tgp.cpp

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/*
 * This file is part of OpenTTD.
 * OpenTTD 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, version 2.
 * OpenTTD 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 OpenTTD. If not, see <http://www.gnu.org/licenses/>.
 */
 
#include "stdafx.h"
#include "clear_map.h"
#include "void_map.h"
#include "genworld.h"
#include "core/random_func.hpp"
#include "landscape_type.h"
 
#include "safeguards.h"
 
/*
 *
 * Quickie guide to Perlin Noise
 * Perlin noise is a predictable pseudo random number sequence. By generating
 * it in 2 dimensions, it becomes a useful random map that, for a given seed
 * and starting X & Y, is entirely predictable. On the face of it, that may not
 * be useful. However, it means that if you want to replay a map in a different
 * terrain, or just vary the sea level, you just re-run the generator with the
 * same seed. The seed is an int32_t, and is randomised on each run of New Game.
 * The Scenario Generator does not randomise the value, so that you can
 * experiment with one terrain until you are happy, or click "Random" for a new
 * random seed.
 *
 * Perlin Noise is a series of "octaves" of random noise added together. By
 * reducing the amplitude of the noise with each octave, the first octave of
 * noise defines the main terrain sweep, the next the ripples on that, and the
 * next the ripples on that. I use 6 octaves, with the amplitude controlled by
 * a power ratio, usually known as a persistence or p value. This I vary by the
 * smoothness selection, as can be seen in the table below. The closer to 1,
 * the more of that octave is added. Each octave is however raised to the power
 * of its position in the list, so the last entry in the "smooth" row, 0.35, is
 * raised to the power of 6, so can only add 0.001838...  of the amplitude to
 * the running total.
 *
 * In other words; the first p value sets the general shape of the terrain, the
 * second sets the major variations to that, ... until finally the smallest
 * bumps are added.
 *
 * Usefully, this routine is totally scalable; so when 32bpp comes along, the
 * terrain can be as bumpy as you like! It is also infinitely expandable; a
 * single random seed terrain continues in X & Y as far as you care to
 * calculate. In theory, we could use just one seed value, but randomly select
 * where in the Perlin XY space we use for the terrain. Personally I prefer
 * using a simple (0, 0) to (X, Y), with a varying seed.
 *
 *
 * Other things i have had to do: mountainous wasn't mountainous enough, and
 * since we only have 0..15 heights available, I add a second generated map
 * (with a modified seed), onto the original. This generally raises the
 * terrain, which then needs scaling back down. Overall effect is a general
 * uplift.
 *
 * However, the values on the top of mountains are then almost guaranteed to go
 * too high, so large flat plateaus appeared at height 15. To counter this, I
 * scale all heights above 12 to proportion up to 15. It still makes the
 * mountains have flattish tops, rather than craggy peaks, but at least they
 * aren't smooth as glass.
 *
 *
 * For a full discussion of Perlin Noise, please visit:
 * http://freespace.virgin.net/hugo.elias/models/m_perlin.htm
 *
 *
 * Evolution II
 *
 * The algorithm as described in the above link suggests to compute each tile height
 * as composition of several noise waves. Some of them are computed directly by
 * noise(x, y) function, some are calculated using linear approximation. Our
 * first implementation of perlin_noise_2D() used 4 noise(x, y) calls plus
 * 3 linear interpolations. It was called 6 times for each tile. This was a bit
 * CPU expensive.
 *
 * The following implementation uses optimized algorithm that should produce
 * the same quality result with much less computations, but more memory accesses.
 * The overall speedup should be 300% to 800% depending on CPU and memory speed.
