Intersection of multivariate graphs

Sanelma shared this question 2 years ago

Answered

Hi, I have two multivariate functions graphed: f(x,y)=x^2 + y^2 and g(x,y) = xy+2. I would like to show the curve of intersection of these two graphs. Is this possible? Couldn't get it to work with regular "intersect" command.

The same question

Comments (7)

Michael Borcherds ● 2 years ago

The projection of the intersection onto the xOyPlane is:

x² + y² - x y - 2 = 0
Curve(2 / sqrt(2) (sin(t) - cos(t) / sqrt(3)), 2 / sqrt(2) (sin(t) + cos(t) / sqrt(3)), t, 0, 2π)

so the intersection is

Curve(2 / sqrt(2) (sin(t) - cos(t) / sqrt(3)), 2 / sqrt(2) (sin(t) + cos(t) / sqrt(3)),f(2 / sqrt(2) (sin(t) - cos(t) / sqrt(3)), 2 / sqrt(2) (sin(t) + cos(t) / sqrt(3))), t, 0, 2π)

https://www.geogebra.org/m/ebkfuyaj

Reply URL

tphanyamada ● 2 years ago

Hi Michael,

I'd like to show the curve of the intersection of x^2+4y^2+9z^2=1 and z = h x + c.

Please see the link below.

I also want to an animation point on this intersection curve.

Is it possible?

https://ggbm.at/tpybbn2y

Thank you so much for your help.

URL

Michael Borcherds ● 2 years ago

That's easier, there's a command for that :)

IntersectPath( <Plane>, <Quadric> )

Try:

c:IntersectPath(a, b)
A=Point(c)
StartAnimation(A)

URL

tphanyamada ● 2 years ago

Thank you, Michael!

Actually I have a surface.Is there a command for Intersection of a surface and a plane?

I try yours but it didn't work.

Thank you for your reply.

URL

mire2 ● 2 years ago

Hi Sanelma!

One possibility is to solve the equation f(x,y)=g(x,y) and to use the solution for drawing one rather two curves.

77094456cbed6ba77f7d184cdf587393

Greetings

mire2

Files: Schnitt_Flaeche...

Reply URL

Michael Borcherds ● 2 years ago

That's very nice!

I think you need an extra +2 on the z-coordinate

URL

mire2 ● 2 years ago

Oh - thank you for your kind words and yes, I forgot the +2 on the z-coordinate, so all must be above the x-y-plane.

Good looks!

Kind regards

mire2

Files: Schnitt_Flaeche... Schnitt_Flaeche...

URL