Apr 17 20:16
you can try, np - it doesn't necessarily mean that I will be on though
Apr 17 20:15
I occasionally look at stack though
Apr 17 20:14
ok, I am not on discord anymore because I am super busy, so welp
Apr 17 20:14
which should give you some kind of texturing - but I kind of doubt this is the texturing you want
Apr 17 20:14
you can of course have colours attached to the moving boundary
Apr 17 20:13
see figure 4
Apr 17 20:13
it starts with some region and evolves it to at the end have it on the boundary of the volume
Apr 17 20:13
just read the paper I linked - or at least the relevant parts of it, to see whether this is what you had in mind
Apr 17 20:12
you can of course have this in 3D
Apr 17 20:12
for example look at figure 4
Apr 17 20:10
du/dt = |nabla u| div(g(|\nabla u|^2) \nabla u / |\nabla u|)
Apr 17 20:10
it basically introduce a diffusivity
Apr 17 20:10
this is probably closer
Apr 17 20:10
there are self-snakes that you start around some object and then they fit to it
Apr 17 20:09
it will reduce the curvature of whatever you start with
Apr 17 20:09
I am not sure this is what you want
Apr 17 20:09
while mcm shrinks things to spheres
Apr 17 20:09
there's also an affine variant that preserves ellipses
Apr 17 20:08
this is just its implicit formulation
Apr 17 20:08
mcm = mean curvature flow
Apr 17 20:08
\nabla f / |\nabla f| = n and div n = curvature
Apr 17 20:08
du/dt = |\nabla f| div( \nabla f / |\nabla f|) is the implicit form of mcm
Apr 17 20:06
then it will be a mean curvature flow
Apr 17 20:06
you can modulate grad f with the curvature yes
Apr 17 20:05
you can of course have a sheet connecting a bunch of particles
Apr 17 20:04
you let it flow
Apr 17 20:04
so starting at p(0) = p_0
Apr 17 20:04
p is the position of some particle
Apr 17 20:04
checker volume*
Apr 17 20:04
imagine space is filled with particles, each colored based on the volume
Apr 17 20:04
e.g. dp/dt = -grad f(p)
Apr 17 20:03
you can do some flow based on the gradient of f then
Apr 17 20:02
they are not in 3D, or are you considering a volume of checkers?
Apr 17 20:02
they are defined on some interval [a,b] in 1D and some interval [a,b] x [c,d] in 2D
Apr 17 20:02
but the checkers are not on the curve to begin with
Apr 17 19:59
I don't get your image
Apr 17 19:59
many papers are dedicated to it
Apr 17 19:59
energy functional design is non-trivial in general
Apr 17 19:59
idk what gravitational field and space distrotion have to do with this
Apr 17 19:58
the volume grid discretization isn't adaptive though, is it?
Apr 17 19:58
then you likely know much more about the problem than anyone on here, I don't think you'll get very good replies considering people don't know the details
Apr 17 19:57
if you insist on the implicit formulation I am not quite sure how that would work out
Apr 17 19:56
there are a number of papers that do texture parametrization on triangular meshes, I am not an expert in that though
Apr 17 19:56
i.e. reconstruct the surface from the implicit function and then apply standard methods I guess
Apr 17 19:55
it probably makes sense to discretize this surface beforehand though, so you would be able to use the standard tools
Apr 17 19:55
I mean, sure you can defined whatever energies you want
Apr 17 19:54
but I guess you want extra stuff
Apr 17 19:54
your conformal map already preserves angles locally
Apr 17 19:52
in this context