 *
 * I will try to explain it on the example below:
 *
 * Have a map of 4 x 4 tiles, our simplified noise generator produces only two
 * values -1 and +1, use 3 octaves with wave length 1, 2 and 4, with amplitudes
 * 3, 2, 1. Original algorithm produces:
 *
 * h00 = lerp(lerp(-3, 3, 0/4), lerp(3, -3, 0/4), 0/4) + lerp(lerp(-2,  2, 0/2), lerp( 2, -2, 0/2), 0/2) + -1 = lerp(-3.0,  3.0, 0/4) + lerp(-2,  2, 0/2) + -1 = -3.0  + -2 + -1 = -6.0
 * h01 = lerp(lerp(-3, 3, 1/4), lerp(3, -3, 1/4), 0/4) + lerp(lerp(-2,  2, 1/2), lerp( 2, -2, 1/2), 0/2) +  1 = lerp(-1.5,  1.5, 0/4) + lerp( 0,  0, 0/2) +  1 = -1.5  +  0 +  1 = -0.5
 * h02 = lerp(lerp(-3, 3, 2/4), lerp(3, -3, 2/4), 0/4) + lerp(lerp( 2, -2, 0/2), lerp(-2,  2, 0/2), 0/2) + -1 = lerp(   0,    0, 0/4) + lerp( 2, -2, 0/2) + -1 =    0  +  2 + -1 =  1.0
 * h03 = lerp(lerp(-3, 3, 3/4), lerp(3, -3, 3/4), 0/4) + lerp(lerp( 2, -2, 1/2), lerp(-2,  2, 1/2), 0/2) +  1 = lerp( 1.5, -1.5, 0/4) + lerp( 0,  0, 0/2) +  1 =  1.5  +  0 +  1 =  2.5
 *
 * h10 = lerp(lerp(-3, 3, 0/4), lerp(3, -3, 0/4), 1/4) + lerp(lerp(-2,  2, 0/2), lerp( 2, -2, 0/2), 1/2) +  1 = lerp(-3.0,  3.0, 1/4) + lerp(-2,  2, 1/2) +  1 = -1.5  +  0 +  1 = -0.5
 * h11 = lerp(lerp(-3, 3, 1/4), lerp(3, -3, 1/4), 1/4) + lerp(lerp(-2,  2, 1/2), lerp( 2, -2, 1/2), 1/2) + -1 = lerp(-1.5,  1.5, 1/4) + lerp( 0,  0, 1/2) + -1 = -0.75 +  0 + -1 = -1.75
 * h12 = lerp(lerp(-3, 3, 2/4), lerp(3, -3, 2/4), 1/4) + lerp(lerp( 2, -2, 0/2), lerp(-2,  2, 0/2), 1/2) +  1 = lerp(   0,    0, 1/4) + lerp( 2, -2, 1/2) +  1 =    0  +  0 +  1 =  1.0
 * h13 = lerp(lerp(-3, 3, 3/4), lerp(3, -3, 3/4), 1/4) + lerp(lerp( 2, -2, 1/2), lerp(-2,  2, 1/2), 1/2) + -1 = lerp( 1.5, -1.5, 1/4) + lerp( 0,  0, 1/2) + -1 =  0.75 +  0 + -1 = -0.25
 *
 *
 * Optimization 1:
 *
 * 1) we need to allocate a bit more tiles: (size_x + 1) * (size_y + 1) = (5 * 5):
 *
 * 2) setup corner values using amplitude 3
 * {    -3.0        X          X          X          3.0   }
 * {     X          X          X          X          X     }
 * {     X          X          X          X          X     }
 * {     X          X          X          X          X     }
 * {     3.0        X          X          X         -3.0   }
 *
 * 3a) interpolate values in the middle
 * {    -3.0        X          0.0        X          3.0   }
 * {     X          X          X          X          X     }
 * {     0.0        X          0.0        X          0.0   }
 * {     X          X          X          X          X     }
 * {     3.0        X          0.0        X         -3.0   }
 *
 * 3b) add patches with amplitude 2 to them
 * {    -5.0        X          2.0        X          1.0   }
 * {     X          X          X          X          X     }
 * {     2.0        X         -2.0        X          2.0   }
 * {     X          X          X          X          X     }
 * {     1.0        X          2.0        X         -5.0   }
 *
 * 4a) interpolate values in the middle
 * {    -5.0       -1.5        2.0        1.5        1.0   }
 * {    -1.5       -0.75       0.0        0.75       1.5   }
 * {     2.0        0.0       -2.0        0.0        2.0   }
 * {     1.5        0.75       0.0       -0.75      -1.5   }
 * {     1.0        1.5        2.0       -1.5       -5.0   }
 *
 * 4b) add patches with amplitude 1 to them
 * {    -6.0       -0.5        1.0        2.5        0.0   }
 * {    -0.5       -1.75       1.0       -0.25       2.5   }
 * {     1.0        1.0       -3.0        1.0        1.0   }
 * {     2.5       -0.25       1.0       -1.75      -0.5   }
 * {     0.0        2.5        1.0       -0.5       -6.0   }
 *
 *
 *
 * Optimization 2:
 *
 * As you can see above, each noise function was called just once. Therefore
 * we don't need to use noise function that calculates the noise from x, y and
 * some prime. The same quality result we can obtain using standard Random()
 * function instead.
 *
 */
 
