I have samples from a 2D Gaussian distribution with zero mean and unit variance ( as shown below).

Gaussian samples

I want to transport these samples i.e. (x,y) pairs into a funky shape like a heart or a spiral. Are there any equations I can use to transport these samples to samples from a heart or spiral distribution.

Note I am not trying to get an equation that transports the points into a shape outline/perimeter. Instead I want the transported points to fill the area of the new shape.

If this isn't possible is there any other funky shape like an S or a triangle or a diamond etc. that I can transport these samples to?



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