Distorted Android

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

// Copyright 2016 Leszek Koltunski                                                               //

//                                                                                               //

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

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

//                                                                                               //

// 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                             //

import java.util.Random;

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

*/

// The way Interpolation between more than 2 Points is done:

// 

// be flying at Point P[i]

//

// We arbitrarily decide that V[i] should be equal to (|curr|*prev + |prev|*curr) / min(|prev|,|curr|)

// where prev = P[i]-P[i-1] and curr = P[i+1]-P[i]

// Given that the flight route (X(t), Y(t), Z(t)) from P(i) to P(i+1)  (0<=t<=1) has to satisfy

// X(1) = P[i+1](x), Y(1)=P[i+1](y), Z(1)=P[i+1](z), X'(1) = V[i+1](x), Y'(1) = V[i+1](y), Z'(1) = V[i+1](z)

// we have the solution:  X(t) = at^3 + bt^2 + ct + d where

// b = -3*P[i](x) - 2*V[i](x) + 3*P[i+1](x) - V[i+1](x)

// c =                V[i](x)

// d =    P[i](x)

// and similarly Y(t) and Z(t).

   * Keep the speed of interpolation always changing. Time to cover one segment (distance between

   * two consecutive points) always the same. Smoothly interpolate the speed between two segments.

   */

  public static final int SPEED_MODE_SMOOTH            = 0;

  /**

   * Make each segment have constant speed. Time to cover each segment is still the same, thus the

   * speed will jump when passing through a point and then keep constant.

   */

  public static final int SPEED_MODE_SEGMENT_CONSTANT  = 1;

  /**

   * Have the speed be always, globally the same across all segments. Time to cover one segment will

   * thus generally no longer be the same.

   */

  public static final int MODE_LOOP = 0; 

  /**

  public static final int MODE_PATH = 1; 

  /**

  public static final int MODE_JUMP = 2; 

   * The default mode of access. When in this mode, we are able to call interpolate() with points in time

   * in any random order. This means one single Dynamic can be used in many effects simultaneously.

   * On the other hand, when in this mode, it is not possible to smoothly interpolate when mDuration suddenly

   * changes.

   */

   * Set the mode to ACCESS_SEQUENTIAL if you need to change mDuration and you would rather have the Dynamic

   * keep on smoothly interpolating.

   * On the other hand, in this mode, a Dynamic can only be accessed in sequential manner, which means one

  protected int mMode;          // LOOP, PATH or JUMP

  protected int mTmpVec, mTmpSeg;

  protected class VectorNoise

    {

    float[][] n;

      }

      {

      for(int i=1; i<NUM_NOISE; i++) n[0][i] = n[0][i-1]+mRnd.nextFloat();

        for(int j=1; j<mDimension; j++) n[j][i] = mRnd.nextFloat()-0.5f;

      }

    }

  protected Vector<VectorNoise> vn;

  protected float[] mFactor;

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

  // (velocity) is the velocity vector.

  // still valid and if not - rebuild the Cache

  protected class VectorCache

    {

    float[] a;

    float[] b;

    float[] c;

    float[] d;

      b = new float[mDimension];

      c = new float[mDimension];

      d = new float[mDimension];

      velocity   = new float[mDimension];

      cached     = new float[mDimension];

      path_ratio = new float[NUM_RATIO];

    }

  protected Vector<VectorCache> vc;

                                           // remember this many 'points' inside the Cache for each segment.

  protected static final float[] mTmpRatio = new float[NUM_RATIO];

  private float[] old;

                                          // where we randomize noise factors to make the way between the two vectors not so smooth.

// hide this from Javadoc

  protected Dynamic(int duration, float count, int dimension)

    {

    vn         = null;

    numPoints  = 0;

    mDuration  = duration;

    mCount     = count;

    buf        = new float[mDimension];

    old        = new float[mDimension];

  void initDynamic()

    {

    mStartTime = -1;

    mCorrectedTime = 0;

    }

  public static void onPause()

    {

    mPausedTime = System.currentTimeMillis();

    }

  protected void computeSegmentAndTime(float time)

    {

    switch(mMode)

      {

      case MODE_LOOP: mTmpTime= time*numPoints;

                      mTmpSeg = (int)mTmpTime;

                      mTmpVec = mTmpSeg;

                      break;

      case MODE_PATH: mTmpSeg = (int)(2*time*(numPoints-1));

                      if( time<=0.5f )  // this has to be <= (otherwise when effect ends at t=0.5, then time=1.0

                        {               // and end position is slightly not equal to the end point => might not get autodeleted!