using Height = int16_t;
static const int height_decimal_bits = 4;
 
using Amplitude = int;
static const int amplitude_decimal_bits = 10;
 
struct HeightMap
{
  std::vector<Height> h; //< array of heights
  /* Even though the sizes are always positive, there are many cases where
   * X and Y need to be signed integers due to subtractions. */
  int      dim_x;      //< height map size_x Map::SizeX() + 1
  int      size_x;     //< Map::SizeX()
  int      size_y;     //< Map::SizeY()
 
  inline Height &height(uint x, uint y)
  {
    return h[x + y * dim_x];
  }
};
 
static HeightMap _height_map = { {}, 0, 0, 0 };
 
#define I2H(i) ((i) << height_decimal_bits)
#define H2I(i) ((i) >> height_decimal_bits)
 
#define A2I(i) ((i) >> amplitude_decimal_bits)
 
#define A2H(a) ((a) >> (amplitude_decimal_bits - height_decimal_bits))
 
static const int MAX_TGP_FREQUENCIES = 10;
 
static const Amplitude _water_percent[4] = {70, 170, 270, 420};
 
static Height TGPGetMaxHeight()
{
  if (_settings_game.difficulty.terrain_type == CUSTOM_TERRAIN_TYPE_NUMBER_DIFFICULTY) {
    /* TGP never reaches this height; this means that if a user inputs "2",
     * it would create a flat map without the "+ 1". But that would
     * overflow on "255". So we reduce it by 1 to get back in range. */
    return I2H(_settings_game.game_creation.custom_terrain_type + 1) - 1;
  }
 
  static const int max_height[5][MAX_MAP_SIZE_BITS - MIN_MAP_SIZE_BITS + 1] = {
    /* 64  128  256  512 1024 2048 4096 */
    {   3,   3,   3,   3,   4,   5,   7 }, 
    {   5,   7,   8,   9,  14,  19,  31 }, 
    {   8,   9,  10,  15,  23,  37,  61 }, 
    {  10,  11,  17,  19,  49,  63,  73 }, 
    {  12,  19,  25,  31,  67,  75,  87 }, 
  };
 
  int map_size_bucket = std::min(Map::LogX(), Map::LogY()) - MIN_MAP_SIZE_BITS;
  int max_height_from_table = max_height[_settings_game.difficulty.terrain_type][map_size_bucket];
 
  /* If there is a manual map height limit, clamp to it. */
  if (_settings_game.construction.map_height_limit != 0) {
    max_height_from_table = std::min<uint>(max_height_from_table, _settings_game.construction.map_height_limit);
  }
 
  return I2H(max_height_from_table);
}
 
uint GetEstimationTGPMapHeight()
{
  return H2I(TGPGetMaxHeight());
}
 
static Amplitude GetAmplitude(int frequency)
{
  /* Base noise amplitudes (multiplied by 1024) and indexed by "smoothness setting" and log2(frequency). */
  static const Amplitude amplitudes[][7] = {
    /* lowest frequency ...... highest (every corner) */
    {16000,  5600,  1968,   688,   240,    16,    16}, 
    {24000, 12800,  6400,  2700,  1024,   128,    16}, 
    {32000, 19200, 12800,  8000,  3200,   256,    64}, 
    {48000, 24000, 19200, 16000,  8000,   512,   320}, 
  };
  /*
   * Extrapolation factors for ranges before the table.
   * The extrapolation is needed to account for the higher map heights. They need larger
   * areas with a particular gradient so that we are able to create maps without too
   * many steep slopes up to the wanted height level. It's definitely not perfect since
   * it will bring larger rectangles with similar slopes which makes the rectangular
   * behaviour of TGP more noticeable. However, these height differentiations cannot
   * happen over much smaller areas; we basically double the "range" to give a similar
   * slope for every doubling of map height.
   */
  static const double extrapolation_factors[] = { 3.3, 2.8, 2.3, 1.8 };
 
  int smoothness = _settings_game.game_creation.tgen_smoothness;
 
  /* Get the table index, and return that value if possible. */
  int index = frequency - MAX_TGP_FREQUENCIES + static_cast<int>(std::size(amplitudes[smoothness]));
  Amplitude amplitude = amplitudes[smoothness][std::max(0, index)];
  if (index >= 0) return amplitude;
 
  /* We need to extrapolate the amplitude. */
  double extrapolation_factor = extrapolation_factors[smoothness];
  int height_range = I2H(16);
  do {
    amplitude = (Amplitude)(extrapolation_factor * (double)amplitude);
    height_range <<= 1;
    index++;
  } while (index < 0);
 
  return Clamp((TGPGetMaxHeight() - height_range) / height_range, 0, 1) * amplitude;
}
 
static inline bool IsValidXY(int x, int y)
{
  return x >= 0 && x < _height_map.size_x && y >= 0 && y < _height_map.size_y;
}
 
 
static inline bool AllocHeightMap()
{
  assert(_height_map.h.empty());
 
  _height_map.size_x = Map::SizeX();
  _height_map.size_y = Map::SizeY();
 
  /* Allocate memory block for height map row pointers */
  size_t total_size = static_cast<size_t>(_height_map.size_x + 1) * (_height_map.size_y + 1);
  _height_map.dim_x = _height_map.size_x + 1;
  _height_map.h.resize(total_size);
 
  return true;
}
 
static inline void FreeHeightMap()
{
  _height_map.h.clear();
}
 
static inline Height RandomHeight(Amplitude rMax)
{
  /* Spread height into range -rMax..+rMax */
  return A2H(RandomRange(2 * rMax + 1) - rMax);
}
 
static void HeightMapGenerate()
{
  /* Trying to apply noise to uninitialized height map */
  assert(!_height_map.h.empty());
 
  int start = std::max(MAX_TGP_FREQUENCIES - (int)std::min(Map::LogX(), Map::LogY()), 0);
  bool first = true;
 
  for (int frequency = start; frequency < MAX_TGP_FREQUENCIES; frequency++) {
    const Amplitude amplitude = GetAmplitude(frequency);
 
