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. 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, f ( x , y , z ) {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 m {displaystyle m} metaballs is filled at ( x , y , z ) {displaystyle (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 ) {displaystyle f(x,y,z)=1/((x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2})} , where ( x 0 , y 0 , z 0 ) {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.