Distorted Android

  protected float[][] baseV;

  private float[] buffer;

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

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

  // (tangent) is the vector tangent to the path.

  // (cached) 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

  protected class VectorCache

    {

    float[] a;

    float[] b;

    float[] c;

    float[] d;

    float[] tangent;

    float[] cached;

    VectorCache(int dim)

      {

      a = new float[dim];

      b = new float[dim];

      c = new float[dim];

      d = new float[dim];

      tangent = new float[dim];

      cached = new float[dim];

      }

    }

  protected Vector<VectorCache> vc;

  protected VectorCache tmp1, tmp2;

  protected Dynamic()

    {

    }

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

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

    vc = new Vector<>();

    vn = null;

    numPoints = 0;

    cacheDirty = false;

    mMode = MODE_LOOP;

    mDuration = duration;

    mCount = count;

    mDimension = dimension;

    baseV = new float[mDimension][mDimension];

    buffer= new float[mDimension];

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

// 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

  private void checkBase()

    {

    float tmp;

    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", "vectors "+i+" and "+j+" : "+tmp);

        }

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

      {

      tmp = 0.0f;

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

        {

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

        }

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

      }

    }

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

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

  protected void computeOrthonormalBase2(Static1D curr, Static1D next)

    {

    switch(mDimension)

      {

      case 1: baseV[0][0] = (next.x-curr.x);

              break;

      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++)

      {

      baseV[0][i] = (3*vc.a[i]*time+2*vc.b[i])*time+vc.c[i];

      baseV[1][i] =  6*vc.a[i]*time+2*vc.b[i];

      }

    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 non_zeros=0;

    int last_non_zero=-1;

    float value;

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

      {

      value = baseV[0][i];

      if( value != 0.0f )

        {

        non_zeros++;

        last_non_zero=i;

        }

      }

                         // velocity is the 0 vector -> two consecutive points we are interpolating

    if( non_zeros==0 )   // through are identical -> no noise, set the base to 0 vectors.

      {

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

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

          baseV[i+1][j]= 0.0f;

      }

    else

      {

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

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

          {

          if( (i<last_non_zero && j==i) || (i>=last_non_zero && j==i+1) )

            baseV[i+1][j]= baseV[0][last_non_zero];

          else

            baseV[i+1][j]= 0.0f;

          }

      // That's it if velocity vector is already one of the standard orthonormal

      // vectors. Otherwise (i.e. non_zeros>1) velocity is linearly independent

      // to what's in baseV right now and we can use (modified!) Gram-Schmidt.

      //

      // b[0] = b[0]

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

      // b[2] = b[2] - (<b[2],b[0]>/<b[0],b[0]>)*b[0] - (<b[2],b[1]>/<b[1],b[1]>)*b[1]

      // 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]|

      if( non_zeros>1 )

        {

        float tmp;

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

          {

          buffer[i-1]=0.0f;

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

            {

            value = baseV[i-1][k];

            buffer[i-1] += value*value;

            }

          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 /= buffer[j];

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

              {

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

              }

            }

          }

        buffer[mDimension-1]=0.0f;

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

          {

          value = baseV[mDimension-1][k];

          buffer[mDimension-1] += value*value;

          }

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

          {

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

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

            {

            baseV[i][k] *= tmp;

            }

          }

        }

      }

    //printBase("end");

    //checkBase();

    }