                        mTmpTime = 2*time*(numPoints-1);

                        mTmpVec = mTmpSeg;

                        }

                      else

                        {

                        mTmpTime = 2*(1-time)*(numPoints-1);

                        mTmpVec  = 2*numPoints-3-mTmpSeg;

                        }

                      break;

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

                      mTmpSeg = (int)mTmpTime;

                      mTmpVec = mTmpSeg;

                      break;

      default       : mTmpVec = 0;

                      mTmpSeg = 0;

      }

    }

  private float valueAtPoint(float t, VectorCache cache)

    {

    float tmp,sum = 0.0f;

    for(int d=0; d<mDimension; d++)

      {

      tmp = (3*cache.a[d]*t + 2*cache.b[d])*t + cache.c[d];

      sum += tmp*tmp;

      }

    return (float)Math.sqrt(sum);

    }

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

  protected float smoothSpeed(float time, VectorCache cache)

    {

    float fndex = time*NUM_RATIO;

    int index = (int)fndex;

    float prev = index==0 ? 0.0f : cache.path_ratio[index-1];

    float next = cache.path_ratio[index];

    return prev + (next-prev)*(fndex-index);

    }

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

// First, compute the approx length of the segment from time=0 to time=(i+1)/NUM_TIME and store this

// in cache.path_ratio[i]. Then the last path_ratio is the length from 0 to 1, i.e. the total length

// of the segment.

// We do this by computing the integral from 0 to 1 of sqrt( (dx/dt)^2 + (dy/dt)^2 ) (i.e. the length

// of the segment) using the approx 'trapezoids' integration method.

//

// Then, for every i, divide path_ratio[i] by the total length to get the percentage of total path

// length covered at time i. At this time, path_ratio[3] = 0.45 means 'at time 3/NUM_RATIO, we cover

// 0.45 = 45% of the total length of the segment.

//

// Finally, invert this function (for quicker lookups in smoothSpeed) so that after this step,

// path_ratio[3] = 0.45 means 'at 45% of the time, we cover 3/NUM_RATIO distance'.

  protected void smoothOutSegment(VectorCache cache)

    {

    float vPrev, sum = 0.0f;

    float vNext = valueAtPoint(0.0f,cache);

    for(int i=0; i<NUM_RATIO; i++)

      {

      vPrev = vNext;

      vNext = valueAtPoint( (float)(i+1)/NUM_RATIO,cache);

      sum += (vPrev+vNext);

      cache.path_ratio[i] = sum;

      }

    float total = cache.path_ratio[NUM_RATIO-1];

    for(int i=0; i<NUM_RATIO; i++) cache.path_ratio[i] /= total;

    int writeIndex = 0;

    float prev=0.0f, next, ratio= 1.0f/NUM_RATIO;

    for(int readIndex=0; readIndex<NUM_RATIO; readIndex++)

      {

      next = cache.path_ratio[readIndex];

      while( prev<ratio && ratio<=next )

        {

        float a = (next-ratio)/(next-prev);

        mTmpRatio[writeIndex] = (readIndex+1-a)/NUM_RATIO;

        writeIndex++;

        ratio = (writeIndex+1.0f)/NUM_RATIO;

        }

      prev = next;

      }

    System.arraycopy(mTmpRatio, 0, cache.path_ratio, 0, NUM_RATIO);

    }

  protected float noise(float time,int vecNum)

    {

    float lower, upper, len;

    float d = time*(NUM_NOISE+1);

    int index = (int)d;

    if( index>=NUM_NOISE+1 ) index=NUM_NOISE;

    VectorNoise tmpN = vn.elementAt(vecNum);

    float t = d-index;

    t = t*t*(3-2*t);

    switch(index)

      {

                      return time + mNoise[0]*(d*tmpN.n[0][0]-time);

      case NUM_NOISE: for(int i=0;i<mDimension-1;i++) mFactor[i] = mNoise[i+1]*tmpN.n[i+1][NUM_NOISE-1]*(1-t);

      default       : float ya,yb;

                      for(int i=0;i<mDimension-1;i++)

                        {

                        yb = tmpN.n[i+1][index  ];

                        ya = tmpN.n[i+1][index-1];

                      len = ((float)index)/(NUM_NOISE+1);

                      return (upper-lower)*(d-index) + lower;

      }

    }

// debugging only

  private void printBase(String str)

    {

    String s;

    float t;

    for(int i=0; i<mDimension; i++)

