Memory Efficient and Robust
Software Implementation of the
Raycast Algorithm
Aline Pina
Cristiana Bentes
Ricardo Farias
COPPE/UFRJ
DESC/UERJ
COPPE/UFRJ
Rio de Janeiro - Brazil
Rio de Janeiro - Brazil
Rio de Janeiro - Brazil
aline@lcg.ufrj.br
cristianabentes@gmail.com
rfarias@cos.ufrj.br
WSCG 2007
Outline
•
•
•
•
•
Volume Visualization
Ray-casting
Proposed Ray-casting Algorithms
Experimental Results
Conclusions
Volume Visualization
• Volumetric data  images
• 3D data  2D plane
• Gains:
– Understanding
– Visual analysis and interpretation
Volumetric Data
• Generated:
– Simulation (Fluid Dynamic)
– Sensors (CT scanner)
– Measured Data (Ocean Buoys)
• Represented:
– 3D grid of voxels (Regular or Irregular)
Volume Visualization Methods
Surface Rendering
x
Volume Rendering
• Discard data between surfaces
• Object is semi-transparent
• Loses information
• Hides internal structures
• Faster to compute
• More information
• Shows internal structures
• Computational intensive
Volume Rendering Algorithms
• Cell projection: cells are projected on the
screen
• Ray-casting: rays are casted through every
pixel
Ray-casting
Ray-casting - History
• First software implementation:
– Garrity(1990) - cell connectivity
• Improvement:
– Bunyk(1998) - entry points + new auxiliary
structures
Ray-casting - History
• Problems:
• Auxiliary data structures - high memory
consumption
• Degenerate cases
Our Goal
• Improvements in Bunyk approach:
– Completely handle degenerate cases
– Smaller data structures
– Deal with tetrahedral and/or hexahedral grids
Ray-casting Algorithms
• ME-Raycast
Memory Efficient Ray-casting
• EME-Raycast
Enhanced Memory Efficient Ray-casting
ME-Raycast
ME-Raycast
• Data Structures
– Points array
– Cells array
– Use_set for each vertex
– Neighbor_set for each cell
– Faces array – on-the-fly
ME-Raycast
• Use_set(v)
– List of all cells incident on v
A
E
B
v
C
D
2D example
Use_set(v) = {A, B, C, D, E}
ME-Raycast
• Neighbor_set(c)
– List of all cells that share a face with c
A
2D example
ME-Raycast
• Neighbor_set(c)
– List of all cells that share a face with c
Neighbor_set(A) = {B, C, D}
B
C
A
D
2D example
ME-Raycast
• Faces array
– List of all faces intersected by the rays
3D example
ME-Raycast
• Faces array
– List of all faces intersected by the rays
3D example
ME-Raycast
• Faces array
– List of all faces intersected by the rays
Faces array
A
3D example
ME-Raycast
• Faces array
– List of all faces intersected by the rays
Faces array
A
B
B
3D example
ME-Raycast
• Faces array
– List of all faces intersected by the rays
Faces array
A
B
B
3D example
ME-Raycast
• Algorithm
– Preprocessing:
• Read data – create arrays Points and Cells
• Create Use_set
• Create Neighbor_set
ME-Raycast
• Algorithm
– Raycasting:
• Project visible faces – entry point
• For each pixel:
– Find next intersection – check other cell's faces
– If (no intersection) – check degenerate cases
– Accumulate color and opacity
EME-Raycast
EME-Raycast
• Data Structures
– Points array
– Cells array
– Use_set for each vertice
– Neighbor_set for each cell
– Faces array
EME-Raycast
• Algorithm
– Verification of intersection:
• Checking the face - recalculate parameters
Handling Degeneracies
Handling Degeneracies
• Ray hits a vertex
a
2D example
Handling Degeneracies
• Ray hits a vertex
Bunyk check
a
A
b
E
2D example
Handling Degeneracies
• Ray hits a vertex
Our check
a
B
A
b
E
C
D
2D example
Handling Degeneracies
• Ray hits a vertex
a
B
A
b
E
C
D
2D example
c
Handling Degeneracies
• Ray hits an edge
3D example
Handling Degeneracies
• Ray hits an edge
a
3D example
Handling Degeneracies
• Ray hits an edge
a
b
3D example
Handling Degeneracies
• Ray hits an edge
a
b
3D example
Handling Degeneracies
• Ray hits an edge
Bunyk check
a
b
3D example
Handling Degeneracies
• Ray hits an edge
Our check
a
b
c
3D example
Experimental Results
Experimental Results
Workload
Datasets
# Cells
Blunt Fin
187 395
Combustion Chamber
215 040
Oxygen Post
513 375
SPX
827 904
Delta Wing
Hexa
1 005 675
1 920
Experimental Results
• Baselines:
– Bunyk (ray-casting)
– ZSweep (cell projection)
Bunyk Algorithm
Step 1
Viewing
Direction
Screen
Bunyk Algorithm
Step 2
Viewing
Direction
Screen
ZSweep Algorithm
Z
Target Z
t
Sweep
Direction
v
P
X
Pixel
P List
ZSweep Algorithm
Z
Target Z
t
v
P
X
Pixel
P List
Experimental Results
Degenerate cases:
5122
10242
Blunt
10
31
Comb
-
2
Oxygen
11
38
Delta
7
17
SPX
5
18
Pixels not rendered
Experimental Results
Memory Consumption
ME-Raycast – 1024 x 1024 image
Bunyk
ZSweep
Blunt
75%
40%
Combustion
76%
76%
Oxygen
66%
70%
Delta
61%
152%
SPX
74%
222%
Experimental Results
Memory Consumption
EME-Raycast – 1024 x 1024 image
Bunyk
ZSweep
Blunt
39%
20%
Combustion
37%
37%
Oxygen
30%
30%
Delta
27%
68%
SPX
27%
83%
Experimental Results
Execution Time
ME-Raycast – 1024 x 1024 image
Bunyk
ZSweep
Blunt
126%
29%
Combustion
106%
38%
Oxygen
136%
38%
Delta
148%
33%
SPX
116%
41%
Experimental Results
Execution Time
EME-Raycast – 1024 x 1024 image
Bunyk
ZSweep
Blunt
304%
70%
Combustion
224%
80%
Oxygen
289%
82%
Delta
271%
61%
SPX
222%
79%
Conclusions
• Two memory-aware ray-casting
algorithms
• Improved Bunyk work: memory,
degenerate cases, handling hexahedral
• Significant gains in memory usage
• Correct images
Future Work
• Software out-of-core version
• GPU implementation
• Parallelization
Thank you!
cristianabentes@gmail.com