Fast Soft SelfShadowing on Dynamic Height Fields

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Fast Soft Self-Shadowing on Dynamic Height Fields
Derek Nowrouzezahrai University of Toronto

• John Snyder
• Microsoft Research

2
Related Work

• horizon mapping Max88
• hard shadows
• precomputed for static geometry

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Related Work

• shadow map filtering Reeves87
• light bleeding artifacts
• small light sources
• no complex environmental lighting

Donnelly06
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Related Work

• ambient occlusion Bunnell05 Kontkanen05
• AO in screen-space Shanmugam07
• cone blocker model Heidrich00

Dimitrov08
Oat07
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Related Work

• static relighting Sloan02 Ng04
• dynamic relighting Bunnell05, Ren06, Sloan07

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Goals

• strong response to lighting direction (cast
  shadows)

ambient occlusion
low-frequency SH Ren06
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Goals

• strong response to lighting direction (cast
  shadows)
• environmental directional lighting

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Goals

• strong response to lighting direction (cast
  shadows)
• environmental directional lighting
• dynamic geometry (not precomputed)
• real-time performance

• limitation geometry is height field
• applications
• terrain rendering (flight simulators, games,
  mapping/navigation)
• data visualization

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Summary of Main Ideas

• approximate horizon map via multi-resolution
• create height field pyramid Burt81
• sample height differences from each pyramid level
• use coarser levels as distance to receiver
  increases
• reduces sampling
• convert horizon map to SH visibility for soft
  shadowing
• use visibility wedges Dimitrov08
• get good directional lighting response
• sharpen shadows by restricting wedges azimuthally
• fast 2D lookup SH z rotation S over wedges

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Horizon Map Max88
height field zf(x)f(x,y), point p(x)
(x,f(x))
horizon angle ?(x,?)
max angle horizon makes at p in azimuthal
direction ?
Sample ? at all points x along set of directions
?i.
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Calculating the Horizon Map
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Calculating the Horizon Map
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Calculating the Horizon Map
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Calculating the Horizon Map
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Calculating the Horizon Map
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Calculating the Horizon Map
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Calculating the Horizon Map
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Calculating the Horizon Map
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Calculating the Horizon Map
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Calculating the Horizon Map
max
Problem aliasing need many samples in
t. Solution prefilter height field, apply
multi-scale derivative.
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Brute Force Sampling Requirements
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Multi-Resolution Approximation
multi-scale derivative
pyramid level i
sampling distance for level i
As t ?, i ? sample coarser levels further from
x.
fi
fi-1
fi-2
fi-3
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Multi-Resolution Horizon Angle
horizon angle sample i
w
w
w
w
i-3
i
i-1
i-2
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Multi-Resolution Horizon Angle
Up-sample coarser levels with 2D B-splines
w
w
w
w
i-3
i
i-1
i-2
knot
mid
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Smooth Interpolation

• non-smooth interpolation (e.g. bilinear) ? shadow
  artifacts
• use 1D b-spline for horizon angle vs. distance
  (?i)
• use 2D b-spline for heights (fi)

linearbilinear
b-splinebilinear
linearb-spline
b-splineb-spline
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Pyramid Level Step

• k 1 (standard power-of-2 pyramid) ? abrupt
  transitions
• k 4 smoothes transitions

k 1
k 2
k 3
k 4
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Pyramid Level Offset

• pyramid level bias when sampling height
  differences
• increasing bias increases shadow sharpness
• increases sampling requirements

o 0
o 1
o 2
o 3
o 4
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Summary of Main Ideas

• approximate horizon map via multi-resolution
• create height field pyramid Burt81
• sample height differences from each pyramid level
• use coarser levels as distance to receiver
  increases
• reduces sampling
• convert horizon map to SH visibility for soft
  shadowing
• use visibility wedges Dimitrov08
• get good directional lighting response
• sharpen shadows by restricting wedges azimuthally
• fast 2D lookup SH z rotation S over wedges

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Reconstructing Visibility

• so far discussed sampling in single azimuthal
  direction
• large lights sample multiple azimuthal directions
• linearly interpolate horizon angle ? as function
  of ?
• sequential pairs of ?i determine visibility
  wedges

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Projecting Visibility to SH

• Visibility for a single wedge

• Project visibility wedge to SH (order 4)
• fix ?i 0 and ?f. Store as 2D table

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Reconstruct Full Visibility

• N azimuthal sampling directions ? N horizon
  angles
• (N 1) adjacent horizon angle pairs (wedge
  boundaries)

