Re:Metaballs and Marching Squares
by GuiA on Thursday August 21, 2014 @06:02PM
(#8209878)
So metaballs aren't distinct mathematical objects that you can model on their own (like a fractal or a cylinder)- rather, they're artefacts that are created when sampling in certain ways circles/spheres intersecting?
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No.
Metaballs are a thing, and marching cubes is one way of implementing them. Another approach is ray-casting.
They don't inherently have to be sampled.
Just like you can define the perimeter of a circle given constants (x_0, y_0, r):
(x-x_0)^2 + (y-y_0)^2 = r^2
you can define the perimeter a metaball on a list of (x_i, y_i, r_i) as described in the post.
Metaballs are a family of implicit equations that are visually interesting and easy to set up. They all come in the form of a summation of some function of distance from a control point over a set of control points. The appearance of spheres/circles intersecting is a consequence of the popular falloff-type functions.
You can think of metaballs as a bunch of glowy points. The implicit surface that is shown is all of the points where the glows add up to some target value.
Re:Metaballs and Marching Squares
by peterfirefly on Friday August 22, 2014 @09:44AM
(#8212038)
Blumenthal, "Introduction to Implicit Surfaces".
Possibly quite dated, though.