Metaballs

Metaballs (not to be confused with meatballs) is the name of a computer graphics technique for rendering organic-looking n-dimensional objects. 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_{i=0}^n metaball_i(x,y,z) \leq 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.

 

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