1. Point-based Graphics for Estimated Surfaces
Tyler Johnson
Department of Computer Science
University of North Carolina at Chapel Hill
COMP 236 Final Project Presentation – Spring, 2006

2. Project Motivation Multi-projector display system
Required for image correction:
projector calibration
display surface representation
viewing location
Surface estimation produces points

3. Outline Surface Splats Sub-sampling point-clouds
Real-time surface splat rendering
Application to projective displays

4. Surface Splats Point-based No connectivity Circular Elliptical
center – c ={x,y,z}
normal – n = {x,y,z}
radius - r
Elliptical
replace r with major, minor axes a and b

5. Sub-sampling Point-clouds
Produce a set of circular surface splats from a set of points
Based on [Wu J., Kobbelt L., “Optimized Sub-sampling of Point Sets for Surface Splatting”]

6. Sub-sampling Point-clouds
Create initial set of splats
At each point pi
Create new splat si with center pi
Find G = {k nearest neighbors of pi}
Fit least squares plane to find normal of si
Determine r by growing si to include points in G until global error tolerance is reached

7. Sub-sampling Point-clouds
Greedy selection of splats until model is closed.
Splat selection based on surface area
Model closed when all points covered by a splat

8. Examples
≈93,000 points sampled from triangle mesh → 41,000 circular surface splats

9. Examples
≈94,000 points sampled from triangle mesh → 34,000 circular surface splats

10. Radii decreased to illustrate underlying splat representation.
Examples
Radii decreased to illustrate underlying splat representation.

11. Rendering Surface Splats
Three-pass algorithm on the GPU
Visibility Pass – Fill depth buffer
Attribute Pass – Splat material properties
Lighting Pass – Normalization and lighting
[Botsch M., Hornung A., Zwicker M., Kobbelt L., “High-Quality Surface Splatting on Today’s GPUs”]

12. Visibility Pass Send all splats down the pipeline as points
Fill depth buffer
vertex program
calc splat size in screen-space, generate fragments fp
invert viewport transform → point on near plane pn
use pn to reconstruct 3D point on splat surface in eye space pe
if pe is within radius of splat, output transformed depth of pe

13. Attribute Pass Send all splats down the pipeline again
Splat material properties vp
calc splat size in screen-space, generate fragments fp
reconstruct pe on the surface of the splat as in visibility pass
weight normal and color of splat with kernel at splat center
add weighted normal and color to separate accumulation textures
output transformed depth of pe minus depth offset

14. Lighting Pass Render full-screen quad to generate fragments
Normalization and lighting vp
nothing fp
divide accumulated color and normal by total weight
use depth texture to reconstruct 3D point
calc per-pixel lighting

15. Application to Projective Display
Display surface Estimation

16. Application to Projective Display
Rendering
Projective texturing
perform in attribute pass to determine color
must also invert viewing transform
Video

17. Conclusions
Surface splat representations suffer from many of the same problems as polygon meshes
holes, insufficient sampling etc.
Local least-squares fitting may reduce noise in estimating planar surfaces
Lack of connectivity may be advantageous in continuous surface estimation