    /* Ignore zero amplitudes; it means our map isn't height enough for this
     * amplitude, so ignore it and continue with the next set of amplitude. */
    if (amplitude == 0) continue;
 
    const int step = 1 << (MAX_TGP_FREQUENCIES - frequency - 1);
 
    if (first) {
      /* This is first round, we need to establish base heights with step = size_min */
      for (int y = 0; y <= _height_map.size_y; y += step) {
        for (int x = 0; x <= _height_map.size_x; x += step) {
          Height height = (amplitude > 0) ? RandomHeight(amplitude) : 0;
          _height_map.height(x, y) = height;
        }
      }
      first = false;
      continue;
    }
 
    /* It is regular iteration round.
     * Interpolate height values at odd x, even y tiles */
    for (int y = 0; y <= _height_map.size_y; y += 2 * step) {
      for (int x = 0; x <= _height_map.size_x - 2 * step; x += 2 * step) {
        Height h00 = _height_map.height(x + 0 * step, y);
        Height h02 = _height_map.height(x + 2 * step, y);
        Height h01 = (h00 + h02) / 2;
        _height_map.height(x + 1 * step, y) = h01;
      }
    }
 
    /* Interpolate height values at odd y tiles */
    for (int y = 0; y <= _height_map.size_y - 2 * step; y += 2 * step) {
      for (int x = 0; x <= _height_map.size_x; x += step) {
        Height h00 = _height_map.height(x, y + 0 * step);
        Height h20 = _height_map.height(x, y + 2 * step);
        Height h10 = (h00 + h20) / 2;
        _height_map.height(x, y + 1 * step) = h10;
      }
    }
 
    /* Add noise for next higher frequency (smaller steps) */
    for (int y = 0; y <= _height_map.size_y; y += step) {
      for (int x = 0; x <= _height_map.size_x; x += step) {
        _height_map.height(x, y) += RandomHeight(amplitude);
      }
    }
  }
}
 
static void HeightMapGetMinMaxAvg(Height *min_ptr, Height *max_ptr, Height *avg_ptr)
{
  Height h_min, h_max, h_avg;
  int64_t h_accu = 0;
  h_min = h_max = _height_map.height(0, 0);
 
  /* Get h_min, h_max and accumulate heights into h_accu */
  for (const Height &h : _height_map.h) {
    if (h < h_min) h_min = h;
    if (h > h_max) h_max = h;
    h_accu += h;
  }
 
  /* Get average height */
  h_avg = (Height)(h_accu / (_height_map.size_x * _height_map.size_y));
 
  /* Return required results */
  if (min_ptr != nullptr) *min_ptr = h_min;
  if (max_ptr != nullptr) *max_ptr = h_max;
  if (avg_ptr != nullptr) *avg_ptr = h_avg;
}
 
static int *HeightMapMakeHistogram(Height h_min, [[maybe_unused]] Height h_max, int *hist_buf)
{
  int *hist = hist_buf - h_min;
 
  /* Count the heights and fill the histogram */
  for (const Height &h : _height_map.h) {
    assert(h >= h_min);
    assert(h <= h_max);
    hist[h]++;
  }
  return hist;
}
 
static void HeightMapSineTransform(Height h_min, Height h_max)
{
  for (Height &h : _height_map.h) {
    double fheight;
 
    if (h < h_min) continue;
 
    /* Transform height into 0..1 space */
    fheight = (double)(h - h_min) / (double)(h_max - h_min);
    /* Apply sine transform depending on landscape type */
    switch (_settings_game.game_creation.landscape) {
      case LT_TOYLAND:
      case LT_TEMPERATE:
        /* Move and scale 0..1 into -1..+1 */
        fheight = 2 * fheight - 1;
        /* Sine transform */
        fheight = sin(fheight * M_PI_2);
        /* Transform it back from -1..1 into 0..1 space */
        fheight = 0.5 * (fheight + 1);
        break;
 
      case LT_ARCTIC:
        {
          /* Arctic terrain needs special height distribution.
           * Redistribute heights to have more tiles at highest (75%..100%) range */
          double sine_upper_limit = 0.75;
          double linear_compression = 2;
          if (fheight >= sine_upper_limit) {
            /* Over the limit we do linear compression up */
            fheight = 1.0 - (1.0 - fheight) / linear_compression;
          } else {
            double m = 1.0 - (1.0 - sine_upper_limit) / linear_compression;
            /* Get 0..sine_upper_limit into -1..1 */
            fheight = 2.0 * fheight / sine_upper_limit - 1.0;
            /* Sine wave transform */
            fheight = sin(fheight * M_PI_2);
            /* Get -1..1 back to 0..(1 - (1 - sine_upper_limit) / linear_compression) == 0.0..m */
            fheight = 0.5 * (fheight + 1.0) * m;
          }
        }
        break;
 
