I have finite a rectangle in R² with M dots. I need to place N more dots in a way, that a minimal distance between each new dot and any of new dots, existing dots and corners of rectangle (basically, +4 dots) is maximal. Moreover, I need to place them inside the rectangle.
In layman terms I need to add dots to a rectangle with existing dots to make them spread as much as possible.
Additionally, I need to do this pretty fast (~10 million times per second, given the other things with dots are happens at speed of ~200 mil per sec). Are there any existing algorithms? Preferably fast and stable.