Metaballs

Two metaballs

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,

[\sum_^n \mathit_i(x,y,z) \leq \mathit]

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.

Metaballs

Further reading