The issue at it's worst can be seen in the test that we created below, which we conducted after we began to notice the presence of the flicker.
In order to get past this issue we spend a huge duration of time testing different variable settings in order to try and diagnose the issue. It also required us to search through forums such as CGTalk, in order to find a diagnosis from others who had experienced the issue before. One of the first semi-successful solutions that we found was adjusting the global illumination settings. "Cinema 4D uses the term Global Illumination to describe their Radiosity solution. Radiosity takes into account direct illumination of each surface, and adds to that secondary illumination — light bounced off other nearby surfaces". (http://planetpixelemporium.com/tutorialpages/global.html). Other C4D users had suggested that sometimes the use of Global Illumination, which adds a realistic depth to the scene, often is the root of shadow flicker. We found that by turning off this setting, a large improvement was made in terms of the levels of flicker. The results can be seen below.
Whilst this made the flicker a fair amount more tolerable, we found that we were still having issues, particularly in the shadows. This lead to us experimenting further with different variables to try and resolve the situation further. Noticing that most of this detail loss appeared in the shadows, we then attempted to experiment with the shadow settings, increasing the shadow mapping on each light, as well as the the shadow subdivisions in the render. This can be seen below.
We found that by increasing both the shadow subdivision, to values such as 4, and the Shadow Map on each light to resolutions of approximately 1000x1000, the issue was largely fixed apart from a few stray flickers. However, the only consequence of adjusting these settings was the significant increase in render time. Whlist a render with minimal shadow subdivisions and small shadow maps, as we carried out originally would take a few hours, this was increasing render times by more than double. However, with the image and final piece in mind, we felt as though this was a sacrifice worth taking. Moreover, the final variable that we found to provide us with success in counteracting the issue was the use of reflectance in the our materials. We found that by removing any trace of reflectance and specular, that the issue was almost entirely eradicated. Although we cannot be sure as to why reflectance was contributing to this issue taking place, we can assume that it is because it contains further detail than a non-reflective surface, making the rendering more of a difficult process.



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