Metaballs

Metaballs are, in computer graphics, 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 (e.g., for three dimensions, ${\displaystyle f(x,y,z)}$; 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,

represents whether the volume enclosed by the surface defined by ${\displaystyle m}$ metaballs is filled at ${\displaystyle (x,y,z)}$ or not.

A typical function chosen for metaballs is ${\displaystyle f(x,y,z)=1/((x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2})}$, where ${\displaystyle (x_{0},y_{0},z_{0})}$ is the center of the metaball. However, due to the division, it is computationally expensive. For this reason, approximate polynomial functions are typically used.

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