I can see both sides of the arguments and it comes down to the complexitys of the maths,

Without getting too deep in the math, the higher quality resize algorythms use cubic or bicubic formulaes, the software analyses each colour and tries to plot a curved line that gives a peak at where the chosen average colour is, problem is there will basically be errors, the more resizes the more errors in the maths. On the other hand when a linear algorythm is used (often the lower quality option in software), it means straight lines rather then curved apporximations, so in some circumstance lots of small steps will approximate closer to a curve and get you closer to the right point.

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Toolset: Blender, GIMP, Indigo Render, LuxRender, TopMod, Knotplot, Ivy Gen, Plant Studio.