTATION TO SH

40. From Sampled NLP to Full SH
given (2 x m) NLP vectors
need full spherical functions (represented in SH)
interpolate between azimuthal samples +
project resulting spherical function into SH
requires only 1 pre-computed matrix!
matrix acts on NLP coefficients at edges of each swath
rotate & sum across swaths for final SH
GIVEN: N.L.P. COEFFS FOR VIS + EACH AZIM DIRECTION
WANT: SH COEFFS OF FULL SPHERICAL FUNCTIONS
[CLICK]
INTERPOLATE B/W SAMPLES + PROJECT INTO SH
1 PRE-COMPUTED LINEAR OPERATOR
MATRIX ACTS ON N.L.P. COEFFS AT EDGES OF A SWATH
VERY EFFICIENT AND SIMPLE TO IMPLEMENT:
SINGLE SHADER SEE SUPP MAT
All operations performed in a single GPGPU shader. See
supplemental material for full source code.

41. Global Illumination Shading with SH
at each shading point:
compute m azimuthal visibility + incident radiance NLP vectors
interpolate & project into SH. Rotate & sum across directions
BRDF: clamped cosine and/or Phong lobe ) ( x f N R or
OUTLINE SHADING REQUIREMENTS:
[CLICK] SAMPLE BLOCKING ANGLES ALONG EACH AZIM DIR. COMPUTE N.L.P. VIS + IR COEFFS
[CLICK] APPLY INTERP/PROJECT OPERATOR YIELDING SH COEFFS OF VIS + IR
[CLICK] COMPUTE VIEW-EVALUATED BRDF SH COEFFS
[CLICK] QUERY EXTERNAL LIGHTING
external lighting environment

42. Global Illumination Shading with SH
Direct Illumination:
BRDF x Visibility SH Product
and take inner product with lighting
Indirect Illumination:
BRDF take inner product with Incident Radiance
SHADING ALGORITHM:
FOR DIRECT ILLUM: SH PRODUCT OF VIS & BRDF DOT WITH LIGHTING
FOR INDIRECT ILLUM: DOT BRDF WITH IR 42

43. Comparison to Ground Truth
ALGORITHM CONVERGENCE: 2 PARAMETERS AFFECT QUALITY { MULTI-RES STEPS, # AZIM DIRs. }
ONLY SHOWING INDIRECT AS K INCREASES, WE CONVERGE  MORE FILTERING & MULTI-RES STEPS
[CLICK] AS # OF AZIM. DIRECTIONS INCREASE, WE CONVERGE
[CLICK] [EXPLAIN]

44. Memory Usage we typically sub-sample visibility & IR
shade with full-resolution geometry & normals
HF resolution
pyramid levels
memory requirements
no sub-sampling
2x sub-sampling
256 x 256
(130k triangles) 33
17.4 MB
4.5 MB
512 x 512
(522k triangles) 37
76 MB
20 MB
1024 x 1024
(2.1M triangles) 41
336 MB
88 MB
2048 x 2048
(8.4M triangles) 45
1.4 GB
360 MB
SUMMARIZE MEMORY REQUIREMENTS: #’S INCLUDE ALL INTERMEDIATE TEXTURES USED FOR STORAGE ON THE GPU
TYPICALLY SUB-SAMPLE VIS + IR COMPUTATION & FULL-RES NORMALS/GEOMETRY
W/O SUB-SAMPLING: MODEST UP TO 1024^2 (2.1 MILLION TRIANGLES)
W/ SUB-SAMPLING: CAN HANDLE WELL OVER 8 MILLION TRIANGLES

45. Measured Performance HF resolution FPS (nVidia GTX 285) no ss 2x ss
(130k triangles) 50
125
229
512 x 512
(522k triangles) 12 36 73
1024 x 1024
(2.1M triangles) 3 8 19
[EXPLAIN]

46. Image Results
[ITERATE]

47. Results
[ITERATE]

48. Results
[ITERATE]

49. Conclusions multi-resolution sampling of: visibility incident radiance
compact, analytic representation of:
elevation-only functions
SH interpolation and projection operators
simple GPU implementation
real-time up to 512x512 dynamic HFs
can sub-sample visibility and incident radiance
performance independent of geometric content
CONCLUSION:
MULTI-RES VIS + IR SAMPLING
EFFICIENT + ANALYTIC REPRESENTATION OF ELEV-ONLY Fn’s
N.L.P.-to-SH INTERPOLATION OPERATORS
SIMPLE IMPLEMENTATION
REAL-TIME IMPLEMENTATION FOR HIGH-RES HFs
PERF. INDEPENDENT OF GEOM. CONTENT

50. Future Work combine with dynamic shadow casters
via [Ren06;Sloan07] (sphere set blocker approximation)
apply to image-space global illumination frameworks
generalize geometry
local height field displacements
tiled height field representations
FUTURE WORK:
COMBINE WITH DYNAMIC SHADOW CASTERS: E.G. CHARACTER WALKING ON MOUNTAIN.
IMAGE-SPACE GI FOR FAR-FIELD SHADOWING AND REFLECTION EFFECTS
GENERALIZED GEOMETRY

51. We acknowledge the helpful suggestions of the anonymous reviewers.
Thanks! Any questions?
Thank you for attending my talk. I’d be more than happy to answer any of your question.