Metaballs, in computer graphics terms, are organic-looking n-dimensional objects. The technique for rendering metaballs was invented by Jim Blinn in the early 1980s.

Each metaball is defined as a function in n-dimensions (ie. for three dimensions, $f(x,y,z)$; three-dimensional metaballs tend to be most common). A thresholding value is also chosen, to define a solid volume. Then,

$\backslash sum\_\{i=0\}^n\; \backslash mathit\{metaball\}\_i(x,y,z)\; \backslash leq\; \backslash mathit\{threshold\}$

represents whether the volume enclosed by the surface defined by $n$ metaballs is filled at $(x,y,z)$ or not.

A typical function chosen for metaballs is $f(x,y,z)\; =\; 1\; /\; ((x-x\_0)^2\; +\; (y-y\_0)^2\; +\; (z-z\_0)^2)$, where $(x\_0,\; y\_0,\; z\_0)$ is the center of the metaball. However, due to the divide, it is computationally expensive. For this reason, approximate polynomial functions are typically used (examples?).

There are a number of ways to render the metaballs to the screen. The two most common are brute force raycasting and the marching cubes algorithm.

2D metaballs used to be a very common demo effect in the 1990s. The effect is also available as an XScreensaver module.

Further reading

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• Blinn, James F.  "A Generalization of Algebraic Surface Drawing." ACM Transactions on Graphics 1(3), July 1982, pp. 235–256.

3D computer graphics | Demo effects

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