#include <math.h>
#define TRUE    1
#define FALSE   0

typedef struct {
        double x;
        double y;
        double z;
        } Vector;

/*
 * Procedural fBm evaluated at "point"; returns value stored in "value".
 *
 * Copyright 1994 F. Kenton Musgrave 
 * 
 * Parameters:
 *    ``H''  is the fractal increment parameter
 *    ``lacunarity''  is the gap between successive frequencies
 *    ``octaves''  is the number of frequencies in the fBm
 */
double
fBm( Vector point, double H, double lacunarity, double octaves )
{

      double            value, frequency, remainder, Noise3();
      int               i;
      static int        first = TRUE;
      static double     *exponent_array;

      /* precompute and store spectral weights */
      if ( first ) {
            /* seize required memory for exponent_array */
            exponent_array = 
                        (double *)malloc( (octaves+1) * sizeof(double) );
            frequency = 1.0;
            for (i=0; i<=octaves; i++) {
                  /* compute weight for each frequency */
                  exponent_array[i] = pow( frequency, -H );
                  frequency *= lacunarity;
            }
            first = FALSE;
      }

      value = 0.0;            /* initialize vars to proper values */
      frequency = 1.0;

      /* inner loop of spectral construction */
      for (i=0; i<octaves; i++) {
            value += Noise3( point ) * exponent_array[i];
            point.x *= lacunarity;
            point.y *= lacunarity;
            point.z *= lacunarity;
      } /* for */

      remainder = octaves - (int)octaves;
      if ( remainder )      /* add in ``octaves''  remainder */
            /* ``i''  and spatial freq. are preset in loop above */
            value += remainder * Noise3( point ) * exponent_array[i];

      return( value );

} /* fBm() */


/*
 * Procedural multifractal evaluated at "point"; 
 * returns value stored in "value".
 *
 * Copyright 1994 F. Kenton Musgrave 
 * 
 * Parameters:
 *    ``H''  determines the highest fractal dimension
 *    ``lacunarity''  is gap between successive frequencies
 *    ``octaves''  is the number of frequencies in the fBm
 *    ``offset''  is the zero offset, which determines multifractality
 */
double
multifractal( Vector point, double H, double lacunarity, 
              double octaves, double offset )
{
      double            value, frequency, remainder, Noise3();
      int               i;
      static int        first = TRUE;
      static double     *exponent_array;

      /* precompute and store spectral weights */
      if ( first ) {
            /* seize required memory for exponent_array */
            exponent_array = 
                        (double *)malloc( (octaves+1) * sizeof(double) );
            frequency = 1.0;
            for (i=0; i<=octaves; i++) {
                  /* compute weight for each frequency */
                  exponent_array[i] = pow( frequency, -H );
                  frequency *= lacunarity;
            }
            first = FALSE;
      }

      value = 1.0;            /* initialize vars to proper values */
      frequency = 1.0;

      /* inner loop of multifractal construction */
      for (i=0; i<octaves; i++) {
            value *= offset * frequency * Noise3( point );
            point.x *= lacunarity;
            point.y *= lacunarity;
            point.z *= lacunarity;
      } /* for */

      remainder = octaves - (int)octaves;
      if ( remainder )      /* add in ``octaves''  remainder */
            /* ``i''  and spatial freq. are preset in loop above */
            value += remainder * Noise3( point ) * exponent_array[i];

      return value;

} /* multifractal() */


/* "Variable Lacunarity Noise"  -or- VLNoise3()
 * A distorted variety of Perlin noise.
 *
 * Copyright 1994 F. Kenton Musgrave 
 */
double
VLNoise3( Vector point, double distortion )
{
        Vector offset, VecNoise3(), AddVectors();
        double Noise3();

        offset.x = point.x +0.5;        /* misregister domain */
        offset.y = point.y +0.5;
        offset.z = point.z +0.5;

        offset = VecNoise3( offset );   /* get a random vector */

        offset.x *= distortion;         /* scale the randomization */
        offset.y *= distortion;
        offset.z *= distortion;

        /* ``point'' is the domain; distort domain by adding ``offset'' */
        point = AddVectors( point, offset );

        return Noise3( point );         /* distorted-domain noise */

} /* VLNoise3() */


/*
 * Heterogeneous procedural terrain function: stats by altitude method.
 * Evaluated at "point"; returns value stored in "value".
 *
 * Copyright 1994 F. Kenton Musgrave 
 * 
 * Parameters:
 *       ``H''  determines the fractal dimension of the roughest areas
 *       ``lacunarity''  is the gap between successive frequencies
 *       ``octaves''  is the number of frequencies in the fBm
 *       ``offset''  raises the terrain from `sea level'
 */
double
Hetero_Terrain( Vector point,
            double H, double lacunarity, double octaves, double offset )
{
      double          value, increment, frequency, remainder, Noise3();
      int             i;
      static int      first = TRUE;
      static double   *exponent_array;

      /* precompute and store spectral weights, for efficiency */
      if ( first ) {
            /* seize required memory for exponent_array */
            exponent_array = 
                        (double *)malloc( (octaves+1) * sizeof(double) );
            frequency = 1.0;
            for (i=0; i<=octaves; i++) {
                  /* compute weight for each frequency */
                  exponent_array[i] = pow( frequency, -H );
                  frequency *= lacunarity;
            }
            first = FALSE;
      }

