Difference between revisions of "Barycenter Command"

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{{command|cas=true|geometry|Barycenter}}
 
{{command|cas=true|geometry|Barycenter}}
 
;Barycenter[  <List of Points>, <List of Weights>  ]
 
;Barycenter[  <List of Points>, <List of Weights>  ]
:Set the center of a system of points in the list, defined as the average of their positions, weighted by their value, using the [http://en.wikipedia.org/wiki/Center_of_mass  proper formula].
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:Set the center of a system of points in the list, defined as the average of their positions, weighted by their value, using the [[w:Center of mass|proper formula]].
  
 
:{{examples|1=<div>
 
:{{examples|1=<div>
 
:*<code>Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {1, 1, 1, 1}]</code> yields point ''A(0, 0)''
 
:*<code>Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {1, 1, 1, 1}]</code> yields point ''A(0, 0)''
 
:*<code>Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {2, 1, 1, 1}]</code> yields point ''B(0.4, 0)''. The ''x''-coordinate of this point was determined by '' <math> \frac{1}{ 2+1+1+1 }*(2*2+1*0+1*(-2)+1*0)</math> = <math>\frac{1}{ 5 }*2</math> = 0.4''</div>}}
 
:*<code>Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {2, 1, 1, 1}]</code> yields point ''B(0.4, 0)''. The ''x''-coordinate of this point was determined by '' <math> \frac{1}{ 2+1+1+1 }*(2*2+1*0+1*(-2)+1*0)</math> = <math>\frac{1}{ 5 }*2</math> = 0.4''</div>}}

Revision as of 11:03, 24 August 2015



Barycenter[ <List of Points>, <List of Weights> ]
Set the center of a system of points in the list, defined as the average of their positions, weighted by their value, using the proper formula.
Examples:
  • Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {1, 1, 1, 1}] yields point A(0, 0)
  • Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {2, 1, 1, 1}] yields point B(0.4, 0). The x-coordinate of this point was determined by \frac{1}{ 2+1+1+1 }*(2*2+1*0+1*(-2)+1*0) = \frac{1}{ 5 }*2 = 0.4
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