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two test cases, but instead <strong>of</strong> the opening there is a diffuse area light source at the<br />

center <strong>of</strong> the ceiling. Again, the error was very low (below 1.3%) and it could be<br />

proved that the s<strong>of</strong>tware used was able to calculate this effect correctly.<br />

The fifth test case dealt with the reflectance <strong>of</strong> the room surfaces. The surfaces<br />

<strong>of</strong> a square room are defined as uni<strong>for</strong>m diffusers. A point light source at the<br />

center <strong>of</strong> the ceiling is used <strong>for</strong> illumination. The errors were within a negligible<br />

margin except <strong>for</strong> the 0 and 0.9 to 1 reflectance values. The authors assumed that<br />

these errors came from an epsilon value being affected at these extreme values,<br />

but also point out that these values rarely exist in reality.<br />

The last test case was specified to verify the calculation <strong>of</strong> the daylight factor,<br />

which is commonly used to evaluate daylighting inside buildings. The geometry is<br />

the same as in the fourth test case. For the analytical solution, a module developed<br />

and validated by Dumortier and Van Roy [Sod06] at the LASH laboratory <strong>of</strong> the<br />

ENTPE–France was used. Un<strong>for</strong>tunately, in this case the s<strong>of</strong>tware yielded errors<br />

<strong>of</strong> over 13%.<br />

The work <strong>of</strong> Maamari and Fontoynont shows that defining a set <strong>of</strong> test cases<br />

where the solution can be derived analytically is a promising approach to validate<br />

global illumination rendering engines. Having a reliable benchmark would help<br />

to classify existing s<strong>of</strong>tware.<br />

2.4 Combined Approaches<br />

2.4.1 Comparison <strong>of</strong> several Rendering Systems<br />

In 1996, Khodulev and Kopylov [KK96] did a comparison <strong>of</strong> three physically<br />

based rendering systems: Lightscape Visualization System (LVS [Lig06], since at<br />

that time Lightscape had been taken over by Autodesk), Specter System [Int06]<br />

and Radiance [War94]. Amongst other criteria they investigated the physical ac-<br />

curacy <strong>of</strong> the global illumination simulation. They combined different approaches<br />

to verification – analytical tests (see section 2.3) and visual comparisons (see sec-<br />

tion 2.1) – to benefit from the advantages <strong>of</strong> each approach.<br />

Three different types <strong>of</strong> test scenes were used. Firstly, they defined a test case<br />

where the result could be calculated analytically. It consisted <strong>of</strong> a diffuse white<br />

cube with a point light source in its center. Six sample points on the inside <strong>of</strong> the<br />

cube were chosen <strong>for</strong> comparisons. In this way, the absolute simulation accuracy<br />

<strong>of</strong> each system could be estimated.<br />

29

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