Editing Talk:482: Height

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;Conversion of pixels to height
 
;Conversion of pixels to height
Because it is a log graph for the y axis
 
height<sub>final</sub> = height<sub>initial</sub> * factor
 
pixels = Log<sub>base</sub>(height)
 
  
Using identities to show that a vertical distance on this graph represents a multiplicative change in true distance from the starting point of measure, and that a vertical change (delta) in the same number of pixels represents a corresponding multiplicative factor on total height.
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height<sub>final</sub> = height<sub>initial</sub> * factor
pixels<sub>final</sub> = Log<sub>base</sub>(height<sub>initial</sub> * factor) = Log<sub>base</sub>(initial) + Log<sub>base</sub>(factor)
 
pixels<sub>final</sub> - pixels<sub>initial</sub> = Log<sub>base</sub>(factor) = pixels<sub>delta</sub>
 
  
Solving for the factor and the base of the log function
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pixels = Log<sub>base</sub>(height)
factor = base<sup>pixels<sub>delta</sub></sup>
 
base = factor<sup>1/pixels<sub>delta</sub></sup>
 
  
From the diagram it appears that  a change (delta) of 550 pixels represents a change of x*1000000 therefore we can determine the base and determine the multiplicative factor for any change in pixels in the original drawing.
 
base = 1000000<sup>1/550</sup>
 
factor = (1000000<sup>1/550</sup>)<sup>pixels<sub>delta</sub></sup> = 1000000<sup>pixels<sub>delta</sub>/550</sup>
 
  
Therefore:
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height<sub>final</sub> = height<sub>initial</sub> * 1000000<sup>pixels<sub>delta</sub>/550</sup>
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pixels<sub>final</sub> = Log<sub>base</sub>(height<sub>initial</sub> * factor) = Log<sub>base</sub>(initial) + Log<sub>base</sub>(factor)
The above can be used as an equation to estimate and validate the heights on the diagram, where height<sub>initial</sub> is the height of the reference point in meters, pixels<sub>delta</sub> is the vertical change in pixels on the diagram, and is positive if height increases and negative if height decreases.
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Therefore vertical distance on this graph represents a multiplicative change in true distance from the starting point of measure. 
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pixels<sub>delta</sub> = pixels<sub>final</sub> - pixels<sub>initial</sub> = Log<sub>base</sub>(factor)
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Therefore a vertical change in pixels always represents the same multiplicative factor.
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base<sup>pixels<sub>delta</sub></sup> = factor
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base = factor<sup>1/pixels<sub>delta</sub></sup>
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From the diagram it appears that 550 pixels represents a change of x*1000000.
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1000000<sub>meters</sub><sup>1/550<sub>pixels</sub></sup> = base
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1000000<sup>1/550<sup>pixels<sub>delta</sub></sup></sup> = 1000000<sup>pixels<sub>delta</sub>/550</sup> = factor
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The following can be used as an equation to estimate and validate the heights on the diagram, where height<sub>initial</sub> is the height of the reference point in meters, pixels<sub>delta</sub> is the vertical change in distance in pixels, and is positive if height increases and negative if height decreases.
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height<sub>final</sub> = height<sub>initial</sub> * 1000000<sup>pixels<sub>delta</sub>/550</sup>
  
 
[[Special:Contributions/108.162.216.149|108.162.216.149]] 12:40, 30 September 2014 (UTC)
 
[[Special:Contributions/108.162.216.149|108.162.216.149]] 12:40, 30 September 2014 (UTC)

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