# How to draw intersection path of two surfaces or curves in 3D and intersection contour in 2D?

Math123 shared this question 3 years ago

How to find and draw path of intersection between two curves in 3D and intersection of contours of both in 2D.

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Which curves?

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Any two surfaces .

f(x,y) = x^2 - y

x^2 + y^2 = 1

How to find/draw path of intersection.. Contours as well.

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Curve(cos(t), sin(t), 1 - sin(t) - sin²(t), t, 0, 2π)

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Thanks for reply. Isn't there any general procedure to draw intersection of both curves. in which we use both functions.

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Also it is not showing the proper intersection Pls see attached.

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you have changed a(x,y)

use Curve(cos(t), sin(t), a(cos(t), sin(t)), t, 0, 2π)

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In any curve can we use

Curve(cos(t), sin(t), a(cos(t), sin(t)), t, 0, 2π) [Pls explain how it work]

for intersections. otherwise pls share general procedure for which i can make intersection.

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general procedure does not exist and never will exist

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so, Pls explain how do you know Curve(cos(t), sin(t), a(cos(t), sin(t)), t, 0, 2π) work for intersection. In this parametrization i can see x=cost , y= sint , z=a(x(t) , y(t)) , where is my constraint equation x^2 + y^2 = 1. what if i change my constraint equation. how do i adjust intersection.

What if more than 2 curves intersects and want to know intersect where all all curves intersects.

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Curve(cos(t), sin(t), a(cos(t), sin(t)), t, 0, 2π)

This work for every a(x,y) but it did not work for when i changes constraint equation. and where is detail of constraint in above command.

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Hello Team,

Pls suggest the solution of my above question.

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Thanks . Found the solution by looking pattern.