• (N 1) table lookups (N 1) SH Z-rotations
• ? rotate wedge from ?i 0 to azimuthal direction
• Sum over all wedges

All operations (including horizon angle
calculation) in a single GPGPU shader. See
Snyder08 for full source code.
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Azimuthal Swaths

• azimuthal swaths contain many visibility wedges
• key lights restrict swath

• get sharper shadows
• acts as a geometric mask
• only sample where necessary

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Restricted Swaths

• smaller swaths ? sharper shadows
• approach limit determined by SH order

?f 45
?f 22.5
?f 11.25
?f 90
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Soft Shadowed Shading with SH
visibility vector at x
diffuse reflectance clamped cosine around normal
Nx
lighting environment
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Soft Shadowed Shading with SH
or BRDF x Visibility SH Product and dot with
lighting
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Comparison with Ground Truth
ground truth
k 1, o 1
k 2, o 2
k 3, o 3
k 4, o 4
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Measured Performance
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Image Results
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Video Results
Clip 1
Clip 2
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Conclusions

• multi-resolution approximation for horizon map
• soft shadowing via fast SH projection
• key env lighting decomposition
• simple GPU implementation
• real-time up to 512x512 dynamic height fields
• performance independent of geometric content

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Future Work

• subsample visibility
• combine with dynamic shadow casters
• via Ren06Sloan07 (sphere set blocker
  approximation)
• advantage of SH over cone models and AO
• simulate inter-reflections
• add local light sources
• generalize geometry
• screen space projection Shanmugam07
• local height field displacements

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Thanks! Any questions?
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Restricted Swaths

• For partial swaths, only directions affected by
  key light are sampled

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Reconstructing Visibility

• So far discussed sampling single azimuthal
  direction
• Large lights require many directional samples

• Calculate horizon angle in many azimuthal
  directions
• Combine together, forming visibility wedges
  Dimitrov08

• Canonically reposition fi 0, tabulate SH
  projection as 2D LUT for fixed azimuthal spacing.

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Pyramid Level Step

• Control the sample spacing reduction
• pyramid level i
• sample spacing at level i

• k is the level step
• k 1 ? standard level-of-2 pyramid (e.g. MIP)
• we use k 4 ? storage 3.4x original HF

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Multi-resolution Horizon Map
As t ?, i ? sample coarser levels further from x
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Background

• The rendering equation for direct illumination is

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Background

• The rendering equation for direct illumination is

assume a diffuse BRDF and combine the
reflectance and the cosine term
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Background

• The rendering equation for direct illumination is

assume a diffuse BRDF and combine the
reflectance and the cosine term
project the lighting, clamped cosine weighted
reflectance, and visibility into SH
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Putting it all together

• Height field geometry ? uniform grid of height
  values
• Generated on the CPU or GPU
• stored in a texture
• A multi-resolution height pyramid is generated
  on-the-fly
• avoid large sampling rates as distance
• from receiver point increases
• Max blocking angles are determined
• Fast LUT fast SH Z-rotation generate visibility
• At every step
• Re-generate height-field and pyramid

51
Putting it all together

• Height field geometry ? uniform grid of height
  values
• Generated on the CPU or GPU
• stored in a texture
• A multi-resolution height pyramid is generated
  on-the-fly
• avoid large sampling rates as distance
• from receiver point increases
• Max blocking angles are determined
• Fast LUT fast SH Z-rotation generate visibility
• At every step
• Re-generate height-field and pyramid

52
Putting it all together

• Height field geometry ? uniform grid of height
  values
• Generated on the CPU or GPU
• stored in a texture
• A multi-resolution height pyramid is generated
  on-the-fly
• avoid large sampling rates as distance
• from receiver point increases
• Max blocking angles are determined
• Fast LUT fast SH Z-rotation generate visibility
• At every step
• Re-generate height-field and pyramid

53
Putting it all together

• Height field geometry ? uniform grid of height
  values
• Generated on the CPU or GPU
• stored in a texture
• A multi-resolution height pyramid is generated
  on-the-fly
• avoid large sampling rates as distance
• from receiver point increases
• Max blocking angles are determined
• Fast LUT fast SH Z-rotation generate visibility
• At every step
• Re-generate height-field and pyramid

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Contributions

• A formulation of the maximum blocking angle as a
  directional derivative
• We analyze the effects of pyramid depth, step
  size and filtering on the final shadow quality
• Determining the visibility amounts to calculating
  a multi-scale directional derivative
• We present an efficient algorithm for determining
  the visibility