Interpolation

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

Example Script

 
//===================================================//
//               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(){}}