rmr@mimsy.UUCP (Randy M. Rohrer) (09/30/89)
Lately, I have started to study scientific visualization (SciVi).
In fact, I attended SIGGRAPH '89 and participated in both SciVI courses.
However, there has been one concept that has puzzled me. Exactly,
what is an iso-surface? I think I have a pretty good idea but I am
hoping that some of you SciVi people can provide a simple, short
definition. It seems that most references use this term (iso-surface)
frequently but they fail to define it.
Any help would be appreciated.
Thanks in advance.
Randy Rohrer
rmr@mimsy.umd.edueugene@eos.UUCP (Eugene Miya) (09/30/89)
Iso surface: (2-D in a 3-D or higher-D)
A geometric structure, or concept with a CONSTANT value (ranging across a
domain). An extention from the concept of isobars (contour lines of constant
pressure), isotherms (constant temperature), isobels, iso-this/iso-that
Always a boundary.
Not to be confused with the International Standards Organization. 8)
Another gross generalization from
--eugene miya, NASA Ames Research Center, eugene@aurora.arc.nasa.gov
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Live free or die.rick@hanauma.stanford.edu (Richard Ottolini) (09/30/89)
In article <19889@mimsy.UUCP> rmr@mimsy.umd.edu (Randy M. Rohrer) writes: > >what is an iso-surface? In a multi-dimensional (2,3,+) sampling of data points, an iso-surface is a surface passes through data of the same value. This implies a certain degree of smoothness in the data samples. For example, the temperature surface of 200-degrees surrounding a flame.
jfh@brunix (John Forbes Hughes) (09/30/89)
In article <5430@portia.Stanford.EDU> rick@hanauma.UUCP (Richard Ottolini) writes: >In article <19889@mimsy.UUCP> rmr@mimsy.umd.edu (Randy M. Rohrer) writes: >> >>what is an iso-surface? >In a multi-dimensional (2,3,+) sampling of data points, an iso-surface >is a surface passes through data of the same value. >This implies a certain degree of smoothness in the data samples. >For example, the temperature surface of 200-degrees surrounding a flame. I don't want to nit-pick (actually, of course, I do, which is why I'm writing), but it might be better to say the following: If f : A --> R is a function, an *iso-set* of f is a set of the form J = { x in A : f(x) = C } where C is some constant in R. (R is the set of real numbers) (footnote 1). In the event that A = n-space, and f is smooth, and its derivative has maximal rank at each point of J, the iso-set is a codimension 1 submanifold of n-space. For example, if A = 3-space, and f is nice, then J will be a (possibly empty) surface. If f is merely continuous, then J may contain various degeneracies. If L is a lattice in n-space, and f is defined only on L, then there are infinitely many functions F such that F|L = f (the restriction of F to L is f). An iso-set of any such function F *can* be called an iso-set of f (footnote 2). If L is a finite lattice, and f is known to come from a function with reasonable behavior (e.g., it has no high-frequency components when fourier analyzed on the lattice), then the "correct" F can sometimes be synthesized from the values of f. The iso-sets of F deserve to be called the iso-sets of f in this case. In the cases where the data samples are taken from data whose exact continuous nature is unknown, typically some "reasonable" inference is made--for example people will do cubic interpolations between nearby sets of data values and use this as F. The results are, of course, only as good as the assumptions about the nature of the original signal. -John Hughes, Dept.'s of Math and CS, Brown University, Providence, RI jfh@cs.brown.edu (1) Actually, the codomain, which I have written as R, can actually be any set, and an "iso-set" is seen to be a specific case of the notion of "inverse image" or "preimage" of a point. (2) This is what is typically done is scientific visualization.
nagle@well.UUCP (John Nagle) (10/02/89)
I've been trying out isosurfaces of vector, rather than scalar, fields,
in hopes that this might be useful in modelling skin on a skeleton. The
idea is that with vector fields, you have more information, and by the
use of suitable combining functions, behaviors other than merging of
surfaces ("waterlike" behavior) can be obtained. The obvious combining
function is just vector addition, but if you just add vectors, the
results are disappointing. Think about what the sum of two vector fields
radiating from two points looks like. Yes, there's a zero at the
midpoint between the two sources, but off the centerline, you have nonzero
values. The resulting isosurface still looks like the one generated from
a scalar field, but there's a hole inside it around the midpoint.
Anyone else tried this approach?
John Nagle