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Topic: intersection of a surface with a plane
Replies: 4   Last Post: Jan 17, 2013 8:19 PM

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 Torsten Hennig Posts: 2,419 Registered: 12/6/04
Re: intersection of a surface with a plane
Posted: Jan 16, 2013 7:20 AM

>
> I tried plotting. I got the plots. But I don't how to
> spot the location(co-ordinates) of the intersection.
>
>
> syms a b
> lhs='2*cos(a)*cosh(b)-(b/a-a/b)*sin(a)*sinh(b)-2';
> rhs='0';
>
> [a]=solve(lhs,a,b);
>
> figure
> ezsurf(lhs,[-5,5,-5,5])
> hold on
> ezsurf(rhs,[-5,5,-5,5])
>
> -----.
> My main aim was to find the roots of the equation.
> So, I plotted the equations, from which I can find
> the roots.
>
> zdiff = lhs - rhs;
> C = contours(lhs, rhs, zdiff, [0 0]);
> % Extract the x- and y-locations from the contour
> matrix C.
> aL = C(1, 2:end);
> bL = C(2, 2:end);
>
> % Interpolate on the first surface to find
> z-locations for the intersection
> % line.
> zL = interp2(a, b, lhs, aL, bL);
>
> % Visualize the line.
> line(aL, bL, zL, 'Color', 'k', 'LineWidth', 3);
>
> Since, I could not able to spot the value of 'a' and
> 'b', i was unable to find the roots of the eqn or the
> intersection of the curves.
> Problem with this : [a]=solve(lhs,a,b); was unable to
> find the explicit solution.
>
> Thank you very much,
> Murthy

What do you mean by
"My main aim was to find the roots of the equation." ?
You have one equation with two unknowns.
Thus there are infinitely many "roots".
The only thing you can do is to solve for a
(dependent on b) or b (dependent on a).
Example:
a^2+b^2-1 = 0
Solve for a:
a=+/- sqrt(1-b^2)
Solve for b:
b=+/- sqrt(1-a^2).
Is it that what you try ?

Then test whether

smys a b
solve(2*cos(a)*cosh(b)-(b/a-a/b)*sin(a)*sinh(b)-2==0,a);
or
solve(2*cos(a)*cosh(b)-(b/a-a/b)*sin(a)*sinh(b)-2==0,b);

works.

Best wishes
Torsten.

Date Subject Author
1/16/13 Murthy
1/16/13 Torsten Hennig
1/16/13 Murthy
1/16/13 Torsten Hennig
1/17/13 Murthy