Metaballs
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1: The influence of 2 positive metaballs on each other. 2: The influence of a negative metaball on a positive metaball by creating an indentation in the positive metaball's surface. 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 (i.e. for three dimensions, ; three-dimensional metaballs tend to be most common, with two-dimensional implementations as well).
Metaballs - Wikipedia
During the 2D era the world and its components were shown by using sprites -- collections of pixels to form an image. As the industry moved into 3 dimensions, this standard-format became the 3D model. Models representing the world, characters, and objects as collections of vertices in 3D space. Both (arguably) represent the most basic element that can be used in the given number of dimensions, but still allow for the greatest amount of speed.
Exploring Metaballs and Isosurfaces in 2D
You could try to solve y from that equation and draw the metaballs like any normal 1-dimensional function, but as the number of balls increases, solving y becomes impossible. Normal approach in drawing 2d metaballs is to scan through some grid (for example, every pixel on screen) and evaluate the metaball formula. If the result is true, draw a pixel there. Here's a picture showing some metaballs drawn this way: Here I introduce a new way of drawing 2-dimensional metaballs, which should be over 200 times faster than the brute force method described at the beginning of this document. I don't know if it could be implemented in 3 dimensions also, but you could give it a try :)
Metaball math
Ryan's Guide to MetaBalls (aka Blobs)
Metaballs (also known as: Blobs) By Ryan Geiss - 3/10/2000 Contents: I. Metaballs II. Rendering III. An Optimization IV.