On Tue, 10 Jul 2001, Alex Yu wrote:
> I am trying to understand Triangular coordinates -- a kind of graph
> which combines four dimensions into 2D
You meant, "condenses four dimensions into 3D", didn't you? Your
subsequent description indicates three dimensions all together, two
of them used to represent 3 variables:
> by joining three axes to form a triangle while the Y axis "stands up."
> The Y axis can be hidden if the plot is depicted as a contour plot or a
> mosaic plot rather than a surface plot.
> I have a hard time to follow how a point is determined with the three
> axes as a triangle.
There must be constraints on the values of the three variables.
Commonly used for situations like a chemical mixture of 3 components.
Each component can have a relative concentration between 0% and 100%,
but if component A is at 100%, components B and C must both be at 0%,
and the point (100%, 0%, 0%) falls at one apex of the triangle. The
formal restriction, of course, is that the sum of all three
concentrations equals 100%, so that there are really only two dimensions'
worth of information available: (A, B, (100%-A-B)), (A, (100%-A-C), C),
or ((100%-B-C), B, C). Since there is usually no reason to treat any
component as more (or less) important than any other, triangular
coordinates are often displayed on an equilateral triangle, and special
graph paper can be purchased that has such a grid. In the absence of
such paper, one can plot, say, A and B at right angles to each other and
let the 45-degree line from (100,0) to (0,100) represent the C axis (and
the upper boundary of the space of possible points).
When there is not some such constraint on the values of the three
variables, triangular coordinates don't make a whole lot of sense and
may be extremely misleading.
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
184 Nashua Road, Bedford, NH 03110 603-471-7128
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