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So metaballs aren't distinct mathematical objects that you can model on their own (like a fractal or a cylinder)- rather, they're artefacts that are created when sampling in certain ways circles/spheres intersecting?


No.

Metaballs are a thing, and marching cubes is one way of implementing them. Another approach is ray-casting.


They don't inherently have to be sampled.

Just like you can define the perimeter of a circle given constants (x_0, y_0, r):

(x-x_0)^2 + (y-y_0)^2 = r^2

you can define the perimeter a metaball on a list of (x_i, y_i, r_i) as described in the post.


Metaballs are a family of implicit equations that are visually interesting and easy to set up. They all come in the form of a summation of some function of distance from a control point over a set of control points. The appearance of spheres/circles intersecting is a consequence of the popular falloff-type functions.

You can think of metaballs as a bunch of glowy points. The implicit surface that is shown is all of the points where the glows add up to some target value.


Blumenthal, "Introduction to Implicit Surfaces".

Possibly quite dated, though.




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