Intersect Command
From GeoGebra Manual
- Intersect[ <Object>, <Object> ]
- Yields the intersection points of two objects.
- Example:
- Let
a: -3x + 7y = -10
be a line andc: x^2 + 2y^2 = 8
be an ellipse.Intersect[a, c]
yields the intersection points E = (-1.02, -1,87) and F = (2.81, -0.22) of the line and the ellipse. Intersect[y = x + 3, Curve[t, 2t, t, 0, 10]]
yields A=(3,6).Intersect[Curve[2s, 5s, s,-10, 10 ], Curve[t, 2t, t, -10, 10]]
yields A=(0,0).
- Let
- Intersect[ <Object>, <Object>, <Index of Intersection Point> ]
- Yields the nth intersection point of two objects.
- Example:Let
a(x) = x^3 + x^2 - x
be a function andb: -3x + 5y = 4
be a line.Intersect[a, b, 2]
yields the intersection point C = (-0.43, 0.54) of the function and the line.
- Intersect[ <Object>, <Object>, <Initial Point> ]
- Yields an intersection point of two objects by using a (numerical) iterative method with initial point.
- Example:Let
a(x) = x^3 + x^2 - x
be a function,b: -3x + 5y = 4
be a line, and C = (0, 0.8) be the initial point.Intersect[a, b, C]
yields the intersection point D = (-0.43, 0.54) of the function and the line by using a (numerical) iterative method.
- Intersect[ <Function>, <Function>, <Start x-Value>, <End x-Value> ]
- Yields the intersection points numerically for the two functions in the given interval.
- Example:Let
f(x) = x^3 + x^2 - x
andg(x) = 4 / 5 + 3 / 5 x
be two functions.Intersect[ f, g, -1, 2 ]
yields the intersection points A = (-0.43, 0.54) and B = (1.1, 1.46) of the two functions in the interval [ -1, 2 ].
- Intersect[ <Curve 1>, <Curve 2>, <Parameter 1>, <Parameter 2> ]
- Finds one intersection point using an iterative method starting at the given parameters.
- Example:Let
a = Curve[cos(t), sin(t), t, 0, π]
andb = Curve[cos(t) + 1, sin(t), t, 0, π]
.Intersect[a, b, 0, 2]
yields the intersection point A = (0.5, 0.87).
CAS Syntax
- Intersect[ <Function>, <Function> ]
- Yields a list containing the intersection points of two objects.
- Example:Let
f(x):= x^3 + x^2 - x
andg(x):= x
be two functions.Intersect[ f(x), g(x) ]
yields the intersection points list: {(1, 1), (0, 0), (-2, -2)} of the two functions.
Note: See also Intersect tool.
Following text is about a feature that is supported only in GeoGebra 5.0.
Note: From GeoGebra 5, this command will work with 3D objects as well |
- Intersect[ <Object>, <Object> ]
Example:
Intersect[ <Line> , <Object> ]
creates the intersection point(s) of a line and a plane, segment, polygon, conic, etc.Intersect[ <Plane> , <Object> ]
creates the intersection point(s) of a plane and segment, polygon, conic, etc.Intersect[ <Conic>, <Conic> ]
creates the intersection point(s) of two conicsIntersect[ <Plane>, <Plane> ]
creates the intersection line of two planesIntersect[ <Plane>, <Polyhedron> ]
creates the polygon(s) intersection of a plane and a polyhedron.Intersect[ <Sphere>, <Sphere> ]
creates the circle intersection of two spheresIntersect[ <Plane>, <Quadric> ]
creates the conic intersection of the plane and the quadric (sphere, cone, cylinder, ...)
Note: See also IntersectConic and IntersectPath commands.