Distorted Android

///////////////////////////////////////////////////////////////////////////////////////////////////

// Copyright 2016 Leszek Koltunski                                                               //

//                                                                                               //

// This file is part of Distorted.                                                               //

//                                                                                               //

// Distorted is free software: you can redistribute it and/or modify                             //

// it under the terms of the GNU General Public License as published by                          //

// the Free Software Foundation, either version 2 of the License, or                             //

// (at your option) any later version.                                                           //

//                                                                                               //

// Distorted is distributed in the hope that it will be useful,                                  //

// but WITHOUT ANY WARRANTY; without even the implied warranty of                                //

// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                                 //

// GNU General Public License for more details.                                                  //

//                                                                                               //

// You should have received a copy of the GNU General Public License                             //

// along with Distorted.  If not, see <http://www.gnu.org/licenses/>.                            //

///////////////////////////////////////////////////////////////////////////////////////////////////

package org.distorted.library.type;

import java.util.Vector;

///////////////////////////////////////////////////////////////////////////////////////////////////

/** 

* A 4-dimensional implementation of the Dynamic class to interpolate between a list

* of Static4Ds.

*/

public class Dynamic4D extends Dynamic implements Data4D

  {

///////////////////////////////////////////////////////////////////////////////////////////////////

// the coefficients of the X(t), Y(t), Z(t), W(t) polynomials: X(t) = ax*T^3 + bx*T^2 + cx*t + dx  etc.

// (x,y,z,w) is the vector tangent to the path.

// (vx,vy,vz,vw) is the original vector from vv (copied here so when interpolating we can see if it is 

// still valid and if not - rebuild the Cache

  private class VectorCache

    {

    float ax, bx, cx, dx;

    float ay, by, cy, dy;

    float az, bz, cz, dz;

    float aw, bw, cw, dw;

    float x,y,z,w;

    float vx,vy,vz,vw;

    }

  private Vector<VectorCache> vc;

  private VectorCache tmp1, tmp2;

  private Vector<Static4D> vv;

  private Static4D prev, curr, next;

  private float vec1X,vec1Y,vec1Z,vec1W;      // vector perpendicular to v(t) and in the same plane as v(t) and a(t) (for >2 points only, in case of 2 points this is calculated differently)

  private float vec2X,vec2Y,vec2Z,vec2W;      // vector perpendicular to v(t) and to vec1.

  private float vec3X,vec3Y,vec3Z,vec3W;      // vector perpendicular to v(t) and to vec1.

///////////////////////////////////////////////////////////////////////////////////////////////////

// no array bounds checking!

  private void vec(int c)

    {

    int p = c>0 ? c-1: numPoints-1;

    int n = c<numPoints-1 ? c+1: 0;

    prev = vv.elementAt(p);

    curr = vv.elementAt(c);

    next = vv.elementAt(n);

    tmp1 = vc.elementAt(c);

    float px = curr.x - prev.x;

    float py = curr.y - prev.y;

    float pz = curr.z - prev.z;

    float pw = curr.w - prev.w;

    float nx = next.x - curr.x;

    float ny = next.y - curr.y;

    float nz = next.z - curr.z;

    float nw = next.w - curr.w;

    float d = nx*nx+ny*ny+nz*nz+nw*nw;

    if( d>0 )

      {

      float q = (float)Math.sqrt((px*px+py*py+pz*pz+pw*pw)/d);

      if( q>1 )

        {

        tmp1.x = nx+px/q;

        tmp1.y = ny+py/q;

        tmp1.z = nz+pz/q;

        tmp1.w = nw+pw/q;

        }

      else

        {

        tmp1.x = px+nx*q;

        tmp1.y = py+ny*q;

        tmp1.z = pz+nz*q;

        tmp1.w = pw+nw*q;

        }

      }

    else

      {

      tmp1.x = 0.0f;

      tmp1.y = 0.0f;

      tmp1.z = 0.0f;  

      tmp1.w = 0.0f;

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private void recomputeCache()

    {  

    if( numPoints==1 )

