Interpolation

Interpolation Library

Float Functions

Linear
Linear interpolation of f0 and f1 with fraction t. <lsl> float fLin(float f0, float f1,float t){ return f0*(1-t) + f1*t;} </lsl> Input Description float f0 Start, 0.0 float f1 End, 1.0 float t Fraction of interpolation Output Description return float fLin Returns linear interpolation of two floats Graph goes here, k. By Nexii Malthus

Cosine
Cosine interpolation of f0 and f1 with fraction t. <lsl> float fCos(float v0,float v1,float t){ float F = (1 - llCos(t*PI))/2; return v0*(1-F)+v1*F;} </lsl> Input Description float f0 Start, 0.0 float f1 End, 1.0 float t Fraction of interpolation Output Description return float fCos Returns cosine interpolation of two floats Graph goes here, k. By Nexii Malthus

Cubic

Cubic interpolation of f0, f1, f2 and f3 with fraction t. <lsl> float fCub(float f0,float f1,float f2,float f3,float t){ float P = (f3-f2)-(f0-f1);float Q = (f0-f1)-P;float R = f2-f0;float S = f1; return P*llPow(t,3) + Q*llPow(t,2) + R*t + S;} </lsl> Input Description float f0 Modifier, 0.33~ float f1 Start, 0.0 float f2 End, 1.0 float f3 Modifier, 0.66~ float t Fraction of interpolation Output Description return float fCub Returns cubic interpolation of four floats Graph goes here, k. By Nexii Malthus

Hermite

Hermite interpolation of f0, f1, f2 and f3 with fraction t, tension and bias. <lsl> float fHem(float f0,float f1,float f2,float f3,float t,float tens,float bias){ float t2 = t*t;float t3 = t2*t; float a0 = (f1-f0)*(1+bias)*(1-tens)/2; a0 += (f2-f1)*(1-bias)*(1-tens)/2; float a1 = (f2-f1)*(1+bias)*(1-tens)/2; a1 += (f3-f2)*(1-bias)*(1-tens)/2; float b0 = 2*t3 - 3*t2 + 1; float b1 = t3 - 2*t2 + t; float b2 = t3 - t2; float b3 = -2*t3 + 3*t2; return ( b0 * f1+b1 * a0+b2 * a1+b3 * f2 );} </lsl> Input Description float f0 Modifier, 0.33~ float f1 Start, 0.0 float f2 End, 1.0 float f3 Modifier, 0.66~ float t Fraction of interpolation float tens Tension of interpolation float bias Bias of interpolation Output Description return float fHem Returns hermite interpolation of four floats with tension and bias Graph goes here, k. By Nexii Malthus

Old non-documented Library

Changes/ 1.0-1.1 - Added rotation types 1.1-1.2 - Added Hermite for float and vector

Example Script

<lsl> //===================================================// // Interpolation Library 1.2 // // "May 12 2008", "6:16:20 GMT-0" // // Copyright (C) 2008, Nexii Malthus (cc-by) // // http://creativecommons.org/licenses/by/3.0/ // //===================================================//

float fLin(float v0, float v1,float t){

   return v0*(1-t) + v1*t;}

float fCos(float v0,float v1,float t){

   float F = (1 - llCos(t*PI))/2;
   return v0*(1-F)+v1*F;}

float fCub(float v0,float v1,float v2,float v3,float t){

   float P = (v3-v2)-(v0-v1);float Q = (v0-v1)-P;float R = v2-v0;float S = v1;
   return P*llPow(t,3) + Q*llPow(t,2) + R*t + S;}

float fHem(float v0,float v1,float v2,float v3,float t,float tens,float bias){

   float t2 = t*t;float t3 = t2*t;
   float a0 =  (v1-v0)*(1+bias)*(1-tens)/2;
         a0 += (v2-v1)*(1-bias)*(1-tens)/2;
   float a1 =  (v2-v1)*(1+bias)*(1-tens)/2;
         a1 += (v3-v2)*(1-bias)*(1-tens)/2;
   float b0 =  2*t3 - 3*t2 + 1;
   float b1 =    t3 - 2*t2 + t;
   float b2 =    t3 -   t2;
   float b3 = -2*t3 + 3*t2;
   return (  b0  *  v1+b1  *  a0+b2  *  a1+b3  *  v2  );}

vector vLin(vector v0, vector v1,float t){

   return v0*(1-t) + v1*t;}

vector vCos(vector v0,vector v1,float t){

   float F = (1 - llCos(t*PI))/2;
   return v0*(1-F)+v1*F;}

vector vCub(vector v0,vector v1,vector v2,vector v3,float t){

   vector P = (v3-v2)-(v0-v1);vector Q = (v0-v1)-P;vector R = v2-v0;vector S = v1;
   return P*llPow(t,3) + Q*llPow(t,2) + R*t + S;}

vector vHem(vector v0,vector v1,vector v2,vector v3,float t,float tens,float bias){

   float t2 = t*t;float t3 = t2*t;
   vector a0 =  (v1-v0)*(1+bias)*(1-tens)/2;
          a0 += (v2-v1)*(1-bias)*(1-tens)/2;
   vector a1 =  (v2-v1)*(1+bias)*(1-tens)/2;
          a1 += (v3-v2)*(1-bias)*(1-tens)/2;
   float b0 =  2*t3 - 3*t2 + 1;
   float b1 =    t3 - 2*t2 + t;
   float b2 =    t3 -   t2;
   float b3 = -2*t3 + 3*t2;
   return (  b0  *  v1+b1  *  a0+b2  *  a1+b3  *  v2  );}

rotation rLin(rotation r0,rotation r1,float t){

   // Spherical-Linear Interpolation
   float ang = llAngleBetween(r0, r1);
   if( ang > PI) ang -= TWO_PI;
   return r0 * llAxisAngle2Rot( llRot2Axis(r1/r0)*r0, ang*t);}

rotation rCos(rotation r0,rotation r1,float t){

   // Spherical-Cosine Interpolation
   float f = (1 - llCos(t*PI))/2;
   float ang = llAngleBetween(r0, r1);
   if( ang > PI) ang -= TWO_PI;
   return r0 * llAxisAngle2Rot( llRot2Axis(r1/r0)*r0, ang*f);}

rotation rCub(rotation r0,rotation r1,rotation r2,rotation r3,float t){

   // Spherical-Cubic Interpolation
   // r0 = Start, r1 = End, r2 and r3 affect path of curve!
   return rLin( rLin(r0,r1,t), rLin(r2,r3,t), 2*t*(1-t) );}

default{state_entry(){}}

</lsl>