      /* first unscaled octave of function; later octaves are scaled */
      value = offset + Noise3( point );
      point.x *= lacunarity;
      point.y *= lacunarity;
      point.z *= lacunarity;

      /* spectral construction inner loop, where the fractal is built */
      for (i=1; i<octaves; i++) {
            /* obtain displaced noise value */
            increment = Noise3( point ) + offset;
            /* scale amplitude appropriately for this frequency */
            increment *= exponent_array[i];
            /* scale increment by current `altitude' of function */
            increment *= value;
            /* add increment to ``value''  */
            value += increment;
            /* raise spatial frequency */
            point.x *= lacunarity;
            point.y *= lacunarity;
            point.z *= lacunarity;
      } /* for */

      /* take care of remainder in ``octaves''  */
      remainder = octaves - (int)octaves;
      if ( remainder ) {
            /* ``i''  and spatial freq. are preset in loop above */
            /* note that the main loop code is made shorter here */
            /* you may want to that loop more like this */
            increment = (Noise3( point ) + offset) * exponent_array[i];
            value += remainder * increment * value;
      }

      return( value );

} /* Hetero_Terrain() */


/* Hybrid additive/multiplicative multifractal terrain model.
 *
 * Copyright 1994 F. Kenton Musgrave 
 *
 * Some good parameter values to start with:
 *
 *      H:           0.25
 *      offset:      0.7
 */
double 
HybridMultifractal( Vector point, double H, double lacunarity, 
                    double octaves, double offset )
{
      double          frequency, result, signal, weight, remainder; 
      double          Noise3();
      int             i;
      static int      first = TRUE;
      static double   *exponent_array;

      /* precompute and store spectral weights */
      if ( first ) {
            /* seize required memory for exponent_array */
            exponent_array = 
                        (double *)malloc( (octaves+1) * sizeof(double) );
            frequency = 1.0;
            for (i=0; i<=octaves; i++) {
                  /* compute weight for each frequency */
                  exponent_array[i] = pow( frequency, -H);
                  frequency *= lacunarity;
            }
            first = FALSE;
      }

      /* get first octave of function */
      result = ( Noise3( point ) + offset ) * exponent_array[0];
      weight = result;
      /* increase frequency */
      point.x *= lacunarity;
      point.y *= lacunarity;
      point.z *= lacunarity;

      /* spectral construction inner loop, where the fractal is built */
      for (i=1; i<octaves; i++) {
            /* prevent divergence */
            if ( weight > 1.0 )  weight = 1.0;

            /* get next higher frequency */
            signal = ( Noise3( point ) + offset ) * exponent_array[i];
            /* add it in, weighted by previous freq's local value */
            result += weight * signal;
            /* update the (monotonically decreasing) weighting value */
            /* (this is why H must specify a high fractal dimension) */
            weight *= signal;

            /* increase frequency */
            point.x *= lacunarity;
            point.y *= lacunarity;
            point.z *= lacunarity;
      } /* for */

      /* take care of remainder in ``octaves''  */
      remainder = octaves - (int)octaves;
      if ( remainder )
            /* ``i''  and spatial freq. are preset in loop above */
            result += remainder * Noise3( point ) * exponent_array[i];

      return( result );

} /* HybridMultifractal() */


/* Ridged multifractal terrain model.
 *
 * Copyright 1994 F. Kenton Musgrave 
 *
 * Some good parameter values to start with:
 *
 *      H:           1.0
 *      offset:      1.0
 *      gain:        2.0
 */
double 
RidgedMultifractal( Vector point, double H, double lacunarity,
                    double octaves, double offset, double gain )
{
      double           result, frequency, signal, weight, Noise3();
      int              i;
      static int       first = TRUE;
      static double    *exponent_array;

      /* precompute and store spectral weights */
      if ( first ) {
            /* seize required memory for exponent_array */
            exponent_array =
                        (double *)malloc( (octaves+1) * sizeof(double) );
            frequency = 1.0;
            for (i=0; i<=octaves; i++) {
                  /* compute weight for each frequency */
                  exponent_array[i] = pow( frequency, -H );
                  frequency *= lacunarity;
            }
            first = FALSE;
      }

      /* get first octave */
      signal = Noise3( point );
      /* get absolute value of signal (this creates the ridges) */
      if ( signal < 0.0 ) signal = -signal;
      /* invert and translate (note that "offset" should be ~= 1.0) */
      signal = offset - signal;
      /* square the signal, to increase "sharpness" of ridges */
      signal *= signal;
      /* assign initial values */
      result = signal;
      weight = 1.0;

      for( i=1; i<octaves; i++ ) {
            /* increase the frequency */
            point.x *= lacunarity;
            point.y *= lacunarity;
            point.z *= lacunarity;

            /* weight successive contributions by previous signal */
            weight = signal * gain;
            if ( weight > 1.0 ) weight = 1.0;
            if ( weight < 0.0 ) weight = 0.0;
            signal = Noise3( point );
            if ( signal < 0.0 ) signal = -signal;
            signal = offset - signal;
            signal *= signal;
            /* weight the contribution */
            signal *= weight;
            result += signal * exponent_array[i];
      }

      return( result );

} /* RidgedMultifractal() */