      {

      tmp1= vc.elementAt(0);

      curr= vv.elementAt(0);

      tmp1.ax = tmp1.ay = tmp1.az = tmp1.aw = 0.0f;

      tmp1.bx = tmp1.by = tmp1.bz = tmp1.bw = 0.0f;

      tmp1.cx = curr.x;

      tmp1.cy = curr.y;

      tmp1.cz = curr.z;

      tmp1.cw = curr.w;

      tmp1.dx = tmp1.dy = tmp1.dz = tmp1.dw = 0.0f;

      }

    else if( numPoints==2 )

      {

      tmp1= vc.elementAt(0);

      tmp2= vc.elementAt(1);

      curr= vv.elementAt(0);

      next= vv.elementAt(1);

      tmp1.ax = tmp1.ay = tmp1.az = tmp1.aw = 0.0f;

      tmp1.bx = tmp1.by = tmp1.bz = tmp1.bw = 0.0f;

      tmp1.cx = next.x - curr.x;

      tmp1.cy = next.y - curr.y;

      tmp1.cz = next.z - curr.z;

      tmp1.cw = next.w - curr.w;

      tmp1.dx = curr.x;

      tmp1.dy = curr.y;

      tmp1.dz = curr.z;

      tmp1.dw = curr.w;

      tmp2.ax = tmp2.ay = tmp2.az = tmp2.aw = 0.0f;

      tmp2.bx = tmp2.by = tmp2.bz = tmp2.bw = 0.0f;

      tmp2.cx = curr.x - next.x;

      tmp2.cy = curr.y - next.y;

      tmp2.cz = curr.z - next.z;

      tmp2.cw = curr.w - next.w;

      tmp2.dx = next.x;

      tmp2.dy = next.y;

      tmp2.dz = next.z;

      tmp2.dw = next.w;

      }

    else

      {

      int i, n;  

      for(i=0; i<numPoints; i++) vec(i);

      for(i=0; i<numPoints; i++)

        {

        n = i<numPoints-1 ? i+1:0;  

        tmp1= vc.elementAt(i);

        tmp2= vc.elementAt(n);

        curr= vv.elementAt(i);

        next= vv.elementAt(n);

        tmp1.vx = curr.x;

        tmp1.vy = curr.y;

        tmp1.vz = curr.z;

        tmp1.vw = curr.w;

        tmp1.ax =  2*curr.x +   tmp1.x - 2*next.x + tmp2.x;

        tmp1.bx = -3*curr.x - 2*tmp1.x + 3*next.x - tmp2.x;

        tmp1.cx = tmp1.x;

        tmp1.dx = curr.x;

        tmp1.ay =  2*curr.y +   tmp1.y - 2*next.y + tmp2.y;

        tmp1.by = -3*curr.y - 2*tmp1.y + 3*next.y - tmp2.y;

        tmp1.cy = tmp1.y;

        tmp1.dy = curr.y;

        tmp1.az =  2*curr.z +   tmp1.z - 2*next.z + tmp2.z;

        tmp1.bz = -3*curr.z - 2*tmp1.z + 3*next.z - tmp2.z;

        tmp1.cz = tmp1.z;

        tmp1.dz = curr.z;

        tmp1.aw =  2*curr.w +   tmp1.w - 2*next.w + tmp2.w;

        tmp1.bw = -3*curr.w - 2*tmp1.w + 3*next.w - tmp2.w;

        tmp1.cw = tmp1.w;

        tmp1.dw = curr.w;

        }

      }

    cacheDirty = false;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// v is the speed vector (i.e. position p(t) differentiated by time)

// a is the acceleration vector (differentiate once more)

//

// Now we construct orthogonal basis with Gram-Schmidt:  

// vec1 = a-delta*v where delta = (v*a)/|v|^2

// vec2 = (0,0,1,0) - coeff1*(vx,vy,vz,vw) - coeff2*(vec1x,vec1y,vec1z,vec1w)                                     where coeff1 = vz/|v|^2, coeff2 = vec1Z/|vec1|^2

// vec3 = (0,0,0,1) - coeff1*(vx,vy,vz,vw) - coeff2*(vec1x,vec1y,vec1z,vec1w) - coeff3*(vec2x,vec2y,vec2z,vec2w)  where coeff1 = vw/|v|^2, coeff2 = vec1W/|vec1|^2, coeff3 = vec2W/|vec2|^2

  private void setUpVectors(float time,VectorCache vc)

    {

    if( vc!=null )

