Difference between revisions of "Intersect Command"
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;Intersect( <Object>, <Object> ) | ;Intersect( <Object>, <Object> ) | ||
:Yields the intersection points of two objects. | :Yields the intersection points of two objects. | ||
− | :{{ | + | :{{examples|1=<div> |
− | :* 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 | + | :* 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 | + | :* <code><nowiki>Intersect(y = x + 3, Curve(t, 2t, t, 0, 10))</nowiki></code> yields ''A''=(3,6). |
− | :*<code><nowiki>Intersect | + | :*<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> ) | ;Intersect( <Object>, <Object>, <Index of Intersection Point> ) | ||
:Yields the n<sup>th</sup> intersection point of two objects. Each object must be a line, conic, polynomial function or implicit curve. | :Yields the n<sup>th</sup> intersection point of two objects. Each object must be a line, conic, polynomial function or implicit curve. | ||
− | :{{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 | + | :{{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> ) | ;Intersect( <Object>, <Object>, <Initial Point> ) | ||
:Yields an intersection point of two objects by using a numerical, iterative method with 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, and ''C'' = (0, 0.8) be the initial point. <code><nowiki>Intersect | + | :{{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> ) | ;Intersect( <Function>, <Function>, <Start x-Value>, <End x-Value> ) | ||
:Yields the intersection points numerically for the two functions in the given interval. | :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 | + | :{{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> ) | ;Intersect( <Curve 1>, <Curve 2>, <Parameter 1>, <Parameter 2> ) | ||
:Finds one intersection point using a numerical, iterative method starting at the given parameters. | :Finds one intersection point using a numerical, iterative method starting at the given parameters. | ||
− | :{{example|1=<div>Let <code>a = Curve | + | :{{example|1=<div>Let <code>a = Curve(cos(t), sin(t), t, 0, π)</code> and <code>b = Curve(cos(t) + 1, sin(t), t, 0, π)</code>. <br><code><nowiki>Intersect(a, b, 0, 2)</nowiki></code> yields the intersection point ''A = (0.5, 0.87)''.</div>}} |
==CAS Syntax== | ==CAS Syntax== | ||
;Intersect( <Function>, <Function> ) | ;Intersect( <Function>, <Function> ) | ||
:Yields a list containing 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 | + | :{{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>}} |
;Intersect( <Object>, <Object> ) | ;Intersect( <Object>, <Object> ) | ||
− | :{{ | + | :{{examples| 1=<div> |
− | :*<code><nowiki>Intersect | + | :*<code><nowiki>Intersect( <Line> , <Object> )</nowiki></code> creates the intersection point(s) of a line and a plane, segment, polygon, conic, etc. |
− | :*<code><nowiki>Intersect | + | :*<code><nowiki>Intersect( <Plane> , <Object> )</nowiki></code> creates the intersection point(s) of a plane and segment, polygon, conic, etc. |
− | :*<code><nowiki>Intersect | + | :*<code><nowiki>Intersect( <Conic>, <Conic> )</nowiki></code> creates the intersection point(s) of two conics |
− | :*<code><nowiki>Intersect | + | :*<code><nowiki>Intersect( <Plane>, <Plane> )</nowiki></code> creates the intersection line of two planes |
− | :*<code><nowiki>Intersect | + | :*<code><nowiki>Intersect( <Plane>, <Polyhedron> )</nowiki></code> creates the polygon(s) intersection of a plane and a polyhedron. |
− | :*<code><nowiki>Intersect | + | :*<code><nowiki>Intersect( <Sphere>, <Sphere> )</nowiki></code> creates the circle intersection of two spheres |
− | :*<code><nowiki>Intersect | + | :*<code><nowiki>Intersect( <Plane>, <Quadric> )</nowiki></code> creates the conic intersection of the plane and the quadric (sphere, cone, cylinder, ...)</div>}} |
{{Notes|1=<div> | {{Notes|1=<div> | ||
− | * to get all the intersection points in a list you can use eg <code>{Intersect | + | * to get all the intersection points in a list you can use eg <code>{Intersect(a,b)}</code> |
* See also [[IntersectConic Command|IntersectConic]] and [[IntersectPath Command|IntersectPath]] commands. | * See also [[IntersectConic Command|IntersectConic]] and [[IntersectPath Command|IntersectPath]] commands. | ||
* See also [[File:Mode intersect.svg|link=|22px]] [[Intersect Tool|Intersect]] tool.</div>}} | * See also [[File:Mode intersect.svg|link=|22px]] [[Intersect Tool|Intersect]] tool.</div>}} |
Latest revision as of 10:20, 11 October 2017
- 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.