      case LT_TROPIC:
        {
          /* Desert terrain needs special height distribution.
           * Half of tiles should be at lowest (0..25%) heights */
          double sine_lower_limit = 0.5;
          double linear_compression = 2;
          if (fheight <= sine_lower_limit) {
            /* Under the limit we do linear compression down */
            fheight = fheight / linear_compression;
          } else {
            double m = sine_lower_limit / linear_compression;
            /* Get sine_lower_limit..1 into -1..1 */
            fheight = 2.0 * ((fheight - sine_lower_limit) / (1.0 - sine_lower_limit)) - 1.0;
            /* Sine wave transform */
            fheight = sin(fheight * M_PI_2);
            /* Get -1..1 back to (sine_lower_limit / linear_compression)..1.0 */
            fheight = 0.5 * ((1.0 - m) * fheight + (1.0 + m));
          }
        }
        break;
 
      default:
        NOT_REACHED();
        break;
    }
    /* Transform it back into h_min..h_max space */
    h = (Height)(fheight * (h_max - h_min) + h_min);
    if (h < 0) h = I2H(0);
    if (h >= h_max) h = h_max - 1;
  }
}
 
static void HeightMapCurves(uint level)
{
  Height mh = TGPGetMaxHeight() - I2H(1); // height levels above sea level only
 
  struct ControlPoint {
    Height x; 
    Height y; 
  };
  /* Scaled curve maps; value is in height_ts. */
#define F(fraction) ((Height)(fraction * mh))
  const ControlPoint curve_map_1[] = { { F(0.0), F(0.0) },                       { F(0.8), F(0.13) },                       { F(1.0), F(0.4)  } };
  const ControlPoint curve_map_2[] = { { F(0.0), F(0.0) }, { F(0.53), F(0.13) }, { F(0.8), F(0.27) },                       { F(1.0), F(0.6)  } };
  const ControlPoint curve_map_3[] = { { F(0.0), F(0.0) }, { F(0.53), F(0.27) }, { F(0.8), F(0.57) },                       { F(1.0), F(0.8)  } };
  const ControlPoint curve_map_4[] = { { F(0.0), F(0.0) }, { F(0.4),  F(0.3)  }, { F(0.7), F(0.8)  }, { F(0.92), F(0.99) }, { F(1.0), F(0.99) } };
#undef F
 
  const std::span<const ControlPoint> curve_maps[] = { curve_map_1, curve_map_2, curve_map_3, curve_map_4 };
 
  std::array<Height, std::size(curve_maps)> ht{};
 
  /* Set up a grid to choose curve maps based on location; attempt to get a somewhat square grid */
  float factor = sqrt((float)_height_map.size_x / (float)_height_map.size_y);
  uint sx = Clamp((int)(((1 << level) * factor) + 0.5), 1, 128);
  uint sy = Clamp((int)(((1 << level) / factor) + 0.5), 1, 128);
  std::vector<uint8_t> c(static_cast<size_t>(sx) * sy);
 
  for (uint i = 0; i < sx * sy; i++) {
    c[i] = RandomRange(static_cast<uint32_t>(std::size(curve_maps)));
  }
 
  /* Apply curves */
  for (int x = 0; x < _height_map.size_x; x++) {
 
    /* Get our X grid positions and bi-linear ratio */
    float fx = (float)(sx * x) / _height_map.size_x + 1.0f;
    uint x1 = (uint)fx;
    uint x2 = x1;
    float xr = 2.0f * (fx - x1) - 1.0f;
    xr = sin(xr * M_PI_2);
    xr = sin(xr * M_PI_2);
    xr = 0.5f * (xr + 1.0f);
    float xri = 1.0f - xr;
 
    if (x1 > 0) {
      x1--;
      if (x2 >= sx) x2--;
    }
 
    for (int y = 0; y < _height_map.size_y; y++) {
 
      /* Get our Y grid position and bi-linear ratio */
      float fy = (float)(sy * y) / _height_map.size_y + 1.0f;
      uint y1 = (uint)fy;
      uint y2 = y1;
      float yr = 2.0f * (fy - y1) - 1.0f;
      yr = sin(yr * M_PI_2);
      yr = sin(yr * M_PI_2);
      yr = 0.5f * (yr + 1.0f);
      float yri = 1.0f - yr;
 
      if (y1 > 0) {
        y1--;
        if (y2 >= sy) y2--;
      }
 
      uint corner_a = c[x1 + sx * y1];
      uint corner_b = c[x1 + sx * y2];
      uint corner_c = c[x2 + sx * y1];
      uint corner_d = c[x2 + sx * y2];
 