      {

      s = "";

      for(int j=0; j<mDimension; j++)

        {

        t = ((int)(1000*baseV[i][j]))/(1000.0f);

        s+=(" "+t);

        }

      android.util.Log.e("dynamic", str+" base "+i+" : " + s);

      }

    }

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

// debugging only

    {

    float[] len= new float[mDimension];

    boolean error=false;

    for(int i=0; i<mDimension; i++)

      {

      len[i] = 0.0f;

      for(int k=0; k<mDimension; k++)

        {

        len[i] += baseV[i][k]*baseV[i][k];

        }

      if( len[i] == 0.0f || len[0]/len[i] < 0.95f || len[0]/len[i]>1.05f )

        {

        android.util.Log.e("dynamic", "length of vector "+i+" : "+Math.sqrt(len[i]));

        error = true;

        }

      }

    for(int i=0; i<mDimension; i++)

      for(int j=i+1; j<mDimension; j++)

        {

        tmp = 0.0f;

        for(int k=0; k<mDimension; k++)

          {

          tmp += baseV[i][k]*baseV[j][k];

          }

          {

          android.util.Log.e("dynamic", "cos angle between vectors "+i+" and "+j+" : "+cosA);

          error = true;

          }

  int getNext(int curr, float time)

    {

    switch(mMode)

      {

      case MODE_LOOP: return curr==numPoints-1 ? 0:curr+1;

      case MODE_PATH: return time<0.5f ? (curr+1) : (curr==0 ? 1 : curr-1);

      case MODE_JUMP: return curr==numPoints-1 ? 1:curr+1;

      default       : return 0;

      }

    }

  private void checkAngle(int index)

    {

    float cosA = 0.0f;

    for(int k=0;k<mDimension; k++)

      cosA += baseV[index][k]*old[k];

    if( cosA<0.0f )

      {

      for(int j=0; j<mDimension; j++)

        baseV[index][j] = -baseV[index][j];

      }

    }

// helper function in case we are interpolating through exactly 2 points

    switch(mDimension)

      {

              Static1D next1 = (Static1D)next;

              baseV[0][0] = (next1.x-curr1.x);

      case 2: Static2D curr2 = (Static2D)curr;

              Static2D next2 = (Static2D)next;

              baseV[0][0] = (next2.x-curr2.x);

              baseV[0][1] = (next2.y-curr2.y);

              break;

      case 3: Static3D curr3 = (Static3D)curr;

              Static3D next3 = (Static3D)next;

              baseV[0][0] = (next3.x-curr3.x);

              baseV[0][1] = (next3.y-curr3.y);

              baseV[0][2] = (next3.z-curr3.z);

              break;

      case 4: Static4D curr4 = (Static4D)curr;

              Static4D next4 = (Static4D)next;

              baseV[0][0] = (next4.x-curr4.x);

              baseV[0][1] = (next4.y-curr4.y);

              baseV[0][2] = (next4.z-curr4.z);

              baseV[0][3] = (next4.w-curr4.w);

              break;

      case 5: Static5D curr5 = (Static5D)curr;

              Static5D next5 = (Static5D)next;

              baseV[0][0] = (next5.x-curr5.x);

              baseV[0][1] = (next5.y-curr5.y);

              baseV[0][2] = (next5.z-curr5.z);

              baseV[0][3] = (next5.w-curr5.w);

              baseV[0][4] = (next5.v-curr5.v);

              break;

      default: throw new RuntimeException("Unsupported dimension");

      }

    if( baseV[0][0] == 0.0f )

      {

      baseV[1][0] = 1.0f;

      baseV[1][1] = 0.0f;

      }

    else

      {

      baseV[1][0] = 0.0f;

      baseV[1][1] = 1.0f;

      }

    for(int i=2; i<mDimension; i++)

      {

      baseV[1][i] = 0.0f;

      }

    computeOrthonormalBase();

    }

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

// helper function in case we are interpolating through more than 2 points

  protected void computeOrthonormalBaseMore(float time,VectorCache vc)

    {

    for(int i=0; i<mDimension; i++)

      {

      old[i]      = baseV[1][i];

      baseV[1][i] =  6*vc.a[i]*time+2*vc.b[i];                 // second derivative,i.e. acceleration vector

    computeOrthonormalBase();

    }

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

// When this function gets called, baseV[0] and baseV[1] should have been filled with two mDimension-al

// vectors. This function then fills the rest of the baseV array with a mDimension-al Orthonormal base.

