Function Repository Resource:

CurveIntersection

Source Notebook

Find the points of intersection of two curves

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["CurveIntersection"][{expr₁,expr₂},{x,y}]

returns the intersections of implicit curves expr₁ and expr₂ as points in the xy plane.

ResourceFunction["CurveIntersection"][{expr₁,expr₂},{x,y},dom]

returns the intersections of expr₁ and expr₂ as points in the xy plane, considered over the domain dom.

ResourceFunction["CurveIntersection"][{expr₁,expr₂},{x,y},dom,type]

returns the intersections with format type.

Details and Options

The domain dom may be Reals, Complexes or Integers, and defaults to Complexes.

The argument type may be Grid, List, Values or "Indexed", and defaults to List.

ResourceFunction["CurveIntersection"] accepts the option "Constraints", which can specify constraints on the input variables.

Examples

Basic Examples (2)

Obtain the points of intersection of x+1 and 2x²:

In[1]:=

$ResourceFunction[ "CurveIntersection", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][{y == x + 1, y == 2 x^2}, {x, y}]$

Out[1]=

Find the intersections of implicitly defined curves:

In[2]:=

$ResourceFunction[ "CurveIntersection", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][{y == x + 1, x^2 + y^2 == 1}, {x, y}]$

Out[2]=

Scope (3)

Find the integer-valued intersections of two implicitly defined curves:

In[3]:=

$ResourceFunction[ "CurveIntersection", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][{y == 1/2 x + 1, x^2 + y^2 == 1}, {x, y}, Integers]$

Out[3]=

If there is no intersection, CurveIntersection returns unevaluated:

In[4]:=

$ResourceFunction[ "CurveIntersection", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][{y == x + 3, x^2 + y^2 == 1}, {x, y}, Reals]$

Out[4]=

The fourth argument changes the format of the output:

In[5]:=

$ResourceFunction[ "CurveIntersection", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][{y == 1/2 x + 1, x^2 + y^2 == 1}, {x, y}, Reals, "Indexed"]$

Out[5]=

Options (1)

Find the intersections of two curves given some constraints:

In[6]:=

$ResourceFunction[ "CurveIntersection", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][{y == x, y == x^2}, {x, y}, Reals, "Constraints" -> 0 < x < 2]$