      /* Bitmask of which curve maps are chosen, so that we do not bother
       * calculating a curve which won't be used. */
      uint corner_bits = 0;
      corner_bits |= 1 << corner_a;
      corner_bits |= 1 << corner_b;
      corner_bits |= 1 << corner_c;
      corner_bits |= 1 << corner_d;
 
      Height *h = &_height_map.height(x, y);
 
      /* Do not touch sea level */
      if (*h < I2H(1)) continue;
 
      /* Only scale above sea level */
      *h -= I2H(1);
 
      /* Apply all curve maps that are used on this tile. */
      for (size_t t = 0; t < std::size(curve_maps); t++) {
        if (!HasBit(corner_bits, static_cast<uint8_t>(t))) continue;
 
        [[maybe_unused]] bool found = false;
        auto &cm = curve_maps[t];
        for (size_t i = 0; i < cm.size() - 1; i++) {
          const ControlPoint &p1 = cm[i];
          const ControlPoint &p2 = cm[i + 1];
 
          if (*h >= p1.x && *h < p2.x) {
            ht[t] = p1.y + (*h - p1.x) * (p2.y - p1.y) / (p2.x - p1.x);
#ifdef WITH_ASSERT
            found = true;
#endif
            break;
          }
        }
        assert(found);
      }
 
      /* Apply interpolation of curve map results. */
      *h = (Height)((ht[corner_a] * yri + ht[corner_b] * yr) * xri + (ht[corner_c] * yri + ht[corner_d] * yr) * xr);
 
      /* Readd sea level */
      *h += I2H(1);
    }
  }
}
 
static void HeightMapAdjustWaterLevel(Amplitude water_percent, Height h_max_new)
{
  Height h_min, h_max, h_avg, h_water_level;
  int64_t water_tiles, desired_water_tiles;
  int *hist;
 
  HeightMapGetMinMaxAvg(&h_min, &h_max, &h_avg);
 
  /* Allocate histogram buffer and clear its cells */
  std::vector<int> hist_buf(h_max - h_min + 1);
  /* Fill histogram */
  hist = HeightMapMakeHistogram(h_min, h_max, hist_buf.data());
 
  /* How many water tiles do we want? */
  desired_water_tiles = A2I(((int64_t)water_percent) * (int64_t)(_height_map.size_x * _height_map.size_y));
 
  /* Raise water_level and accumulate values from histogram until we reach required number of water tiles */
  for (h_water_level = h_min, water_tiles = 0; h_water_level < h_max; h_water_level++) {
    water_tiles += hist[h_water_level];
    if (water_tiles >= desired_water_tiles) break;
  }
 
  /* We now have the proper water level value.
   * Transform the height map into new (normalized) height map:
   *   values from range: h_min..h_water_level will become negative so it will be clamped to 0
   *   values from range: h_water_level..h_max are transformed into 0..h_max_new
   *   where h_max_new is depending on terrain type and map size.
   */
  for (Height &h : _height_map.h) {
    /* Transform height from range h_water_level..h_max into 0..h_max_new range */
    h = (Height)(((int)h_max_new) * (h - h_water_level) / (h_max - h_water_level)) + I2H(1);
    /* Make sure all values are in the proper range (0..h_max_new) */
    if (h < 0) h = I2H(0);
    if (h >= h_max_new) h = h_max_new - 1;
  }
}
 
static double perlin_coast_noise_2D(const double x, const double y, const double p, const int prime);
 
static void HeightMapCoastLines(uint8_t water_borders)
{
  int smallest_size = std::min(_settings_game.game_creation.map_x, _settings_game.game_creation.map_y);
  const int margin = 4;
  int y, x;
  double max_x;
  double max_y;
 
  /* Lower to sea level */
  for (y = 0; y <= _height_map.size_y; y++) {
    if (HasBit(water_borders, BORDER_NE)) {
      /* Top right */
      max_x = abs((perlin_coast_noise_2D(_height_map.size_y - y, y, 0.9, 53) + 0.25) * 5 + (perlin_coast_noise_2D(y, y, 0.35, 179) + 1) * 12);
      max_x = std::max((smallest_size * smallest_size / 64) + max_x, (smallest_size * smallest_size / 64) + margin - max_x);
      if (smallest_size < 8 && max_x > 5) max_x /= 1.5;
      for (x = 0; x < max_x; x++) {
        _height_map.height(x, y) = 0;
      }
    }
 
    if (HasBit(water_borders, BORDER_SW)) {
      /* Bottom left */
      max_x = abs((perlin_coast_noise_2D(_height_map.size_y - y, y, 0.85, 101) + 0.3) * 6 + (perlin_coast_noise_2D(y, y, 0.45,  67) + 0.75) * 8);
      max_x = std::max((smallest_size * smallest_size / 64) + max_x, (smallest_size * smallest_size / 64) + margin - max_x);
      if (smallest_size < 8 && max_x > 5) max_x /= 1.5;
      for (x = _height_map.size_x; x > (_height_map.size_x - 1 - max_x); x--) {
        _height_map.height(x, y) = 0;
      }
    }
  }
 
