Difference between revisions of "Intersect Command"

Revision as of 09:48, 15 July 2013

Intersect[ <Object>, <Object> ]

Yields the intersection points of two objects.

Example:

Let a: -3x + 7y = -10 be a line with A = (1, -1) and B = (8, 2) and c: x^2 + 2y^2 = 8 be an ellipse with focuses C = (-2, 0) und D = (2, 0). 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[ <Object>, <Object>, <Index of Intersection Point> ]: Yields the n^th intersection point of two objects.; Example:
Let a(x) = x^3 + x^2 - x be a function and b: -3x + 5y = 4 be a line with A = (-3, -1) and B = (2, 2). 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 with A = (-3, -1) and B = (2, 2) 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 and g(x) = 4 / 5 + 3 / 5 x be two functions. Intersect[ f, g, -1, 2 ] yields for the intervall [ -1, 2 ] the intersectionpoints A = (-0.43, 0.54) and B = (1.1, 1.46) of the two functions.

CAS

Intersect[ <Function>, <Function> ]: Yields the intersection points of two objects.; Example:
Let f(x):= x^3 + x^2 - x and g(x):= x be two functions. Intersect[ f(x), g(x) ] yields the intersection points {(1, 1), (0, 0), (-2, -2)} of the two functions.

Note: See also

Intersect Two Objects tool.

Following text is about a feature that is supported only in GeoGebra 5.0.

Intersect[ <Line> , <Object> ]: Creates the intersection point of a line and a plane, segment, polygon, etc
Intersect[ <Plane> , <Object> ]: Creates the intersection point of a plane and segment, polygon, etc
Intersect[ <Plane>, <Plane> ]: Creates the intersection line of two planes
Intersect[ <Plane>, <Polyhedron> ]: Creates the polygon(s) intersection of plane and polyhedron
Intersect[ <Sphere>, <Sphere> ]: Creates the circle intersection of two spheres
Intersect[ <Plane>, <Quadric> ]: Creates the conic intersection of the plane and the quadric (sphere, cone, cylinder, ...)