      {

      float vx = (3*vc.ax*time+2*vc.bx)*time+vc.cx;

      float vy = (3*vc.ay*time+2*vc.by)*time+vc.cy;

      float vz = (3*vc.az*time+2*vc.bz)*time+vc.cz;

      float vw = (3*vc.aw*time+2*vc.bw)*time+vc.cw;

      float ax = 6*vc.ax*time+2*vc.bx;

      float ay = 6*vc.ay*time+2*vc.by;

      float az = 6*vc.az*time+2*vc.bz;

      float aw = 6*vc.aw*time+2*vc.bw;

      float v_sq = vx*vx+vy*vy+vz*vz+vw*vw;

      float delta = (vx*ax+vy*ay+vz*az+vw*aw)/v_sq;

      vec1X = ax-delta*vx;

      vec1Y = ay-delta*vy;

      vec1Z = az-delta*vz;

      vec1W = aw-delta*vw;

      float vec1_sq = vec1X*vec1X+vec1Y*vec1Y+vec1Z*vec1Z+vec1W*vec1W;

      // construct vec2 and vec3. Cross product does not work in 4th dimension!

      float coeff21 = vz/v_sq;

      float coeff22 = vec1Z/vec1_sq;

      vec2X = 0.0f - coeff21*vx - coeff22*vec1X;

      vec2Y = 0.0f - coeff21*vy - coeff22*vec1Y;

      vec2Z = 1.0f - coeff21*vz - coeff22*vec1Z;

      vec2W = 0.0f - coeff21*vw - coeff22*vec1W;

      float vec2_sq = vec2X*vec2X+vec2Y*vec2Y+vec2Z*vec2Z+vec2W*vec2W;

      float coeff31 = vw/v_sq;

      float coeff32 = vec1W/vec1_sq;

      float coeff33 = vec2W/vec2_sq;

      vec3X = 0.0f - coeff31*vx - coeff32*vec1X - coeff33*vec2X;

      vec3Y = 0.0f - coeff31*vy - coeff32*vec1Y - coeff33*vec2Y;

      vec3Z = 0.0f - coeff31*vz - coeff32*vec1Z - coeff33*vec2Z;

      vec3W = 1.0f - coeff31*vw - coeff32*vec1W - coeff33*vec2W;

      float vec3_sq = vec3X*vec3X+vec3Y*vec3Y+vec3Z*vec3Z+vec3W*vec3W;

      float len1 = (float)Math.sqrt(v_sq/vec1_sq);   

      float len2 = (float)Math.sqrt(v_sq/vec2_sq);   

      float len3 = (float)Math.sqrt(v_sq/vec3_sq);

      vec1X*=len1;

      vec1Y*=len1;

      vec1Z*=len1;

      vec1W*=len1;

      vec2X*=len2;

      vec2Y*=len2;

      vec2Z*=len2;

      vec2W*=len2;

      vec3X*=len3;

      vec3Y*=len3;

      vec3Z*=len3;

      vec3W*=len3;

      }

    else

      {

      curr = vv.elementAt(0);

      next = vv.elementAt(1); 

      float vx = (next.x-curr.x);

      float vy = (next.y-curr.y);

      float vz = (next.z-curr.z);

      float vw = (next.w-curr.w);

      float b = (float)Math.sqrt(vx*vx+vy*vy+vz*vz);

      if( b>0.0f )

        {

        vec1X = vx*vw/b;

        vec1Y = vy*vw/b;

        vec1Z = vz*vw/b;

        vec1W = -b;

        float v_sq = vx*vx+vy*vy+vz*vz+vw*vw;

        float vec1_sq = vec1X*vec1X+vec1Y*vec1Y+vec1Z*vec1Z+vec1W*vec1W;

        // construct vec2 and vec3. Cross product does not work in 4th dimension!

