llRotBetween

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/LSL

RotBetween

llRotBetween

Summary

Function: rotation llRotBetween( vector start, vector end );

0.0	Forced Delay
10.0	Energy

Returns a rotation that is the shortest rotation between the direction start and the direction end

• vector	start
• vector	end

Specification

start and end are directions and are relative to the origin <0.0, 0.0, 0.0>. If you have coordinates relative to a different origin, subtract that origin from the input vectors.

Caveats

• start * llRotBetween(start, end) == end is only true if start and end have the same magnitude and neither have a magnitude of zero (see #Useful Snippets for a workaround).
  • This of course is ignoring floating point precision errors.
• Rotations are from -PI to +PI around each axis.

Examples

<lsl>llRotBetween(<1.0, 0.0, 0.0>, <0.0, -1.0, 0.0>) // will return <0.00000, 0.00000, -0.70711, 0.70711> (which represents -90 degrees on the z axis)

llRotBetween(<0.0, 0.0, 0.0>, <0.0, -1.0, 0.0>) // will return <0.00000, 0.00000, 0.00000, 1.00000> (which represents a zero angle on all axis)

// because <0.0, 0.0, 0.0> does not convey a direction.</lsl>

Useful Snippets

This function adjusts the magnitude of the quaternion so start * llRotBetween(start, end) == end is true as long as neither have a magnitude really close to zero. They do not have to have the same magnitude. (If either is too close to zero than this will return an unadjusted quaternion). <lsl>rotation RotBetween(vector start, vector end) //adjusts quaternion magnitude so (start * return == end) {//Authors note: I have never had a use for this but it's good to know how to do it if I did.

   rotation rot = llRotBetween(start, end);
   float d = start * start;
   if(d)//is 'start' zero?
       if((d = llPow(end * end / d, 0.25)))//is 'end' zero?
           return <rot.x * d, rot.y * d, rot.z * d, rot.s * d>;
   return rot;

}//Strife Onizuka</lsl>

Notes

Vectors that are near opposite each other in direction may lead to erroneous results. <lsl> // First Vector is due north second vector is ALMOST due south. rotation lRotation = llRotBetween( <0., 1., 0.>, <-0.001, -.1, 0.> ); llSay(0, lRotation ); // Provides a result of <1.00000, 0.00000, 0.00000, 0.00000>. </lsl>

See Also

Functions

•

llAngleBetween

Deep Notes

<lsl>//Loosely based on SL source code rotation llRotBetween(vector start, vector end) {

   vector v1 = llVecNorm(start);
   vector v2 = llVecNorm(end);
   float dot = v1 * v2;
   vector axis = v1 % v2;
   if (dot < -0.9999999) {
       // 180 degrees or there abouts
       vector ortho_axis = llVecNorm(<1.f, 0.f, 0.f> - (sn * (sn.x / (sn * sn))));
       if (ortho_axis)
           return < ortho_axis.x, ortho_axis.y, ortho_axis.z, 0.f>;
       return <0.0, 0.0, 1.0, 0.0>;
   }
   else if(dot > 0.9999999) {
       //parallel
       return ZERO_ROTATION;
   }
   dot = dot + 1.0;
   float m = llPow((axis * axis) + (dot * dot), -0.5);
   return <axis.x * m, axis.y * m, axis.z * m, dot * m>;

}</lsl>

Source

viewer - indra/llmath/llquaternion.cpp

Signature
function rotation llRotBetween( vector start, vector end );