How to restrict domain of surface to a curve?

justincc shared this question 7 months ago
Answered

Hello,

Is there a way to restrict a function of two variables to points on a curve in the xy-plane?

For example, f(x,y) = x^2-3y^2 restricted to x^2+y^2=1.

Best Answer
photo

depende de la complejidad de la curva y de sus parametrizaciones

en tu ejemplo a = Curve(cos(t), sin(t), f(cos(t), sin(t)), t, 0, 2π)

pero si la curva no es parametrizable yo uso locus()

Files: foro.ggb

Comments (4)

photo
2

How about

f(x,y) = (x^2-3y^2)*(x^2+y^2<1)

photo
1

Thanks for the input Michael. This wasn't exactly what I was looking for, but I can see this being useful in the future.

photo
photo
3

depende de la complejidad de la curva y de sus parametrizaciones

en tu ejemplo a = Curve(cos(t), sin(t), f(cos(t), sin(t)), t, 0, 2π)

pero si la curva no es parametrizable yo uso locus()

Files: foro.ggb
photo
1

Thanks mathmagic. This definitely works, but I was wondering if there was a nonparametric method for more difficult curves in the xy-plane. If not, no worries, as I mostly need to create ellipses in the xy-plane. Thanks again.

photo
© 2020 International GeoGebra Institute