Intersect Command
From GeoGebra Manual
- Intersect( <Object>, <Object> )
- Yields the intersection points of two objects.
- Examples:
- 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. Each object must be a line, conic, polynomial function or implicit curve.
- 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 a numerical, 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.
- Intersect( <Object>, <Object> )
- Examples:
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, ...)
Notes:
- to get all the intersection points in a list you can use eg
{Intersect(a,b)}
- See also IntersectConic and IntersectPath commands.
- See also Intersect tool.