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[[Image:Metaballs.png|thumb|1: The influence of 2 positive metaballs on each other. <br /> 2: The influence of a negative metaball on a positive metaball by creating an indentation in the positive metaball's surface.|200px]]
'''Metaballs''' are, in [[computer graphics]], organic-looking n-dimensional objects. The technique for [[rendering (computer graphics)|rendering]] metaballs was invented by [[Jim Blinn]] in the early 1980s.

Each metaball is defined as a [[function (mathematics)|function]] in ''n''-dimensions (i.e. for three dimensions, <math>f(x,y,z)</math>; three-dimensional metaballs tend to be most common, with two-dimensional implementations popular as well). A thresholding value is also chosen, to define a solid volume. Then,
:<math>\sum_{i=0}^n \mbox{metaball}_i(x,y,z) \leq \mbox{threshold}</math>
represents whether the volume enclosed by the surface defined by <math>n</math> metaballs is filled at <math>(x,y,z)</math> or not.

A typical function chosen for metaballs is <math>f(x,y,z) = 1 / ((x-x_0)^2 + (y-y_0)^2 + (z-z_0)^2)</math>, where <math>(x_0, y_0, z_0)</math> is the center of the metaball. However, due to the divide, it is [[computationally expensive]]. For this reason, approximate [[polynomial function]]s are typically used.{{Citation needed|date=February 2007}}

When seeking a more efficient falloff function, several qualities are desired:
* [[Finite support]]. A function with finite support goes to zero at a maximum radius. When evaluating the metaball field, any points beyond their maximum radius from the sample point can be ignored. A hierarchical [[culling]] system can thus ensure only the closest metaballs will need to be evaluated regardless of the total number in the field.
* [[Smoothness]]. Because the [[isosurface]] is the result of adding the fields together, its smoothness is dependent on the smoothness of the falloff curves.

The simplest falloff curve that satisfies these criteria is: <math>f(r) = (1 - r^2)^2</math>, where r is the distance to the point. This formulation avoids expensive [[square root]] calls.

More complicated models use a [[Gaussian]] potential constrained to a finite radius or a mixture of polynomials to achieve smoothness. The Soft Object model by the Wyvill brothers provides higher degree of smoothness and still avoids square roots.

A simple generalization of metaballs is to apply the falloff curve to distance-from-lines or distance-from-surfaces.

There are a number of ways to render the metaballs to the screen. In the case of three dimensional metaballs, the two most common are [[raycasting|brute force raycasting]] and the [[marching cubes]] algorithm.

2D metaballs were a very common [[demo effect]] in the 1990s. The effect is also available as an [[XScreensaver]] module.

[[Image:Metaball contact sheet.png|frame|left|The interaction between two differently coloured 3D positive metaballs, created in [[Bryce (software)|Bryce]].<br />''Note that the two smaller metaballs combine to create one larger object.'']]
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==Further reading==
*{{cite doi|10.1145/357306.357310}}

==External links==
* [http://local.wasp.uwa.edu.au/~pbourke/miscellaneous/implicitsurf/ Implicit Surfaces article] by Paul Bourke
* [http://wiki.blender.org/index.php/Manual/Meta_Objects Meta Objects article] from [[Blender (software)|Blender]] wiki
* [http://www.siggraph.org/education/materials/HyperGraph/modeling/metaballs/metaballs.htm Metaballs article] from [[SIGGRAPH]] website
* [http://www.gamedev.net/page/resources/_//feature/fprogramming/exploring-metaballs-and-isosurfaces-in-2d-r2556 Exploring Metaballs and Isosurfaces in 2D] by Stephen Whitmore (gamedev article)
* [http://www.digitalartform.com/archives/2009/06/simulating_2d_m.html Simulating 2D Metaball Blobbies with Photoshop]

==References==
*[http://steve.hollasch.net/cgindex/misc/metaballs.html Intro to Metaballs]

[[Category:3D computer graphics]]
[[Category:Demo effects]]

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