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May 17, 2001
POP: A Hybrid Point and Polygon Rendering System for Large Data
Baoquan ChenMinh X. Nguyen
Computer Science & Engineering DepartmentUniversity of Minnesota at Twin Cities
http://www.cs.umn.edu/~baoquan
This work is to appear in IEEE Visualization 2001
2Baoquan Chen 2001 4 millions samples
3Baoquan Chen 200114 millions samples
4Baoquan Chen 2001
Volumetric DataVolumetric Data
MRICTPETUltrasonography
Confocal Microscopy
Micro-Tomography
Simulated DatasetsVoxelized
5Baoquan Chen 2001
Mixing of Polygons and Volumes
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Surface model Novel view
Key view
Texture mapping
Image-based Rendering
Filling holes(ray casting)
7Baoquan Chen 2001
Architecture Design
UnifiedPipeline
Texture
Me
mo
ry
8Baoquan Chen 2001
3D Volume Rotation
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x
y
z
a y
b z
x beam shear:
x = x + a y + b z
Rotation by 4 2D Beam Shears
10Baoquan Chen 2001
Rotation by 4 2D Beam Shears
original
1. y beam shear 2. z beam shear
3. x beam shear 4. y beam shear
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x
y
z
a y
b y
y slice shear:
x = x + a yz = z + b y
Rotation by 4 2D Slice Shears
12Baoquan Chen 2001
Rotation by 4 2D Slice Shears
1. y slice shear 2. z slice shear
3. x slice shear 4. y slice shear
original
13Baoquan Chen 2001
x
y
z
b y
g z
a y x-beam y-slice shear:
Rotation by 3 2D Beam-Slice Shears
x = x + a y + g z z = z + b y
14Baoquan Chen 2001
Rotation by 3 2D Beam-Slice Shears
3. y beam shear2. x beam y slice shear
1. y beam x slice shear
original
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x
y
z
y-slice
z-slice
x-beamR = Sx Sz
3D 3D
Rotation by 2 3D Beam Shears
16Baoquan Chen 2001
Rotation by 2 3D Beam Shears
original gazebo after interpolation
first 3D integer shear second 3D integer shear
17Baoquan Chen 2001
POP System
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Goals
•Maintain interactive frame rate for large models (108 – 109 samples) on commodity graphics hardware
+
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Previous Systems (I)
•Level of detail representation and control [Funkhouser 93] [Duchaineau 97] [Hoppe 96, Hoppe 97][Xia 97] ……
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Previous Systems (II)• Visibility Culling
[Greene & Kass 93][Zhang et al. 97] ……
21Baoquan Chen 2001
Previous Systems (III)•Point representation and rendering
Levoy & Whitted 1985Shade, et al. 1998 (LDI)Grossman & Dally 1998Rusinkiewicz & Levoy 2000 (Qsplat)Pfister, et al. 2000 (Surfel)……
Wand, et al. 2001Zwicker, et al. 2001Pauly & Gross 2001
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Qsplat (I)
•Place a sphere at each node, large enough to touch neighbor spheres
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Qsplat (II)
•Build-up a bounding sphere hierarchy to facilitate efficient rendering
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Surfel• A given mesh is sampled on multiresolution
rectilinear grids.• Points on the same level have the same size.
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Problems (I)
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Problems (II)
Polygon Point
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PointsPolygons
Polygons vs. Points
Good for large, flat orsubtly curved regions
Good for models withdetail everywhere
Incremental rasterization Independent rasterization
LOD data structuresmore complex (expensive)
LOD data structures straightforward
Backward processing Forward processing
Connectivity ensuresinterpolation
No connectivitythus, holes/splats
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POP system
PreprocessingView Information
Rendering Engine
Screen Image
MeshPreprocessed
Data
• Preprocessing: Build-up data hierarchy
• Rendering: traverse tree and render points or polygons
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Hierarchical structure of POP
V 0V 2V 1 V 0V 4V 1 V 0V 3V 2V 0V 4V 3
V 2
V 1
V 3
V 4
V 0
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QSplatPOP
POP vs. Qsplat
Works best when the faces of models have uniform size
The topology of the mesh is discarded
The topology of the mesh is partially kept
Works for arbitrary models
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Node Structure
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&RORU�2SWLRQDO�
V 0V 2V 1 V 0V 4V 1 V 0V 3V 2V 0V 4V 3
32Baoquan Chen 2001
Node Structure
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• Tight bounding sphere• Error can be accumulated• Compact representation
