标题: Real Time Ambient Occlusion by Curvature Dependent Occlusion Function [打印本页] 作者: 彬彬 时间: 2012-1-3 10:46 标题: Real Time Ambient Occlusion by Curvature Dependent Occlusion Function 1 Introduction
We present the novel technique to compute ambient occlusion
[2008] on real-time graphics hardware. Because current real-time
ambient occlusion techniques like SSAO need at least 16 rays sampling
and too high computational cost to implement on computer
games. Our method approximates occlusion as a local illumination
model by introducing curvature-dependent function.
2 Ambient Occlusion
The ambient occlusion A at a point ⃗P with surface normal ⃗n is
given by
A( ⃗P, ⃗n) =
1
π
∫
Ω+
(V (⃗ω, ⃗P)⌊⃗ω · ⃗n⌋)dω (1)
Here ⃗ω represents the random directions at ⃗P along the unit hemisphere
area Ω+. V (⃗ω, ⃗P) is the visibility function which has the
value 0 when no geometry is visible in direction ⃗ω from ⃗P, and the
value 1 otherwise.
SSAO [2008] is one of the most effective and fast ambient occlusion
solution. In this method, Monte-Carlo collision detection is calculated
by z-buffer’s depth and normal on GPU on real-time process.
Our method reduces the computational cost much more than the
conventional method by introducing a curvature dependent function
which approximates ambient occlusion as a local illumination
model.
3 Curvature approximation of occlusion
From Hattori et al’s research [2010], we obtain the following occlusion
estimation function.
A(κmax, κmin) =
∫ 2
0
∫
0
r2ϕ sin θ
′
dθ
′
dϕ (2)
Here, θ = arccos(
−1±
√
1+A2
A ), (A = R(κ1 cos2 ϕ+κ2 sin2 ϕ)).
This function, depending on curvature alone, is a local illumination
approximation of occlusion. Adopting this approximation, we can
obtain an ambient occlusion effect at low cost, thus the implementation
is very easy. When we obtain the occlusion from a static
object, we do not need any other process. In this paper, we more
simplify equation(2) as follows by using a symmetry between x
and y, because it is difficult to implement equation(2) for current
computer.
A(κmax, κmin) =
2 arccos(
−1±
√
1+(max+min)2r2
(max+min)2 )
π
(3)
This is an important update from ”Curvature depended local illumination
approximation of ambient occlusion” [2010]. In the paper,
∗e-mail: httr-zodiac@fuji.waseda.jp
†e-mail : shigeo@waseda.jp
we have to adopt some look-up table(LUT) or quite rough approximated
function which ignore physical property to implement equation(
2). Now, using this equation(3), we are able to implement our
ambient occlusion correctly and in real-time.
4 GPU-Based Curvature Estimation
To implement the proposed method to current graphics hardware
supported computer games, we adopt the screen-space curvature
estimation [2009] which is a multi render technique on GPU. In this
technique, the curvature is obtained by analyzing depth and normal
on screen-space in order to implement in real-time.
5 Results
Figure1-(a) shows a Lambert-rendered image (b) shows our
method, and Figure 1-(c) is an image composed of (a) and (b). The
speed of rendering 1280×960 pixels image by applying our method
is 60fps and by applying SSAO(16 rays sampling with no blur) is
26fps by Intel 1.6GHz dual core cpu and nVIDIA GeForce 320M
machine.
6 Conclusion
(a) SSAO (b) CurvAO
Figure 2: More detailed image SSAO(a) and Our method(b)
We have proposed a novel method for approximating the effects
of ambient occlusion using a curvature-dependent algorithm. Since
the function is a local illumination model, we are able to render ambient
occlusion in real-time, and the proposed method can be easily
implemented. And this method gets smooth, more detailed and
equal or higher quality occlusion than conventional method (Figure
2), because a curvature is continuous on surface
References
AKENINE-M¨O LLER, T., HAINES, E., AND HOFFMAN, N. 2008.
Real-Time Rendering 3rd Edition. A. K. Peters, Ltd., Natick,
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BAVOIL, L., SAINZ, M., AND DIMITROV, R. 2008. Image-space
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talks, ACM, New York, NY, USA, SIGGRAPH ’08, 22:1–22:1.
HATTORI, T., KUBO, H., AND MORISHIMA, S. 2010. Curvature
depended local illumination approximation of ambient occlusion.
In ACM SIGGRAPH 2010 Posters, ACM, New York,
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