  /* Lower to sea level */
  for (x = 0; x <= _height_map.size_x; x++) {
    if (HasBit(water_borders, BORDER_NW)) {
      /* Top left */
      max_y = abs((perlin_coast_noise_2D(x, _height_map.size_y / 2, 0.9, 167) + 0.4) * 5 + (perlin_coast_noise_2D(x, _height_map.size_y / 3, 0.4, 211) + 0.7) * 9);
      max_y = std::max((smallest_size * smallest_size / 64) + max_y, (smallest_size * smallest_size / 64) + margin - max_y);
      if (smallest_size < 8 && max_y > 5) max_y /= 1.5;
      for (y = 0; y < max_y; y++) {
        _height_map.height(x, y) = 0;
      }
    }
 
    if (HasBit(water_borders, BORDER_SE)) {
      /* Bottom right */
      max_y = abs((perlin_coast_noise_2D(x, _height_map.size_y / 3, 0.85, 71) + 0.25) * 6 + (perlin_coast_noise_2D(x, _height_map.size_y / 3, 0.35, 193) + 0.75) * 12);
      max_y = std::max((smallest_size * smallest_size / 64) + max_y, (smallest_size * smallest_size / 64) + margin - max_y);
      if (smallest_size < 8 && max_y > 5) max_y /= 1.5;
      for (y = _height_map.size_y; y > (_height_map.size_y - 1 - max_y); y--) {
        _height_map.height(x, y) = 0;
      }
    }
  }
}
 
static void HeightMapSmoothCoastInDirection(int org_x, int org_y, int dir_x, int dir_y)
{
  const int max_coast_dist_from_edge = 35;
  const int max_coast_Smooth_depth = 35;
 
  int x, y;
  int ed; // coast distance from edge
  int depth;
 
  Height h_prev = I2H(1);
  Height h;
 
  assert(IsValidXY(org_x, org_y));
 
  /* Search for the coast (first non-water tile) */
  for (x = org_x, y = org_y, ed = 0; IsValidXY(x, y) && ed < max_coast_dist_from_edge; x += dir_x, y += dir_y, ed++) {
    /* Coast found? */
    if (_height_map.height(x, y) >= I2H(1)) break;
 
    /* Coast found in the neighborhood? */
    if (IsValidXY(x + dir_y, y + dir_x) && _height_map.height(x + dir_y, y + dir_x) > 0) break;
 
    /* Coast found in the neighborhood on the other side */
    if (IsValidXY(x - dir_y, y - dir_x) && _height_map.height(x - dir_y, y - dir_x) > 0) break;
  }
 
  /* Coast found or max_coast_dist_from_edge has been reached.
   * Soften the coast slope */
  for (depth = 0; IsValidXY(x, y) && depth <= max_coast_Smooth_depth; depth++, x += dir_x, y += dir_y) {
    h = _height_map.height(x, y);
    h = static_cast<Height>(std::min<uint>(h, h_prev + (4 + depth))); // coast softening formula
    _height_map.height(x, y) = h;
    h_prev = h;
  }
}
 
static void HeightMapSmoothCoasts(uint8_t water_borders)
{
  int x, y;
  /* First Smooth NW and SE coasts (y close to 0 and y close to size_y) */
  for (x = 0; x < _height_map.size_x; x++) {
    if (HasBit(water_borders, BORDER_NW)) HeightMapSmoothCoastInDirection(x, 0, 0, 1);
    if (HasBit(water_borders, BORDER_SE)) HeightMapSmoothCoastInDirection(x, _height_map.size_y - 1, 0, -1);
  }
  /* First Smooth NE and SW coasts (x close to 0 and x close to size_x) */
  for (y = 0; y < _height_map.size_y; y++) {
    if (HasBit(water_borders, BORDER_NE)) HeightMapSmoothCoastInDirection(0, y, 1, 0);
    if (HasBit(water_borders, BORDER_SW)) HeightMapSmoothCoastInDirection(_height_map.size_x - 1, y, -1, 0);
  }
}
 
static void HeightMapSmoothSlopes(Height dh_max)
{
  for (int y = 0; y <= (int)_height_map.size_y; y++) {
    for (int x = 0; x <= (int)_height_map.size_x; x++) {
      Height h_max = std::min(_height_map.height(x > 0 ? x - 1 : x, y), _height_map.height(x, y > 0 ? y - 1 : y)) + dh_max;
      if (_height_map.height(x, y) > h_max) _height_map.height(x, y) = h_max;
    }
  }
  for (int y = _height_map.size_y; y >= 0; y--) {
    for (int x = _height_map.size_x; x >= 0; x--) {
      Height h_max = std::min(_height_map.height(x < _height_map.size_x ? x + 1 : x, y), _height_map.height(x, y < _height_map.size_y ? y + 1 : y)) + dh_max;
      if (_height_map.height(x, y) > h_max) _height_map.height(x, y) = h_max;
    }
  }
}
 
