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traversal for each filter kernel sample. Note that this technique scales well with

the complexity of the hair model (the more complex, the larger the speedup),

because the lookup times become roughly constant as long as there is sucient

coherence. Also observe that this technique even scales well with larger filter

kernels, since spatial coherence is only required between neighboring pixels. In

case of small transmittance functions (e.g., due to high opacity), the gain from the

links are minor, which nevertheless only results in a barely noticeable constant

overhead due to the links (of about 2%).

Apart from PCF, we also adapted another antialiasing algorithm, exponential

shadow mapping, for use with DSM.

Exponential shadow mapping.
The standard binary shadow map test causes an-

tialiasing artifacts since it is effectively a step function that jumps between 0

and 1. Hence
exponential shadow mapping
(ESM) [Annen et al. 08] approxi-

mates the shadow test with an exponential function (yielding continuous results

between [0
..
1]). This continuous value is subsequently used to attenuate the

shading of a pixel.

The DSM algorithm can be combined with ESM in a straightforward fashion,

and we denote this combination as
exponential deep shadow mapping
(EDSM).

The resulting transmittance is weighted with the continuous shadow test value.

As can be seen in
Figure 1.6
,
EDSM performs much better than PCF in terms of

visual quality. Note that while the original ESM algorithm supports prefiltering,

this feature cannot be used in combination with DSM since the lookup depth

along the transmittance function is not known beforehand.

1.4

Results

We computed all our results on an Intel Core i7-2700K Processor (using one core)

and using a Geforce GTX 680. All images were rendered in resolution 1
,
280
×
720

and using a deferred rendering pipeline with four 32-bit render targets. The hair

model used in our experiments has 10
,
000 individual strands of hairs and about

87,000 vertices.

SM res

SM

DSM

DSM3

DSM5

EDSM

EDSM3

EDSM5

256

222.8

220.9

192.4

160.3

207.2

166.2

121.6

512

121.2

120.2

111.9

98.4

116.0

99.5

79.9

768

70.7

70.2

66.4

61.4

69.2

60.8

51.0

Tab l e 1 . 1 .
This table compares typical FPS values for binary shadow mapping by using

only the first fragment of a DSM for shading (SM), our method without filtering (DSM)

and with PCF (DSM3 and DSM5), and our EDSM algorithm using different filter kernel

footprints. The number after the algorithm's name is the filter kernel size (e.g., a 3
×
3

kernel for EDSM3).

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