Other Meta-Shapes

Balls are certainly the most popular shape to apply this effect to, largely due to the simple nature of the equation of a circle, but it's not hard to modify the original equation to form other interesting 'blobby' shapes.

Ellipses

An ellipse isn't really a far cry from a circle, so its equation might be the easiest to fathom. The equation for an elliptical Metaball is much the same as our original equation, but with floating-point multipliers (Xm and Ym respectively) applied to the X and Y squares:

M(x,y) = R / sqrt( Xm*(x-x0)^2 + Ym*(y-y0)^2 )

(An elliptical shape generated from a metaball.)

When Xm and Ym are both 1, it will be identical to a regular Metaball, but supplying numbers between zero and one will stretch the Meta-Ellipse, while numbers greater than one will shrink it.

Diamonds

The equation for a Meta-Diamond is as follows:

M(x,y) = R / ( |x-x0| + |y-y0| )

(A simple diamond shape generated from a metaball.)

There is a much simpler formula here, where we are simply dividing the radius (or 'size') by the sum of the X-distance from the centre and the Y-distance from the centre, via the absolute-value (ie. '|') symbols. These shapes are particularly fast to render, compared to Metaballs, since they only consist of a few relatively inexpensive operators and functions.

Donuts

We can define a donut-like shape by considering a function that passes our threshold value twice: once near the centre, and again further away. We can accomplish this by introducing an offset to the distance calculated (ie. the value in the denominator) to make the meta-shape cross our threshold more than once. Consider:

M(x,y) = Radius_1 / |Radius_2 - sqrt( (x-x0)^2 + (y-y0)^2 )|

(A donut shape generated from a metaball.)

Given two radius values, somewhat alike to an inner- and outer-radius, the threshold for our points to draw will become both Radius_2 units toward the centre of the shape, and Radius_2 units away from the centre of the shape, thus producing a donut-like shape. Note that these are a little slower to draw, since the equation requires an additional subtraction and absolute-value compared to regular Metaballs.

Optimizations and Improvements