Real Time Ambient Occlusion by Curvature Dependent Occlusion Function

彬彬

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,

MA, USA.

BAVOIL, L., SAINZ, M., AND DIMITROV, R. 2008. Image-space

horizon-based ambient occlusion. In ACM SIGGRAPH 2008

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,

NY, USA, SIGGRAPH ’10, 122:1–122:1.

VERGNE, R., PACANOWSKI, R., BARLA, P., GRANIER, X., AND

SCHLICK, C. 2009. Light warping for enhanced surface depiction.

ACM Trans. Graph. 28 (July), 25:1–25:8.

tc

有意思！学习了！

晃晃

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晃晃

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奇

顶!学习了!阅!

tc

不错 非常经典  实用

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无聊时可以刷屏幕 灌水 也可以试试 帖子的标题究竟可以写多长