Difference between revisions of "Intersect Command"

Revision as of 12:48, 11 February 2014

Intersect[ <Object>, <Object> ]

Yields the intersection points of two objects.

Example:

Let a: -3x + 7y = -10 be a line and c: 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).

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. 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 and g(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] and b = 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 and g(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.

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 4: / Line 4: @@
 :Yields the intersection points of two objects.
 :{{example|1=<div>
-:* 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)'' and ''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.
+:* Let <code><nowiki>a: -3x + 7y = -10</nowiki></code> be a line and <code><nowiki>c: x^2 + 2y^2 = 8</nowiki></code> be an ellipse. <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.
-:* <code><nowiki>Intersect[y = x + 3, Curve[t, 2t, t, 0, 10]]</nowiki></code> yields ''A(3,6)''.
+:* <code><nowiki>Intersect[y = x + 3, Curve[t, 2t, t, 0, 10]]</nowiki></code> yields ''A''=(3,6).
-:*<code><nowiki>Intersect[Curve[2s, 5s, s,-10, 10 ], Curve[t,2t,t,-10,10]]</nowiki></code> yields ''A(0,0)''. </div>}}
+:*<code><nowiki>Intersect[Curve[2s, 5s, s,-10, 10 ], Curve[t, 2t, t, -10, 10]]</nowiki></code> yields ''A''=(0,0). </div>}}
 ;Intersect[ <Object>, <Object>, <Index of Intersection Point> ]
 :Yields the n<sup>th</sup> intersection point of two objects.
-:{{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>}}
+:{{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. <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[ <Object>, <Object>, <Initial Point> ]
 :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>}}
+:{{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, 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 intersection points ''A = (-0.43, 0.54)'' and ''B = (1.1, 1.46)'' of the two functions.</div>}}
+:{{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  the intersection points ''A'' = (-0.43, 0.54) and ''B'' = (1.1, 1.46) of the two functions in the interval [ -1, 2 ].</div>}}
 ;Intersect[ <Curve 1>, <Curve 2>, <Parameter 1>, <Parameter 2> ]
 :Finds one intersection point using an iterative method starting at the given parameters.
@@ Line 22: / Line 22: @@
 ==CAS Syntax==
 ;Intersect[ <Function>, <Function> ]
-:Yields the intersection points of two objects.
+:Yields a list containing 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>}}
+:{{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 list: ''{(1, 1), (0, 0), (-2, -2)}'' of the two functions.</div>}}
 {{Note| See also [[Image:Tool Intersect Two Objects.gif]] [[Intersect Tool|Intersect]] tool.}}

Difference between revisions of "Intersect Command"

Revision as of 12:48, 11 February 2014

Intersect

Command Categories (All commands)

CAS Syntax