MaplePrimes - answers and comments on Question, Finding the intersection of two implicitly built surfaces - problem

Something to adjust

Markiyan Hirnyk — Sun, 20 Jan 2013 17:46:57 Z

There are problems with the construction of eq1 and eq2. See executed_qn_for_MP.mw

what exactly?

Denis — Sun, 20 Jan 2013 18:23:14 Z

You mean the problems are because of the very complicated equations?

But in this case why implicitplot3d builds plot of eq1 without any problem?

Reply

Markiyan Hirnyk — Sun, 20 Jan 2013 19:00:54 Z

@Denis

1. In http://www.mapleprimes.com/questions/127821-How-To-Plot-The-Intersection-Of-Three-Surfaces the transparency option is used. You apply the ?intersectplot command so your words "that doesn't work in my case" are not based.

2. Executing

> plots[intersectplot](eq1, eq2, `ϵbfib` = 0.1e-3 .. 0.40e-2, C1 = -.2 .. .2, beta = 0 .. (1/180)*(89*3.14));,

I obtain
Error, (in plots/intersectplot) input surface expressions must be algebraic, and only depend upon the plotting variables

3. Indeed, the command

works.

See executed2.mw

By procedures

Markiyan Hirnyk — Mon, 21 Jan 2013 20:42:59 Z

I rewrote eq1 and eq2 as procedures (for example,
eq1 := proc (`ϵbfib`, C1, beta) Nz+evalf(int(`σb`(v)*bv(v),
v = vmin .. vmax)+add(`σs`(BRSuv[n, 2])*3.14*BRSxy[n, 3]^2/4, n = 1 .. brsnum)) = 0
end proc ).
Having executed the modified code (only the below command after eq1 and eq2) during a few hours, I obtained
> plots[intersectplot](eq1, eq2, 0.1e-3 .. 0.40e-2, -.2 .. .2, 0 .. (1/180)*(89*3.14));
Error, (in plots/intersectplot) Maple was unable to allocate enough memory to complete this computation.
Please see ?alloc

See

executed3.mw

the same

Denis — Tue, 22 Jan 2013 13:45:46 Z

@Markiyan Hirnyk

I achieved the same result as you executing the file.

I still can not understand why every surface (eq1 and eq2) is plotting so good by implicitplot3d in few seconds,

but finding the intersection of them is unsolvable task for intersectplot???

Thank you for you help and time!

Timing

Markiyan Hirnyk — Wed, 23 Jan 2013 10:53:26 Z

@Denis > with(plots);
> st := time(); for j to 10^2 do implicitplot3d(x^2+y^2+z^2 = 1, x = -2 .. 2, y = -2 .. 2, z = -2 .. 2) end do; time()-st;

0.218
> st := time(); for j to 10^2 do intersectplot(x^2+y^2+z^2 = 1, x+y+z = 1, x = -2 .. 2, y = -2 .. 2, z = -2 .. 2) end do; time()-st;

38.469

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