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I would like to add that Painters' algorithm can be run from front to back with transparency provided your blending operations are associative. I would recommend reading Jim Blinn's "Compositing, Part 1: Theory". (Indeed, reading anything graphics related by Jim Blinn is highly recommended). In this article, Blinn explains (amongst their other advantages) ...


It may be worth mentioning that the reverse painter's algorithm does not handle transparency. If you read and understand @Chris's answer the reason for this is straightforward. Combining the already rendered color (using alpha blending) does not work if the objects behind your transparent object have not been rendered yet.


Probably the easiest way to get an arbitrary precision Mandelbrot set using full-precision integers is to combine two integers into a rational number $p/q$. These numbers are added by finding the common denominator: $$ \frac{m}{n} + \frac{p}{q} = \frac{mq + np}{nq} $$ and multiplied by just multiplying the respective numerators and denominators: $$ \frac{m}{...


If you just want to explicitly sample an area light, then here's the general procedure you should follow. Pick light $i$ out of $L$ lights with some probability $p_i$ (the other probabilities being $p_1,...,p_L$, a light may be picked through inverse transform sampling). Pick a point $\pmb{y}$ on the surface of the light with some probability $q_i(\pmb{y})$. ...

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