interpolation/Spline/Vectors

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/LSL

Interpolation/Spline/Vectors

Summary

Function: vector pSpline( list v, float t, integer Loop );

B-Spline Interpolation between four vector points in a list of vectors that define a path.
Returns a vector

• list	v
• float	t	–	Ranges between [0, 1]
• integer	Loop	–	Whether the list is a curved line or loops into a closed shape.

Specification

<lsl>vector pSpline(list v, float t, integer Loop) {

   integer l = llGetListLength(v); t *= l-1;
   integer f = llFloor(t); t -= f;
   float t2 = t * t; float t3 = t2 * t;
   return (
     ( (-t3 + (3.*t2) - (3.*t) + 1.) * llList2Vector(v, pIndex(f-1,l,Loop)) )
   + ( ((3.*t3) - (6.*t2) + 4.) * llList2Vector(v, pIndex(f,l,Loop)) )
   + ( ((-3.*t3) + (3.*t2) + (3.*t) + 1.) * llList2Vector(v, pIndex(f+1,l,Loop)) )
   + ( t3 * llList2Vector(v, pIndex(f+2,l,Loop)) )
   ) / 6.0;

} integer pIndex( integer Index, integer Length, integer Loop) {

   if(Loop) return Index % Length;
   if(Index < 0) return 0;
   if(Index > --Length) return Length;
   return Index;

} // Released into public domain. By Nexii Malthus.</lsl>

Examples

<lsl></lsl>