I'm looking for references on approximating implicit surfaces with meshes.
I have access to the ACM library, but that's about it, so any other
free-as-in-beer references would be appreciated ;-).
But seriously, this topic appears in the FAQ, and is often discussed.
"Subject 5.10: What is the marching cubes algorithm?"
Google keeps newsgroup archives which you can easily search.
Eberly has free Magic-Software which is often mentioned, even though
it does not appear under that FAQ topic.
I'm fairly well aware of all of these things. What I'm after is not so muchQuote:> On Fri, 11 Jul 2003 09:12:53 +0200, "David Turner"
> You could look at Bloomenthal's bibiliography; the *references* are
> free, even if the contents are not. ;)
> But seriously, this topic appears in the FAQ, and is often discussed.
> "Subject 5.10: What is the marching cubes algorithm?"
> Google keeps newsgroup archives which you can easily search.
> Eberly has free Magic-Software which is often mentioned, even though
> it does not appear under that FAQ topic.
The reason I ask is precisely to see what's *missing* from the FAQ, so that
I can avoid reinventing a wheel or two.
>The reason I ask is precisely to see what's *missing* from the FAQ, so that
>I can avoid reinventing a wheel or two.
There have been several threads of research. One tradition eschews any
polygonization, since implicit surfaces are a natural to ray trace.
Even so, booleans constructions for CAD were sometimes converted to
boundary representations; but these were usually curved surfaces, not
polygons. Quadrics were the implicit primitives, and sculpted surfaces
not much in evidence.
Another tradition sought to model more artistic surfaces. At first
these were mostly in the blobby/metaball tradition, based on point set
"skeletons" with potential functions. Art demanded interaction, so ray
tracing was no longer enough.
The mathematically inclined simply wanted to visualize objects from
algebraic geometry; but typically they chose ray tracing. This line of
inquiry later included modeling with algebraic surfaces, but never too
much interest in polygonization.
Then we began to get these volume data sets of enormous size such as
CAT scans and weather measurements. Isosurfaces (level sets) were one
way to cope with the complexity.
Personally, although I find implicit surfaces interesting, I'm not
enthusiastic about polygonizing them, so I can't tell you the latest
and greatest ideas along each of the different threads. But I think
it's important to realize the diversity of interests and needs as you
seek and study solutions.
Very little of this is explicit in the FAQ. The bibliography expanded
from "Introduction to Implicit Surfaces" tends, I think, to reflect
the art and mathematics threads more than the volume data thread. UNC
spawned much of the latter, though it has scattered more widely now.
Phrases like "volume visualization" and "segmentation" may help find
more of that literature.
Can anyone help me with literature or algorithms concerning the
conversion from surfaces in an implicit formulation into a parametric
one. What are the classic and state of the art works on this topic?
I am not looking merely for a tesselation of an implicit surface, but
for a mathematical conversion into a parametric function that possibly
fulfills certain constraints as regularity of the grid and so on.
Thanks for any information.
Nils H. Busch
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