33Baoquan Chen 2001
Node Structure
• Number of children (0, 2, 3, or 4)• Rendering flags
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&RORU�2SWLRQDO�
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34Baoquan Chen 2001
Node Structure
• Average of children’s normals• Or, if leaf child, average of the normals
of the leaf triangle’s three vertices• Normal quantized to grid on faces of a
cube
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:LGWK�RI&RQH�RI1RUPDOV
&RORU�2SWLRQDO�
PPuuPPuu��
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35Baoquan Chen 2001
Node Structure
• Each node contains bounding cone ofchildren’s normals
• Hierarchical backface culling [Kumar 96]
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&RORU�2SWLRQDO�
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CulledCulled Not CulledNot Culled
9LHZHU
36Baoquan Chen 2001
Node Structure
• The intermediate node color is the average of children nodes’ colors
• The leaf node color is the average of the whole triangle (pre-texture mapping)
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37Baoquan Chen 2001
Rendering Algorithm (I)
•T raverse hierarchy recursively
LI��QRGH�QRW�YLVLEOH�LI��QRGH�QRW�YLVLEOH�6NLS�WKLV�EUDQFK6NLS�WKLV�EUDQFK
HOVH�LI��OHDI�QRGH�HOVH�LI��OHDI�QRGH�'UDZ�D�WULDQJOH'UDZ�D�WULDQJOH
HOVH�LI��VL]H�RQ�VFUHHQ���WKUHVKROG�HOVH�LI��VL]H�RQ�VFUHHQ���WKUHVKROG�'UDZ�D�VSODW'UDZ�D�VSODW
HOVHHOVH7UDYHUVH�FKLOGUHQ7UDYHUVH�FKLOGUHQ
+LHUDUFKLFDO�IUXVWXP��+LHUDUFKLFDO�IUXVWXP��EDFNIDFH�FXOOLQJEDFNIDFH�FXOOLQJ
$GMXVWHG�WR�PDLQWDLQ$GMXVWHG�WR�PDLQWDLQGHVLUHG�IUDPH�UDWHGHVLUHG�IUDPH�UDWH
/HYHO�RI�GHWDLO/HYHO�RI�GHWDLOFRQWUROFRQWURO
7ULDQJOH�UHQGHULQJ7ULDQJOH�UHQGHULQJ
3RLQW�UHQGHULQJ3RLQW�UHQGHULQJ
38Baoquan Chen 2001
Rendering Algorithm (II)
• Utilize coherence
– RHFRUG�QRGHV�WKDW�DUH�GLVSOD\HG�IRU�HFRUG�QRGHV�WKDW�DUH�GLVSOD\HG�IRU�WKH�SUHYLRXV�IUDPHWKH�SUHYLRXV�IUDPH
²² 6WDUW�WKH�WUHH�WUDYHUVDO�IURP�WKHVH�6WDUW�WKH�WUHH�WUDYHUVDO�IURP�WKHVH�QRGHVQRGHV
39Baoquan Chen 2001
Source image
Target image
High Quality Texture Mapping
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magnification
mixed
minification
mixed
Four-Region Subdivision
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Forward Footprint Projection (Splatting)
Source image Target image
Texture Mapping Methods (I)
ExpensiveExpensive(Ellipsoid evaluation)(Ellipsoid evaluation)
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Forward Point Projection
Source image Target image
Texture Mapping Methods (II)
•• Efficient (Circular filter)Efficient (Circular filter)•• Good forGood for minificationminification
regionregion
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Backward Footprint Projection (EWA)
Source image Target image
Texture Mapping Methods (III)
ExpensiveExpensive(Ellipsoid evaluation)(Ellipsoid evaluation)
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Backward Point Projection (BiLin or MIPMAP)
Source image Target image
Texture Mapping Methods (IV)
•• Efficient (Efficient (bibi-- or trior tri--linear interpolationlinear interpolation))
•• Good for magnification Good for magnification regionregion
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•• For For minificationminification region: forward point region: forward point projection (projection (splattingsplatting) )
•• For magnification region: backward For magnification region: backward point projectionpoint projection
Hybrid Order Rendering
Point renderingPoint rendering
Polygon renderingPolygon rendering
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Backward Bilinear Interpolation
AliasingAliasing
Good qualityGood quality
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Pure Point Rendering
Good qualityGood quality
Bad qualityBad quality
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Hybrid Polygon-Point Rendering
Good qualityGood quality
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Results
•Hardware: 800 MHZ Pentium III PC w/ 256 MB
•NVIDIA GeForce2 GTS
1,087,716 triangles654,666 triangles
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Results
51Baoquan Chen 2001QSplat POP
Results
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QSplat POP
Results
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Results
QSplatPOP
Thres = 1.0272,047 pts,255,708 tris,1.62fps
Thres = 1.0317,557 pts,
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Results
Thres = 2.0267,567 pts,48,143 tris,2.84 fps
Thres = 3.4147,263 pts,7,348 tris,5.43 fps
POPPOP QSplat
Thres = 1.0317,557 pts,
