Metaball

1 = two positive metaballs merge into one another, 2 = a negative metaball presses a positive one

A metaball is the result of an algorithm that creates a stretchable surface that creates the shape of a sphere (for exactly one) or a set of interlocking spheres. The algorithm was developed by Jim Blinn in the early 1980s .

A metaball is defined as a function in dimensions, i.e. correspondingly for the usual three dimensions . A threshold value is chosen to create a volume . ${\displaystyle n}$ ${\displaystyle f(x,y,z)}$

${\displaystyle \sum _{i=0}^{n}{\mathit {Metaball}}_{i}(x,y,z)\leq {\mathit {Schwellenwert}}}$

then defines whether the body defined by Metaballs is filled at the point . ${\displaystyle n}$ ${\displaystyle (x,y,z)}$

A typical Metaball function is

${\displaystyle f(x,y,z)={\frac {1}{(x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}}}}$

where indicates the center of the ball and the point to be examined. if the strength of the ball then returns at this point, if the sum of the strengths of all balls at this point is greater than the threshold value, the body is filled there. Since the function is computationally intensive due to the division , polynomial approximations are also used. ${\displaystyle (x_{0},y_{0},z_{0})}$ ${\displaystyle (x,y,z)}$ ${\displaystyle f(x,y,z)}$

There are many ways to render metaballs , the two most common being raycasting and the marching cubes algorithm.

literature

• James F. Blinn: A Generalization of Algebraic Surface Drawing . In: ACM Transactions on Graphics , 1 (3), July 1982, pp. 235-256.