        float coeff21 = vz/v_sq;

        float coeff22 = vec1Z/vec1_sq;

        vec2X = 0.0f - coeff21*vx - coeff22*vec1X;

        vec2Y = 0.0f - coeff21*vy - coeff22*vec1Y;

        vec2Z = 1.0f - coeff21*vz - coeff22*vec1Z;

        vec2W = 0.0f - coeff21*vw - coeff22*vec1W;

        float vec2_sq = vec2X*vec2X+vec2Y*vec2Y+vec2Z*vec2Z+vec2W*vec2W;

        float coeff31 = vw/v_sq;

        float coeff32 = vec1W/vec1_sq;

        float coeff33 = vec2W/vec2_sq;

        vec3X = 0.0f - coeff31*vx - coeff32*vec1X - coeff33*vec2X;

        vec3Y = 0.0f - coeff31*vy - coeff32*vec1Y - coeff33*vec2Y;

        vec3Z = 0.0f - coeff31*vz - coeff32*vec1Z - coeff33*vec2Z;

        vec3W = 1.0f - coeff31*vw - coeff32*vec1W - coeff33*vec2W;

        float vec3_sq = vec3X*vec3X+vec3Y*vec3Y+vec3Z*vec3Z+vec3W*vec3W;

        float len1 = (float)Math.sqrt(v_sq/vec1_sq);    

        float len2 = (float)Math.sqrt(v_sq/vec2_sq);    

        float len3 = (float)Math.sqrt(v_sq/vec3_sq);

        vec1X*=len1;

        vec1Y*=len1;

        vec1Z*=len1;

        vec1W*=len1;

        vec2X*=len2;

        vec2Y*=len2;

        vec2Z*=len2;

        vec2W*=len2;

        vec3X*=len3;

        vec3Y*=len3;

        vec3Z*=len3;

        vec3W*=len3;

        }

      else

        {

        vec1X = vw;

        vec1Y = 0.0f;

        vec1Z = 0.0f;

        vec1W = 0.0f;

        vec2X = 0.0f;

        vec2Y = vw;

        vec2Z = 0.0f;

        vec2W = 0.0f;

        vec3X = 0.0f;

        vec3Y = 0.0f;

        vec3Z = vw;

        vec3W = 0.0f;

        }

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// PUBLIC API

///////////////////////////////////////////////////////////////////////////////////////////////////

/**

 * Default constructor.

 */

  public Dynamic4D()

    {

    this(0,0.5f);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

/**

 * Default constructor.

 *

 * @param duration number of milliseconds it takes to do a full loop/path from first vector to the

 *                 last and back to the first

 * @param count    number of loops/paths we will do; mCount = 1.5 means we go from the first vector

 *                 to the last, back to first, and to the last again.

 */

  public Dynamic4D(int duration, float count)

    {

    vv = new Vector<>();

    vc = new Vector<>();

    vn = null;

    numPoints = 0;

    cacheDirty = false;

    mMode = MODE_LOOP;

    mDuration = duration;

    mCount = count;

    mDimension = 4;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

/**

 * Returns the location'th Static4D.

 *   

 * @param location the index of the Point we are interested in.

 * @return The Static4D, if 0<=location&lt;getNumPoints(), or null otherwise.

 */  

  public synchronized Static4D getPoint(int location)

    {

    return (location>=0 && location<numPoints) ? vv.elementAt(location) : null;  

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

/**

 * Resets the location'th Point.

 * 

 * @param location the index of the Point we are setting.

 * @param x New value of its first float.

 */

  public synchronized void setPoint(int location, float x, float y, float z, float w)

    {

    if( location>=0 && location<numPoints )

      {

      curr = vv.elementAt(location);

      if( curr!=null )

        {

        curr.set(x,y,z,w);

        cacheDirty=true;

        }

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

/**

 * Adds a new Static4D to the end of our list of Points to interpolate through.

 * <p>   

 * Only a reference to the Point gets added to the List; this means that one can add a Point 

 * here, and later on {@link Static4D#set(float,float,float,float)} it to some new value and

 * the change will be seamlessly reflected in the interpolated path.  

 * <p>

 * A Point can be added multiple times.

 *   

 * @param v The Point to add.

 */    

  public synchronized void add(Static4D v)

    {

    if( v!=null )

      {

      vv.add(v);

      if( vn!=null ) vn.add(new VectorNoise(4));

       switch(numPoints)

         {

         case 0: break;

         case 1: setUpVectors(0.0f,null);

                 break;

         case 2: vc.add(new VectorCache());

                 vc.add(new VectorCache());

                 vc.add(new VectorCache());

                 break;

         default:vc.add(new VectorCache());

         }

       numPoints++;

       cacheDirty = true;

       }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

/**

 * Adds a new Static4D to the location'th place in our List of Points to interpolate through.