// (mDimension-2 vectors, pairwise orthogonal to each other and to the original 2). The function always

// leaves base[0] alone but generally speaking must adjust base[1] to make it orthogonal to base[0]!

// The whole baseV is then used to compute Noise.

//

// When computing noise of a point travelling along a N-dimensional path, there are three cases:

// a) we may be interpolating through 1 point, i.e. standing in place - nothing to do in this case

// b) we may be interpolating through 2 points, i.e. travelling along a straight line between them -

//    then pass the velocity vector in baseV[0] and anything linearly independent in base[1].

//    The output will then be discontinuous in dimensions>2 (sad corollary from the Hairy Ball Theorem)

//    but we don't care - we are travelling along a straight line, so velocity (aka baseV[0]!) does

//    not change.

// c) we may be interpolating through more than 2 points. Then interpolation formulas ensure the path

//    will never be a straight line, even locally -> we can pass in baseV[0] and baseV[1] the velocity

//    and the acceleration (first and second derivatives of the path) which are then guaranteed to be

//    linearly independent. Then we can ensure this is continuous in dimensions <=4. This leaves

//    dimension 5 (ATM WAVE is 5-dimensional) discontinuous -> WAVE will suffer from chaotic noise.

//

// Bear in mind here the 'normal' in 'orthonormal' means 'length equal to the length of the original

// velocity vector' (rather than the standard 1)

  protected void computeOrthonormalBase()

    {

    int last_non_zero=-1;

      if( baseV[0][i] != 0.0f )

      for(int i=0; i<mDimension-1; i++)                                   //  consecutive points we are interpolating

        for(int j=0; j<mDimension; j++)                                   //  through are identical -> no noise,

          baseV[i+1][j]= 0.0f;                                            //  set the base to 0 vectors.

      }                                                                   ///

      {

        {                                                                 //  (aka b[i]), the i-th orthonormal vector.

        buf[i-1]=0.0f;                                                    //

                                                                          //  We can use (modified!) Gram-Schmidt.

        for(int k=0; k<mDimension; k++)                                   //

          {                                                               //

          if( i>=2 )                                                      //  b[0] = b[0]

            {                                                             //  b[1] = b[1] - (<b[1],b[0]>/<b[0],b[0]>)*b[0]

            old[k] = baseV[i][k];                                         //  b[2] = b[2] - (<b[2],b[0]>/<b[0],b[0]>)*b[0] - (<b[2],b[1]>/<b[1],b[1]>)*b[1]

            baseV[i][k]= (k==i-(last_non_zero>=i?1:0)) ? 1.0f : 0.0f;     //  b[3] = b[3] - (<b[3],b[0]>/<b[0],b[0]>)*b[0] - (<b[3],b[1]>/<b[1],b[1]>)*b[1] - (<b[3],b[2]>/<b[2],b[2]>)*b[2]

            }                                                             //  (...)

                                                                          //  then b[i] = b[i] / |b[i]|  ( Here really b[i] = b[i] / (|b[0]|/|b[i]|)

          tmp = baseV[i-1][k];                                            //

          buf[i-1] += tmp*tmp;                                            //

          }                                                               //

                                                                          //

        for(int j=0; j<i; j++)                                            //

          {                                                               //

          tmp = 0.0f;                                                     //

          for(int k=0;k<mDimension; k++) tmp += baseV[i][k]*baseV[j][k];  //

          tmp /= buf[j];                                                  //

          for(int k=0;k<mDimension; k++) baseV[i][k] -= tmp*baseV[j][k];  //

          }                                                               //

                                                                          //

        checkAngle(i);                                                    //

        }                                                                 /// end compute baseV[i][*]

      buf[mDimension-1]=0.0f;                                             /// Normalize

      for(int k=0; k<mDimension; k++)                                     //

        {                                                                 //

        tmp = baseV[mDimension-1][k];                                     //

        buf[mDimension-1] += tmp*tmp;                                     //

        }                                                                 //

                                                                          //

      for(int i=1; i<mDimension; i++)                                     //

        {                                                                 //

        tmp = (float)Math.sqrt(buf[0]/buf[i]);                            //

        for(int k=0;k<mDimension; k++) baseV[i][k] *= tmp;                //

        }                                                                 /// End Normalize

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

// PUBLIC API

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

 * Sets the mode of the interpolation to Loop, Path or Jump.

 * <ul>

 * <li>Loop is when we go from the first point all the way to the last, and the back to the first through 

 * the shortest way.

 * <li>Path is when we come back from the last point back to the first the same way we got there.