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Re: Potential Blocks and Potential Particles - Documentation


Bruno Chareyre said:     (by the date of Fri, 25 Jan 2019 13:20:08 +0100)

> On 1/24/19 8:07 PM, Janek Kozicki wrote:
> >
> > Actually PotentialParticles are not Minkowski sums. [...] he adds x^2+y^2+z^2-R^2 to this
> > formula. This means that he is adding a sphere to this formula, and
> > all the shapes suddenly look like cushions with soft corners instead
> > of polyhedral Minkowki sums.  
> What you describe seems to be what I called Minkowski sum (polyhedron + 
> sphere).
> It boils down geometrically to a set of spheres, cylinders, and planar 
> faces. That's what we have with PFacets.
> You can see an example with examples/pfacet/mesh-pfacet.py (note that 
> the edges are not sharp).

This addition is not by sweeping a sphere along the edges. It is by
modifying the scalar field equation. The isosurface where this
equation satisfies f(x,y,z)==0 is the surface of that particle.

I would say it is even difficult to find the radius or curvature of
this surface of the particle. This is why Chia used marching cubes.

To explain it in simplest terms: a triangular side of a polyhedron is
not flat. It has some curvature, calculation of this curvature would
require solving equation f(x,y,z)==0. And this is difficult.

I am attaching screenshot from Chia's thesis from page 222.
( http://www2.eng.ox.ac.uk/civil/publications/theses/boon ).
Are you still certain that this can be plotted using pfacets?

Janek Kozicki

Attachment: PotentialParticle.png
Description: PNG image

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