 *   

 * @param location Index in our List to add the new Point at.

 * @param v The Static4D to add.

 */  

  public synchronized void add(int location, Static4D v)

    {

    if( v!=null )

      {

      vv.add(location, v);

      if( vn!=null ) vn.add(new VectorNoise(4));

      switch(numPoints)

        {

        case 0: break;

        case 1: setUpVectors(0.0f,null);

                break;

        case 2: vc.add(new VectorCache());

                vc.add(new VectorCache());

                vc.add(new VectorCache());

                break;

        default:vc.add(location,new VectorCache());

        }

      numPoints++;

      cacheDirty = true;

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

/**

 * Removes all occurrences of Point v from the List of Points to interpolate through.  

 * 

 * @param v The Point to remove.

 * @return <code>true</code> if we have removed at least one Point.

 */

  public synchronized boolean remove(Static4D v)

    {

    int n = vv.indexOf(v);

    boolean found = false;

    while( n>=0 ) 

      {

      vv.remove(n);

      if( vn!=null ) vn.remove(0);

      switch(numPoints)

        {

        case 0:

        case 1: 

        case 2: break;

        case 3: vc.removeAllElements();

                setUpVectors(0.0f,null);

                break;

        default:vc.remove(n);

        }

      numPoints--;

      found = true;

      n = vv.indexOf(v);

      }

    if( found ) 

      {

      cacheDirty=true;

      }

    return found;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

/**

 * Removes a location'th Point from the List of Points we interpolate through.

 * 

 * @param location index of the Point we want to remove. 

 * @return <code>true</code> if location is valid, i.e. if 0<=location&lt;getNumPoints().

 */

  public synchronized boolean remove(int location)

    {

    if( location>=0 && location<numPoints ) 

      {

      vv.removeElementAt(location);

      if( vn!=null ) vn.remove(0);

      switch(numPoints)

        {

        case 0:

        case 1: 

        case 2: break;

        case 3: vc.removeAllElements();

                setUpVectors(0.0f,null);

                break;

        default:vc.removeElementAt(location);

        }

      numPoints--;

      cacheDirty = true; 

      return true;

      }

    return false;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

/**

 * Removes all Points.

 */

  public synchronized void removeAll()

    {

    numPoints = 0;

    vv.removeAllElements();

    vc.removeAllElements();

    cacheDirty = false;

    if( vn!=null ) vn.removeAllElements();

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

/**

 * Writes the results of interpolation between the Points at time 'time' to the passed float buffer.

 * <p>

 * Since this is a 4-dimensional Dynamic, the resulting interpolated Static4D gets written

 * to four locations in the buffer: buffer[offset], buffer[offset+1], buffer[offset+2] and buffer[offset+3]. 

 * 

 * @param buffer Float buffer we will write the resulting Static4D to.

 * @param offset Offset in the buffer where to write the result.

 * @param time Time of interpolation. Time=0.0 would return the first Point, Time=0.5 - the last,

 *             time=1.0 - the first again, and time 0.1 would be 1/5 of the way between the first and the last Points.

 */    

  public synchronized void interpolate(float[] buffer, int offset, float time)

    {  

    switch(numPoints)

      {

      case 0: buffer[offset  ] = 0.0f;

              buffer[offset+1] = 0.0f;

              buffer[offset+2] = 0.0f;

              buffer[offset+3] = 0.0f;

              break;

      case 1: curr = vv.elementAt(0);

              buffer[offset  ] = curr.x;

              buffer[offset+1] = curr.y;

              buffer[offset+2] = curr.z;

              buffer[offset+3] = curr.w;

              break;

      case 2: curr = vv.elementAt(0);

              next = vv.elementAt(1);

              if( mMode==MODE_LOOP || mMode==MODE_PATH ) time = (time>0.5f ? 2-2*time : 2*time);

              if( vn!=null )