static void HeightMapNormalize()
{
  int sea_level_setting = _settings_game.difficulty.quantity_sea_lakes;
  const Amplitude water_percent = sea_level_setting != (int)CUSTOM_SEA_LEVEL_NUMBER_DIFFICULTY ? _water_percent[sea_level_setting] : _settings_game.game_creation.custom_sea_level * 1024 / 100;
  const Height h_max_new = TGPGetMaxHeight();
  const Height roughness = 7 + 3 * _settings_game.game_creation.tgen_smoothness;
 
  HeightMapAdjustWaterLevel(water_percent, h_max_new);
 
  uint8_t water_borders = _settings_game.construction.freeform_edges ? _settings_game.game_creation.water_borders : 0xF;
  if (water_borders == BORDERS_RANDOM) water_borders = GB(Random(), 0, 4);
 
  HeightMapCoastLines(water_borders);
  HeightMapSmoothSlopes(roughness);
 
  HeightMapSmoothCoasts(water_borders);
  HeightMapSmoothSlopes(roughness);
 
  HeightMapSineTransform(I2H(1), h_max_new);
 
  if (_settings_game.game_creation.variety > 0) {
    HeightMapCurves(_settings_game.game_creation.variety);
  }
 
  HeightMapSmoothSlopes(I2H(1));
}
 
static double int_noise(const long x, const long y, const int prime)
{
  long n = x + y * prime + _settings_game.game_creation.generation_seed;
 
  n = (n << 13) ^ n;
 
  /* Pseudo-random number generator, using several large primes */
  return 1.0 - (double)((n * (n * n * 15731 + 789221) + 1376312589) & 0x7fffffff) / 1073741824.0;
}
 
 
static inline double linear_interpolate(const double a, const double b, const double x)
{
  return a + x * (b - a);
}
 
 
static double interpolated_noise(const double x, const double y, const int prime)
{
  const int integer_X = (int)x;
  const int integer_Y = (int)y;
 
  const double fractional_X = x - (double)integer_X;
  const double fractional_Y = y - (double)integer_Y;
 
  const double v1 = int_noise(integer_X,     integer_Y,     prime);
  const double v2 = int_noise(integer_X + 1, integer_Y,     prime);
  const double v3 = int_noise(integer_X,     integer_Y + 1, prime);
  const double v4 = int_noise(integer_X + 1, integer_Y + 1, prime);
 
  const double i1 = linear_interpolate(v1, v2, fractional_X);
  const double i2 = linear_interpolate(v3, v4, fractional_X);
 
  return linear_interpolate(i1, i2, fractional_Y);
}
 
 
static double perlin_coast_noise_2D(const double x, const double y, const double p, const int prime)
{
  double total = 0.0;
 
  for (int i = 0; i < 6; i++) {
    const double frequency = (double)(1 << i);
    const double amplitude = pow(p, (double)i);
 
    total += interpolated_noise((x * frequency) / 64.0, (y * frequency) / 64.0, prime) * amplitude;
  }
 
  return total;
}
 
 
static void TgenSetTileHeight(TileIndex tile, int height)
{
  SetTileHeight(tile, height);
 
  /* Only clear the tiles within the map area. */
  if (IsInnerTile(tile)) {
    MakeClear(tile, CLEAR_GRASS, 3);
  }
}
 
void GenerateTerrainPerlin()
{
  if (!AllocHeightMap()) return;
  GenerateWorldSetAbortCallback(FreeHeightMap);
 
  HeightMapGenerate();
 
  IncreaseGeneratingWorldProgress(GWP_LANDSCAPE);
 
  HeightMapNormalize();
 
  IncreaseGeneratingWorldProgress(GWP_LANDSCAPE);
 
  /* First make sure the tiles at the north border are void tiles if needed. */
  if (_settings_game.construction.freeform_edges) {
    for (uint x = 0; x < Map::SizeX(); x++) MakeVoid(TileXY(x, 0));
    for (uint y = 0; y < Map::SizeY(); y++) MakeVoid(TileXY(0, y));
  }
 
  int max_height = H2I(TGPGetMaxHeight());
 
  /* Transfer height map into OTTD map */
  for (int y = 0; y < _height_map.size_y; y++) {
    for (int x = 0; x < _height_map.size_x; x++) {
      TgenSetTileHeight(TileXY(x, y), Clamp(H2I(_height_map.height(x, y)), 0, max_height));
    }
  }
 
  IncreaseGeneratingWorldProgress(GWP_LANDSCAPE);
 
  FreeHeightMap();
  GenerateWorldSetAbortCallback(nullptr);
}