@@ Line 1: / Line 1: @@
 <noinclude>{{Manual Page|version=4.2}}</noinclude>
 {{command|cas=true|geometry}}
-; Intersect[<Line g>, <Line h>]: Yields the intersection point of lines ''g'' and ''h''.
-; Intersect[<Line>, <Conic>]: Yields all intersection points of the line and conic section (max. 2).
+;Intersect[ <Object>, <Object> ]
-; Intersect[<Line>, <Conic>, <Number n>]: Yields the ''n''<sup>th</sup> intersection point of the line and the conic section.
+:Yields the intersection points of two objects.
-; Intersect[<Conic c1>, <Conic c2>]: Yields all intersection points of conic sections ''c1'' and ''c2'' (max. 4).
+:{{example|1=<div>
-; Intersect[<Conic c1>, <Conic c2>, <Number n>]: Yields the ''n''<sup>th</sup> intersection point of conic sections ''c1'' and ''c2''.
+:* Let <code><nowiki>a: -3x + 7y = -10</nowiki></code> be a line with ''A = (1, -1)'' and ''B = (8, 2)'' and <code><nowiki>c: x^2 + 2y^2 = 8</nowiki></code> be an ellipse with focuses ''C = (-2, 0)'' und ''D = (2, 0)''. <code><nowiki>Intersect[a, c]</nowiki></code> yields the intersection points ''E = (-1.02, -1,87)'' and ''F = (2.81, -0.22)'' of the line and the ellipse.
-; Intersect[<Polynomial f1>, <Polynomial f2>]: Yields all intersection points of polynomials ''f1'' and ''f2''.
+:* <code><nowiki>Intersect[y = x + 3, Curve[t, 2t, t, 0, 10]]</nowiki></code> yields ''A(3,6)''.</div>}}
-; Intersect[<Polynomial f1>, <Polynomial f2>, <Number n>]: Yields the ''n''<sup>th</sup> intersection point of polynomials ''f1'' and ''f2''.
-; Intersect[<Polynomial>, <Line>]: Yields all intersection points of the polynomial and the line.
-; Intersect[<Polynomial>,< Line>, <Number n>]: Yields the ''n''<sup>th</sup> intersection point of the polynomial and the line.
+;Intersect[ <Object>, <Object>, <Index of Intersection Point> ]
-; Intersect[<Function f>, <Function g>, <Point A>]: Calculates an intersection point of functions ''f'' and ''g'' by using a (numerical) iterative method with initial point ''A''.
+:Yields the n<sup>th</sup> intersection point of two objects.
-; Intersect[<Function>, <Line>, <Point A>]: Calculates an intersection point of the function and the line by using a (numerical) iterative method with initial point ''A''.
+:{{example|1=<div>Let <code><nowiki>a(x) = x^3 + x^2 - x</nowiki></code> be a function and <code><nowiki>b: -3x + 5y = 4</nowiki></code> be a line with ''A = (-3, -1)'' and ''B = (2, 2)''. <code><nowiki>Intersect[a, b, 2]</nowiki></code> yields the intersection point ''C = (-0.43, 0.54)'' of the function and the line.</div>}}
-; Intersect[<Function f>, <Function g>, <left-x>, <right-x>]
-:Calculates the intersection points numerically for the two functions in the given interval.
-; Intersect[ <Line>, <Parametric Curve>]: Yields the intersection points of a line and a [[Curves|parametric curve]].
+;Intersect[ <Object>, <Object>, <Initial Point> ]
-:{{example|1=<code>Intersect[y = x + 3, Curve[t, 2t, t, 0, 10]]</code> yields ''A(3,6)''}}
+:Yields an intersection point of two objects by using a (numerical) iterative method with initial point.
+:{{example|1=<div>Let <code><nowiki>a(x) = x^3 + x^2 - x</nowiki></code> be a function, <code><nowiki>b: -3x + 5y = 4</nowiki></code> be a line with ''A = (-3, -1)'' and ''B = (2, 2)'' and ''C = (0, 0.8)'' be the initial point. <code><nowiki>Intersect[a, b, C]</nowiki></code> yields the intersection point ''D = (-0.43, 0.54)'' of the function and the line by using a (numerical) iterative method.</div>}}
+;Intersect[ <Function>, <Function>, <Start x-Value>, <End x-Value> ]
+:Yields the intersection points numerically for the two functions in the given interval.
+:{{example|1=<div>Let <code><nowiki>f(x) = x^3 + x^2 - x</nowiki></code> and <code><nowiki>g(x) = 4 / 5 + 3 / 5 x</nowiki></code> be two functions. <code><nowiki>Intersect[ f, g, -1, 2 ]</nowiki></code> yields for the intervall [ -1, 2 ] the intersectionpoints ''A = (-0.43, 0.54)'' and ''B = (1.1, 1.46)'' of the two functions.</div>}}
+==CAS==
+;Intersect[ <Function>, <Function> ]
+:Yields the intersection points of two objects.
+:{{example|1=<div>Let <code><nowiki>f(x):= x^3 + x^2 - x</nowiki></code> and <code><nowiki>g(x):= x</nowiki></code> be two functions. <code><nowiki>Intersect[ f(x), g(x) ]</nowiki></code> yields the intersection points ''{(1, 1), (0, 0), (-2, -2)}'' of the two functions.</div>}}
 {{Note| See also [[Image:Tool Intersect Two Objects.gif]] [[Intersect Two Objects Tool|Intersect Two Objects]] tool.}}
 {{betamanual|version=5.0|
-; Intersect[<Line> , <Object> ]: Creates the intersection point of a line and a plane, segment, polygon, etc
+; Intersect[ <Line> , <Object> ]: Creates the intersection point of a line and a plane, segment, polygon, etc
 ; Intersect[ <Plane> , <Object> ]: Creates the intersection point of a plane and segment, polygon, etc
-; Intersect[<Plane>, <Plane>]: Creates the intersection line of two planes
+; Intersect[ <Plane>, <Plane> ]: Creates the intersection line of two planes
 ; Intersect[ <Plane>, <Polyhedron> ]: Creates the polygon(s) intersection of plane and polyhedron
 ; Intersect[ <Sphere>, <Sphere> ]: Creates the circle intersection of two spheres
 ; Intersect[ <Plane>, <Quadric> ]: Creates the conic intersection of the plane and the quadric (sphere, cone, cylinder, ...)
 }}

Difference between revisions of "Intersect Command"

Revision as of 09:48, 15 July 2013

Intersect

Command Categories (All commands)

CAS