Difference between revisions of "Sector Command"

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<noinclude>{{Manual Page|version=4.2}}</noinclude>
 
<noinclude>{{Manual Page|version=4.2}}</noinclude>
 
{{command|geometry}}
 
{{command|geometry}}
; Sector[ <Conic>, <Point A>, <Point B> ]: Yields a conic sector between two points ''A'' and ''B'' on the conic section.
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; Sector[ <Conic>, <Point>, <Point> ]
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:Yields a conic sector between two points on the conic section.
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:{{example|1=<div>
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:* Let <code><nowiki>c: x^2 + 2y^2 = 8</nowiki></code> be an ellipse, <code><nowiki>D = (-2.83, 0)</nowiki></code> and <code><nowiki>E = (0, -2)</nowiki></code> two points on the ellipse. <code><nowiki>Sector[ c, D, E ]</nowiki></code> yields ''d = 4.44''.
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:* Let <code><nowiki>c: x^2 + y^2 = 9</nowiki></code> be a circle, <code><nowiki>A = (3, 0)</nowiki></code> and <code><nowiki>B = (0, 3)</nowiki></code> two points on the circle. <code><nowiki>Sector[ c, A, B ]</nowiki></code> yields ''d = 7.07''</div>}}
 
:{{Note|1=This works only for a circle or ellipse.}}
 
:{{Note|1=This works only for a circle or ellipse.}}
  
; Sector[ <Conic>, <Number t1>, <Number t2> ]: Yields a conic sector between two parameter values ''t1'' and ''t2'' on the conic section.
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;Sector[ <Conic>, <Parameter Value>, <Parameter Value> ]
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:Yields a conic sector between two parameter values on the conic section.
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:{{example|1=<div> Let <code><nowiki>c: x^2 + y^2 = 9</nowiki></code> be a circle. <code><nowiki>Sector[ c, 0, 3/4 π ]</nowiki></code> yields ''d = 10.6''</div>}}
 
:{{Note|1=Internally the following parametric forms are used:  
 
:{{Note|1=Internally the following parametric forms are used:  
 
:*Circle: ''(r cos(t), r sin(t))'' where ''r'' is the circle's radius.  
 
:*Circle: ''(r cos(t), r sin(t))'' where ''r'' is the circle's radius.  
 
:*Ellipse: ''(a cos(t), b sin(t))'' where ''a'' and ''b'' are the lengths of the semimajor and semiminor axes.}}
 
:*Ellipse: ''(a cos(t), b sin(t))'' where ''a'' and ''b'' are the lengths of the semimajor and semiminor axes.}}

Revision as of 10:04, 15 July 2013



Sector[ <Conic>, <Point>, <Point> ]
Yields a conic sector between two points on the conic section.
Example:
  • Let c: x^2 + 2y^2 = 8 be an ellipse, D = (-2.83, 0) and E = (0, -2) two points on the ellipse. Sector[ c, D, E ] yields d = 4.44.
  • Let c: x^2 + y^2 = 9 be a circle, A = (3, 0) and B = (0, 3) two points on the circle. Sector[ c, A, B ] yields d = 7.07
Note: This works only for a circle or ellipse.


Sector[ <Conic>, <Parameter Value>, <Parameter Value> ]
Yields a conic sector between two parameter values on the conic section.
Example:
Let c: x^2 + y^2 = 9 be a circle. Sector[ c, 0, 3/4 π ] yields d = 10.6
Note: Internally the following parametric forms are used:
  • Circle: (r cos(t), r sin(t)) where r is the circle's radius.
  • Ellipse: (a cos(t), b sin(t)) where a and b are the lengths of the semimajor and semiminor axes.
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