Difference between revisions of "Trigonometry Functions"

374 bytes added ,  12:45, 29 May 2006
commenting comments again, directing to quest variables, and making things fit on the page
imported>DragoonWraith
imported>DragoonWraith
(commenting comments again, directing to quest variables, and making things fit on the page)
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This [[:Category:Stage Functions|function]] requires the following variables to be declared in your [[Global Script]]:
This [[:Category:Stage Functions|function]] requires the following variables to be declared in your [[Global Script]]:
  float ang (the measure of the angle)
  float ang ;(the measure of the angle)
  float n (used internally)
  float n ;(used internally)
  float t2 (used internally)
  float t2 ;(used internally)
  float sin (sine of the angle)
  float sin ;(sine of the angle)
  float cos (cosine of the angle)
  float cos ;(cosine of the angle)
  float tan (tangent of the angle)
  float tan ;(tangent of the angle)
You may rename these if you wish, but that means changing the code to match. All of them must be floats.
You may rename these if you wish, but that means changing the code to match. All of them must be floats.


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This [[:Category:Stage Functions|function]] requires the following variables to be declared in your [[Global Script]]:
This [[:Category:Stage Functions|function]] requires the following variables to be declared in your [[Global Script]]:
  float ang (the measure of the angle)
  float ang ;(the measure of the angle)
  float rad (used internally)
  float rad ;(used internally)
  float exp (used internally)
  float exp ;(used internally)
  float sin (the sine of the angle)
  float sin ;(the sine of the angle)
  float cos (the cosine of the angle)
  float cos ;(the cosine of the angle)
  float tan (the tangent of the angle)
  float tan ;(the tangent of the angle)
You may rename these if you wish, but that means changing the code, which is not advised, as there are a lot of variables here. All of them must be floats.
You may rename these if you wish, but that means changing the code, which is not advised, as there are a lot of variables here. All of them must be floats.


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This [[:Category:Stage Functions|function]] requires the following variables to be declared in your [[Global Script]]:
This [[:Category:Stage Functions|function]] requires the following variables to be declared in your [[Global Script]]:
  float angle (measure of the angle)
  float angle ;(measure of the angle)
  float t1 (used internally)
  float t1 ;(used internally)
  float t2 (used internally)
  float t2 ;(used internally)
  float t5 (used internally)
  float t5 ;(used internally)
  float t6 (used internally)
  float t6 ;(used internally)
  float sina  (sine of the angle)
  float sina  ;(sine of the angle)
  float cosa  (cosine of the angle)
  float cosa  ;(cosine of the angle)
  float tana  (tangent of the angle)
  float tana  ;(tangent of the angle)
All must be floats. Though they can be renamed, doing so means changing the function code to match.
All must be floats. Though they can be renamed, doing so means changing the function code to match.
  ; script originally by JOG
  ; script originally by JOG
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  set Wiki.t5 to Wiki.t2*Wiki.t2*Wiki.t1
  set Wiki.t5 to Wiki.t2*Wiki.t2*Wiki.t1
  set Wiki.t6 to Wiki.t5*Wiki.t1
  set Wiki.t6 to Wiki.t5*Wiki.t1
  set Wiki.sina to Wiki.t1 - Wiki.t1*Wiki.t2/6 + Wiki.t5/120 - Wiki.t5*t2/5040 + Wiki.t6*Wiki.t2*Wiki.t1/362880  
  set Wiki.sina to Wiki.t1 - Wiki.t1*Wiki.t2/6 + Wiki.t5/120 - Wiki.t5*t2/5040  
set Wiki.sina to Wiki.sina + Wiki.t6*Wiki.t2*Wiki.t1/362880
;note that the previous two lines have been split in order to display properly
;they should be on one line in your code
  set Wiki.cosa to 1 - Wiki.t2/2 + Wiki.t2*Wiki.t2/24 - Wiki.t6/720 + Wiki.t6*Wiki.t2/40320
  set Wiki.cosa to 1 - Wiki.t2/2 + Wiki.t2*Wiki.t2/24 - Wiki.t6/720 + Wiki.t6*Wiki.t2/40320
  set Wiki.tana to Wiki.sina/Wiki.cosa
  set Wiki.tana to Wiki.sina/Wiki.cosa
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This [[:Category:Stage Functions|function]] requires the following variables to be declared in your [[Global Script]]:
This [[:Category:Stage Functions|function]] requires the following variables to be declared in your [[Global Script]]:
  float x (the sine of the angle)
  float x ;(the sine of the angle)
  float n (used internally)
  float n ;(used internally)
  float arcsinx (the arcsine, that is, the measure of the angle)
  float arcsinx ;(the arcsine, that is, the measure of the angle)
These may be renamed, but doing so means changing them in the code.
These may be renamed, but doing so means changing them in the code.


