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Particle Splatting implementation

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I was wondering if anyone knew how to implement the splatting algorithm. I'm trying to program a software based particle rendering system from scratch. My idea was to use the idea of splatting but I've found few resources that describe the nitty gritty details of it all. My main confusion right now would be how to convert a 3d sphere (or disk) into it's corresponding pixel representation and how to fade the opacity along the radius. Thanks

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