Metaballs

In computer graphics, metaballs are organic-looking n-dimensional isosurfaces, characterised by their ability to meld together when in close proximity to create single, contiguous objects. In solid modelling, polygon meshes are commonly used. In certain instances, however, metaballs are superior. A metaball's "blobby" appearance makes them versatile tools, often used to model organic objects and also to create base meshes for sculpting. The technique for rendering metaballs was invented by Jim Blinn in the early 1980s to model atom interactions for Carl Sagan's 1980 TV series Cosmos. It is also referred to colloquially as the "jelly effect" in the motion and UX design community, commonly appearing in UI elements such as navigations and buttons. Metaball behavior corresponds to mitosis in cell biology, where chromosomes generate identical copies of themselves through cell division. Each metaball is defined as a function in n dimensions (e.g., for three dimensions, ; 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, determines whether the volume enclosed by the surface defined by the metaballs is filled at or not. A typical function chosen for metaballs is the inverse-square law, that is, the contribution to the thresholding function falls off in a bell-shaped curve as the distance from the centre of the metaball increases. For the three-dimensional case, where is the center of the metaball. However, due to the division, it is computationally expensive. For this reason, approximate polynomial functions are typically used. 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. Nearest neighbor search can ensure only adjacent metaballs need to be evaluated regardless of the total number in the field.