Hardware-accelerated Point-based
Rendering of Surfaces and Volumes
Eduardo Tejada, Tobias Schafhitzel, Thomas Ertl
Universität Stuttgart, Germany
Motivation
 Point-bases Surfaces




No explicit connectivity or topology information.
Easy manipulation (modeling).
Easy serializability.
Compact storing.
 Point Set Surfaces (Alexa et al., 2003).
 Smooth surfaces.
 Low-frequency noise handling.
 User-defined minimum feature size.
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Motivation
 Graphics hardware new capabilities.
 Shader Model 3: Dynamic flow control.
 Floating-point textures (also as RT).
 Numerical algorithms on the GPU.
 Ray-tracing PSS slow on the CPU: on the GPU?
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Point-based Rendering
p i 1
pi 2
pi
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Point-based Rendering
ni
n i 1
ni
p i 1
pi 2
pi
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Point-based Rendering
ni
n i 1
ni
p i 1
pi 2
pi
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Our Method - Idea
 Normal vectors: covariance analysis
ni
n i 1
ni
p i 1
pi 2
pi
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Our Method - Idea
 Polynomial approximation: MLS.
ni
pi 2
p i 1
pi
gi  A x  B y  Ci xi yi  Di
2
i i
2
i i
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method - Idea
g i 1
p i 1
pi 2
pi
gi
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method - Idea
g i 1
p i 1
gi  2
pi 2
pi
gi
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method - Idea
g i 1
p i 1
gi  2
pi 2
pi
gi
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Our Method - Textures
Texture positions
g i 1
p i 1
gi  2
pi 2
pi
gi
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Our Method - Textures
Texture positions
pi p i 1 pi  2
Texture neighbors
(1) (1)
(1)
i
i 1 i  2
n n n
n
(1)
i2
n
( 2)
i2
n
( 3)
i2
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Our Method – Pre-processing (Render Pass)
Texture positions
pi p i 1 pi  2
Texture base_a
a i a i 1 a i  2
Texture base_b
Render a single quad of size equal to texture
bi b i positions’
1 bi 2
For each fragment
1. Calculate texture coordinates Texture base_c
Texture neighbors
n i(1) n i(2.1)1 Access
ni(1)2 positions and neighborsc i ci 1 c i  2
3. Estimate normal (n) with covariance analysis
Texture c
polynomial
4. Create local system {a, b, c}, where
=n
5. Transform neighbors positions to
gi local
g i 1system
gi  2
6. Calculate local approximation gi (A, B, C, D)
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method – Rendering (First Render Pass)
Texture base_a
a i a i 1 a i  2
Texture base_b
bi b i 1 bi  2
Texture base_c
c i ci 1 c i  2
Texture polynomial
gi g i 1 gi  2
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Our Method – Rendering (First Render Pass)
Texture base_a
a i a i 1 a i  2
Texture intersection
x0 x1 x 2
Texture base_b
aligned disc for each pi
bi Render
b i 1 bai viewport
2
Texture normal
For each fragment of point pi
1. Fetch texture coordinates m 0 m1 m 2
Texture base_c
the base {ai, bi, ci} and polynomial gi
c i ci 1 2.c i Fetch
2
3. Transform the ray to the base {ai, bi, ci}
Texture polynomial
4. Find intersection of the ray with gi
the normal (derivative of gi)
gi g i 1 5.giCalculate
2
6. Write intersection, normal and depth
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Results – First Intersection
28 fps
20 fps
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method – Introducing Refraction
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method – Introducing Refraction
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method – Introducing Refraction
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method – Introducing Refraction
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method – Introducing Refraction
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method – Introducing Refraction
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method – Introducing Refraction
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method – Introducing Refraction
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method – Introducing Refraction
Eduardo Tejada - Hardware-accelerated point-based rendering of surfaces and volumes
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Our Method – Buckets
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Our Method – Buckets
Texture pointers
z k z k 1 z k 2
Texture buckets
r000 r100 r200
Texture positions
pi p i 1 pi  2
Texture neighbors
(1) (1)
(1)
i
i 1 i  2
n n n
r200 r201 r202
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Our Method – Rendering (Iterative Render Pass)
Texture buckets
r000 r100 r200
Texture pointers
Texture current_position
P0 P1 P2
z k zRender
k 1 z k  2
Texture current_direction
a single quad covering the viewport
Forbase_a
each fragment
Texture
D0 D1 D 2
a i a i 1 a i  2 1. Fetch the points in the cell.
Texture base_b
3. Find the nearest intersectionTexture current_cell
bi b i 1 b i  2 4. If an intersection is found B
0 B1 B 2
Texture base_c4.1 Update position, direction and color
Texture accumulated_color
c i ci 1 c i  2
5. Otherwise determine next cell.
Texture polynomial
C0 C1 C2
gi g i 1 gi  2
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Results – Shadows
10 fps
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Results – Refraction
1.33 fps
2.16 fps
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Results – Multiple Indices of Refraction
0.25 fps
0.22 fps
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Our Method – Introducing Volumetric Effects
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Results – Volumetric Effects
1.08 fps
0.96 fps
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Conclusion
 We do not use specialized HW (e.g. Wald and Seidel).
 Neighbors search on the GPU not solved.
 Kd-trees better than grid for ray-intersection, but for
neighbors search?
 Future: full PSS computation.
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Questions?