Difference between revisions of "LlAtan2"

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{{LSLFunctionAll
+
{{LSL Function
|func=llAtan2
+
|func_id=3|func_sleep=0.0|func_energy=10.0
|func_id=3
+
|func=llAtan2|sort=Atan2
|func_sleep=0.0
+
|p1_type=float|p1_name=y|p1_desc
|func_energy=10.0
+
|p2_type=float|p2_name=x|p2_desc
|func_footnote=Similar to the arctangent(y/x) except it utilizes the signs of x & y to determine the quadrant.
+
|p1_type=float
+
|p1_name=y
+
|p1_desc
+
|p2_type=float
+
|p2_name=x
+
|p2_desc
+
 
|return_type=float
 
|return_type=float
|return_text=that is the arctangent2 of y, x.
+
|return_text=that is the {{wikipedia|Atan2|arctangent2}} of {{LSLP|y}}, {{LSLP|x}}.
|spec
+
|func_footnote=Similar to the <span class="plainlinks">{{wikipedia|Inverse_trigonometric_functions|arctangent}}</span>({{LSLP|y}}/{{LSLP|x}}) except it utilizes the signs of {{LSLP|x}} & {{LSLP|y}} to determine the quadrant and avoids  division by zero. <br />
 +
|spec=
 +
If {{LSLP|x}} is positive zero and...
 +
* {{LSLP|y}} is zero, '''zero''' is returned.
 +
* {{LSLP|y}} is positive, '''PI/2''' is returned.
 +
* {{LSLP|y}} is negative, '''-PI/2''' is returned.
 +
If {{LSLP|x}} is negative zero and...
 +
* {{LSLP|y}} is positive zero, '''PI''' is returned.
 +
* {{LSLP|y}} is negative zero, '''-PI''' is returned.
 +
* {{LSLP|y}} is positive, '''PI/2''' is returned.
 +
* {{LSLP|y}} is negative, '''-PI/2''' is returned.
 +
 
 +
Or
 +
<source lang="lsl2">
 +
if((string)x != (string)0.0 && y == 0.0)//negative zero
 +
    return PI * ~-2*((string)y != (string)0.0));
 +
return ((y > 0) - (y < 0)) * PI_BY_TWO;
 +
</source>
 +
The returned value is in the range {{Interval|gte=-[[PI]]|gteh=-PI|lte=PI|center=return}}{{Interval/Footnote}}.
 
|caveats
 
|caveats
|examples
+
|constants
 +
|examples=<source lang="lsl2">default
 +
{
 +
  state_entry()
 +
  {
 +
    float num1 = llFrand(100.0);
 +
    float num2 = llFrand(100.0);
 +
 
 +
    llOwnerSay("y = " + (string)num1);
 +
    llOwnerSay("x = " + (string)num2);
 +
 
 +
    llOwnerSay("The arctangent of y divided by x is " + (string)llAtan2(num1, num2));
 +
  }
 +
}</source><source lang="lsl2">//Function with input of a vector determining the position of a target and returning
 +
//a string with the literal compass-direction of that target towards your position
 +
//by Ramana Sweetwater 2009/01, any use allowed license :-)
 +
//corrected by Patrick Muggins
 +
 
 +
string compass (vector target)
 +
{
 +
    vector source = llGetPos();
 +
    list DIRS =["W","NW","N","NE","E","SE","S","SW","W"];
 +
    integer index = llCeil(3.5 - (4 * llAtan2(target.y - source.y, target.x - source.x) / PI));
 +
    return llList2String(DIRS, index);
 +
}</source>
 +
[[/Compass QA]]
 
|helpers
 
|helpers
 
|also_functions=
 
|also_functions=
*{{LSLG|llAcos}}
+
{{LSL DefineRow|[[llSin]]|[[llAsin]]|sine & inverse Sine}}
*{{LSLG|llAcos}}
+
{{LSL DefineRow|[[llCos]]|[[llAcos]]|cosine & inverse cosine}}
 +
{{LSL DefineRow|[[llTan]]||tangent}}
 
|also_articles=
 
|also_articles=
*{{wikipedia|Atan2}}
+
{{LSL DefineRow||{{wikipedia|Atan2}}|}}
*{{wikipedia|Inverse_trigonometric_function}}
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{{LSL DefineRow||{{wikipedia|Inverse trigonometric function}}|}}
 
|notes
 
|notes
 +
|haiku=
 +
{{Haiku|An analog clock|passes through infinity|twice every single hour}}
 +
|cat1=Math/Trigonometry
 +
|cat2
 +
|cat3
 +
|cat4
 
}}
 
}}
 
[[Category:LSL_Stub]]
 
[[Category:LSL_Math/Trigonometry]]
 

Latest revision as of 07:32, 15 June 2016

Summary

Function: float llAtan2( float y, float x );

Returns a float that is the arctangent2 of y, x.

• float y
• float x

Similar to the arctangent(y/x) except it utilizes the signs of x & y to determine the quadrant and avoids division by zero.

Specification

If x is positive zero and...

  • y is zero, zero is returned.
  • y is positive, PI/2 is returned.
  • y is negative, -PI/2 is returned.

If x is negative zero and...

  • y is positive zero, PI is returned.
  • y is negative zero, -PI is returned.
  • y is positive, PI/2 is returned.
  • y is negative, -PI/2 is returned.

Or

if((string)x != (string)0.0 && y == 0.0)//negative zero
    return PI * ~-2*((string)y != (string)0.0));
return ((y > 0) - (y < 0)) * PI_BY_TWO;

The returned value is in the range [-PI, PI][1].

Examples

default
{
  state_entry()
  {
    float num1 = llFrand(100.0);
    float num2 = llFrand(100.0);
 
    llOwnerSay("y = " + (string)num1);
    llOwnerSay("x = " + (string)num2);
 
    llOwnerSay("The arctangent of y divided by x is " + (string)llAtan2(num1, num2));
  }
}
//Function with input of a vector determining the position of a target and returning

//a string with the literal compass-direction of that target towards your position //by Ramana Sweetwater 2009/01, any use allowed license :-) //corrected by Patrick Muggins   string compass (vector target) {

   vector source = llGetPos();
   list DIRS =["W","NW","N","NE","E","SE","S","SW","W"];
   integer index = llCeil(3.5 - (4 * llAtan2(target.y - source.y, target.x - source.x) / PI));
   return llList2String(DIRS, index);
}
/Compass QA

See Also

Functions

• llSin llAsin sine & inverse Sine
• llCos llAcos cosine & inverse cosine
• llTan tangent

Articles

•  Wikipedia:Atan2
•  Wikipedia:Inverse trigonometric function

Deep Notes

Search JIRA for related Issues

Footnotes

  1. ^ The ranges in this article are written in Interval Notation.

Signature

function float llAtan2( float y, float x );

Haiku

An analog clock
passes through infinity
twice every single hour