                {

                time = noise(time,0);

                buffer[offset  ] = (next.x-curr.x)*time + curr.x + (vec1X*mFactor[0] + vec2X*mFactor[1] + vec3X*mFactor[2]);

                buffer[offset+1] = (next.y-curr.y)*time + curr.y + (vec1Y*mFactor[0] + vec2Y*mFactor[1] + vec3Y*mFactor[2]);

                buffer[offset+2] = (next.z-curr.z)*time + curr.z + (vec1Z*mFactor[0] + vec2Z*mFactor[1] + vec3Z*mFactor[2]);

                buffer[offset+3] = (next.w-curr.w)*time + curr.w + (vec1W*mFactor[0] + vec2W*mFactor[1] + vec3W*mFactor[2]);

                }

              else

                {

                buffer[offset  ] = (next.x-curr.x)*time + curr.x;

                buffer[offset+1] = (next.y-curr.y)*time + curr.y;

                buffer[offset+2] = (next.z-curr.z)*time + curr.z;

                buffer[offset+3] = (next.w-curr.w)*time + curr.w;

                }

              break;

      default:float t = time;

              switch(mMode)

                {

                case MODE_LOOP: time = time*numPoints;

                                break;

                case MODE_PATH: time = (time<=0.5f) ? 2*time*(numPoints-1) : 2*(1-time)*(numPoints-1);

                                break;

                case MODE_JUMP: time = time*(numPoints-1);

                                break;

                }

              int vecCurr = (int)time;

              time = time-vecCurr;

              if( vecCurr>=0 && vecCurr<numPoints )

                {

                if( cacheDirty ) recomputeCache();    // recompute cache if we have added or remove vectors since last computation

                else if( mVecCurr!= vecCurr )         // ...or if we have just passed a vector and the vector we are currently flying to has changed

                  {

                  int vecNext;   

                  mVecCurr = vecCurr;

                  switch(mMode)

                    {

                    case MODE_LOOP: vecNext = vecCurr==numPoints-1 ? 0:vecCurr+1; 

                                    break;

                    case MODE_PATH: if( t<0.5f ) vecNext = vecCurr==numPoints-1 ? numPoints-2: vecCurr+1;  

                                    else         vecNext = vecCurr==0 ? 1 : vecCurr-1;  

                                    break;

                    case MODE_JUMP: vecNext = vecCurr==numPoints-1 ? 1:vecCurr+1;

                                    break;

                    default       : vecNext = 0;                

                    }

                  next = vv.elementAt(vecNext);

                  tmp2 = vc.elementAt(vecNext);

                  if( tmp2.vx!=next.x || tmp2.vy!=next.y || tmp2.vz!=next.z || tmp2.vw!=next.w ) recomputeCache();

                  }

                tmp1 = vc.elementAt(vecCurr);

                if( vn!=null )

                  {

                  time = noise(time,vecCurr);

                  setUpVectors(time,tmp1);

                  buffer[offset  ]= ((tmp1.ax*time+tmp1.bx)*time+tmp1.cx)*time+tmp1.dx + (vec1X*mFactor[0] + vec2X*mFactor[1] + vec3X*mFactor[2]);

                  buffer[offset+1]= ((tmp1.ay*time+tmp1.by)*time+tmp1.cy)*time+tmp1.dy + (vec1Y*mFactor[0] + vec2Y*mFactor[1] + vec3Y*mFactor[2]);

                  buffer[offset+2]= ((tmp1.az*time+tmp1.bz)*time+tmp1.cz)*time+tmp1.dz + (vec1Z*mFactor[0] + vec2Z*mFactor[1] + vec3Z*mFactor[2]);

                  buffer[offset+3]= ((tmp1.aw*time+tmp1.bw)*time+tmp1.cw)*time+tmp1.dw + (vec1W*mFactor[0] + vec2W*mFactor[1] + vec3W*mFactor[2]);

                  }

                else

                  {

                  buffer[offset  ]= ((tmp1.ax*time+tmp1.bx)*time+tmp1.cx)*time+tmp1.dx;

                  buffer[offset+1]= ((tmp1.ay*time+tmp1.by)*time+tmp1.cy)*time+tmp1.dy;

                  buffer[offset+2]= ((tmp1.az*time+tmp1.bz)*time+tmp1.cz)*time+tmp1.dz;

                  buffer[offset+3]= ((tmp1.aw*time+tmp1.bw)*time+tmp1.cw)*time+tmp1.dw;

                  }

                break;

                }

      }

    }  

  }

///////////////////////////////////////////////////////////////////////////////////////////////////

//