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See also the help file on 3.7.9.3 math.inc file, vectors and functions - there
are some great functions for divergence, curl, gradient, length, direction...
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Well, I've given up on finding a parametric solution (at least in special cases)
for these types of surfaces. Instead I'm going to teach myself a marching
cubes-like method of getting coordinates.
In the meantime I could really benefit from an answer to this relatively simple
question I asked on Stack Exchange:
http://math.stackexchange.com/questions/484488/flowlines-of-blobs
Someone did attempt an answer but hasn't followed up on the thread.
Mike
"Bald Eagle" <cre### [at] netscape net> wrote:
> Well then it seems to me that you'll need to get a firm grasp on the Laplacian
> Operator "del" or "nabla".
> http://en.wikipedia.org/wiki/Laplacian
>
> Since it is used frequently in many fields of study, including "blob" and "edge
> detection", you may wish to ask the folks who program the POV-Ray render engine,
> look at the source code, talk to the brainiacs at http://math.stackexchange.com
>
>
http://math.stackexchange.com/questions/5076/what-does-upside-down-triangle-symbol-mean-in-this-problem
>
> Check out Paul Nylander's page www.bugman123.com
>
> and basically play around with "systematizing" the operator.
> What I mean by that is if you can find a correlation between where you start,
> and where you want to go, you may be able to bypass 5 pages of math because you
> can work out a little system to jump from
> x^6 + 3x^5 + 9x^4 + 10x^3 + 32x^2 + 975.4x + 111.125 pi
>
> to
>
> 6x^5 + 15x^4 + 36x^3 + 30x^2 + 64x + 975.4
>
> in a heartbeat, without actually "doing" any "math".
>
> Once you can systematize and parameterize the more complex equation into smaller
> subsets of usuable and changeable fragments, you can then play around and
> visualize what's going on with the remaining parts and further dissect the
> equations until you have as close to a general solution as possible.
>
> You should be able to bang out something workable in a spreadsheet, SDL,
> Mathematica, Matlab, MathCad, etc.
>
> In short, don't get yourself bogged down with understanding the fundamentals of
> taking the above derivative if your real goal is to find a _practical_ solution
> and USE the results of solving the Laplacian (or any other) complex operator.
>
> If you use POV-Ray to solve / simulate what you want graphically, then you can
> Trace() the elements of the grid, come up with some numerical solutions, and
> sort of work backwards, or at least have numbers in had to guide you in
> unraveling the equations since you can "see" if what you're doing with del this
> and del that of x y and z is converging onto or diverging from what you already
> know is purty darned close to the "real" mathematical solution.
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