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  set Wiki.n to (Wiki.arcsinx+(Wiki.n/Wiki.arcsinx))/2
  set Wiki.n to (Wiki.arcsinx+(Wiki.n/Wiki.arcsinx))/2
   
   
  set arcsinx to 57.2957795*(1.5707963-Wiki.n*(1.5707288-0.2121144*Wiki.x+0.0742610*Wiki.x*Wiki.x-0.0187293*Wiki.x*Wiki.x*Wiki.x))
  set Wiki.arcsinx to 57.2957795*(1.5707963-Wiki.n*(1.5707288-0.2121144*Wiki.x+0.0742610*Wiki.x*Wiki.x-0.0187293*Wiki.x*Wiki.x*Wiki.x))
;note that this does not display properly - be sure to get the entire line with copy and paste


This approximation is very accurate (99.9% - 99.9999%) for angles of 45 degrees and higher. For smaller angles you can get a higher precision when you use a taylor series with 15+ iterations.
This approximation is very accurate (99.9% - 99.9999%) for angles of 45 degrees and higher. For smaller angles you can get a higher precision when you use a taylor series with 15+ iterations.
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This can be approximated by Oblivion using a [[:Category:Staged Functions|function]]. This function requires the following variables be declared in your [[Global Script]]:  
This can be approximated by Oblivion using a [[:Category:Staged Functions|function]]. This function requires the following variables be declared in your [[Global Script]]:  
  float z (the sine of the angle)
  float z ;(the sine of the angle)
  float z3 (used internally)
  float z3 ;(used internally)
  float z5 (used internally)
  float z5 ;(used internally)
  float z7 (used internally)
  float z7 ;(used internally)
  float arcsinz (the arcsine, that is, the measure of the angle)
  float arcsinz ;(the arcsine, that is, the measure of the angle)
These can be renamed, but must also be changed in the code.
These can be renamed, but must also be changed in the code.
  ;script originally by DragoonWraith
  ;script originally by DragoonWraith
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  set Wiki.z7 to (Wiki.z5*Wiki.z*Wiki.z)
  set Wiki.z7 to (Wiki.z5*Wiki.z*Wiki.z)
   
   
  set arcsinz to (Wiki.z+(1/2)*(Wiki.z3/3)+(3/8)*(Wiki.z5/5)+(15/48)*(Wiki.z7/7))
  set Wiki.arcsinz to (Wiki.z+(1/2)*(Wiki.z3/3)+(3/8)*(Wiki.z5/5)+(15/48)*(Wiki.z7/7))
More terms will increase accuracy. The larger the angle, the more terms are needed to get acceptable accuracy. As a rough guide use 3 terms for every 10° to get an accuracy of at least 1 decimal digit.
More terms will increase accuracy. The larger the angle, the more terms are needed to get acceptable accuracy. As a rough guide use 3 terms for every 10° to get an accuracy of at least 1 decimal digit.


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This function requires the following variables be declared in your [[Global Script]]:  
This function requires the following variables be declared in your [[Global Script]]:  
  float z (the tangent of the angle)
  float z ;(the tangent of the angle)
  float z3 (used internally)
  float z3 ;(used internally)
  float z5 (used internally)
  float z5 ;(used internally)
  float z7 (used internally)
  float z7 ;(used internally)
  float arcsinz (the arctangent, that is, the measure of the angle)
  float arcsinz ;(the arctangent, that is, the measure of the angle)
These can be renamed, but must also be changed in the code.
These can be renamed, but must also be changed in the code.
  ;modified from arcsine script supplied by DragoonWraith
  ;modified from arcsine script supplied by DragoonWraith
   set z3 to ( z * z * z )
   set Wiki.z3 to ( Wiki.z * Wiki.z * Wiki.z )
   set z5 to ( z3 * z * z )
   set Wiki.z5 to ( Wiki.z3 * Wiki.z * Wiki.z )
   set z7 to ( z5 * z * z )
   set Wiki.z7 to ( Wiki.z5 * Wiki.z * Wiki.z )
   
   
   set arctanz to ( z - (z3/3) + (z5/5) - (z7/7) )
   set Wiki.arctanz to ( Wiki.z - (Wiki.z3/3) + (Wiki.z5/5) - (Wiki.z7/7) )


Again, more terms equals more accuracy.
Again, more terms equals more accuracy.