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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 <https://www.gnu.org/licenses/old-licenses/gpl-2.0>.
*/
/**
* @file tgp.cpp OTTD Perlin Noise Landscape Generator, aka TerraGenesis Perlin.
*
* 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 4x4 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.
*
*/
#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"
/** Fixed point type for heights */
using Height = int16_t;
static const int HEIGHT_DECIMAL_BITS = 4;
/** Fixed point array for amplitudes */
using Amplitude = int;
static const int AMPLITUDE_DECIMAL_BITS = 10;
/** Height map - allocated array of heights (Map::SizeX() + 1) * (Map::SizeY() + 1) */
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()
/**
* Height map accessor
* @param x X position
* @param y Y position
* @return height as fixed point number
*/
inline Height &height(uint x, uint y)
{
return h[x + y * dim_x];
}
};
/** Global height map instance */
static HeightMap _height_map = { {}, 0, 0, 0 };
/**
* Convert tile height to fixed point Height.
* @param i The tile height.
* @return The converted fixed point height.
*/
static Height I2H(int i)
{
return i << HEIGHT_DECIMAL_BITS;
}
/**
* Convert fixed point Height to tile height.
* @param i The fixed point Height.
* @return The tile height.
*/
static int H2I(Height i)
{
return i >> HEIGHT_DECIMAL_BITS;
}
/**
* Convert Amplitude to fixed point Height.
* @param i The amplitude.
* @return The converted fixed point height.
*/
static Height A2H(Amplitude i)
{
return i >> (AMPLITUDE_DECIMAL_BITS - HEIGHT_DECIMAL_BITS);
}
/** Maximum number of TGP noise frequencies. */
static const int MAX_TGP_FREQUENCIES = 10;
static constexpr int WATER_PERCENT_FACTOR = 1024;
/** Desired water percentage (100% == 1024) - indexed by _settings_game.difficulty.quantity_sea_lakes */
static const int64_t _water_percent[4] = {70, 170, 270, 420};
/**
* Gets the maximum allowed height while generating a map based on
* mapsize, terraintype, and the maximum height level.
* @return The maximum height for the map generation.
* @note Values should never be lower than 3 since the minimum snowline height is 2.
*/
static Height TGPGetMaxHeight()
{
if (_settings_game.difficulty.terrain_type == GenworldMaxHeight::Custom) {
/* 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;
}
/**
* Desired maximum height - indexed by:
* - _settings_game.difficulty.terrain_type
* - min(Map::LogX(), Map::LogY()) - MIN_MAP_SIZE_BITS
*
* It is indexed by map size as well as terrain type since the map size limits the height of
* a usable mountain. For example, on a 64x64 map a 24 high single peak mountain (as if you
* raised land 24 times in the center of the map) will leave only a ring of about 10 tiles
* around the mountain to build on. On a 4096x4096 map, it won't cover any major part of the map.
*/
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 }, ///< Very flat
{ 5, 7, 8, 9, 14, 19, 31 }, ///< Flat
{ 8, 9, 10, 15, 23, 37, 61 }, ///< Hilly
{ 10, 11, 17, 19, 49, 63, 73 }, ///< Mountainous
{ 12, 19, 25, 31, 67, 75, 87 }, ///< Alpinist
};
int map_size_bucket = std::min(Map::LogX(), Map::LogY()) - MIN_MAP_SIZE_BITS;
int max_height_from_table = max_height[to_underlying(_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);
}
/**
* Get an overestimation of the highest peak TGP wants to generate.
* @return The estimated map tile height.
*/
uint GetEstimationTGPMapHeight()
{
return H2I(TGPGetMaxHeight());
}
/**
* Get the amplitude associated with the currently selected
* smoothness and maximum height level.
* @param frequency The frequency to get the amplitudes for
* @return The amplitudes to apply to the map.
*/
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}, ///< Very smooth
{24000, 12800, 6400, 2700, 1024, 128, 16}, ///< Smooth
{32000, 19200, 12800, 8000, 3200, 256, 64}, ///< Rough
{48000, 24000, 19200, 16000, 8000, 512, 320}, ///< Very rough
};
/*
* 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;
}
/**
* Check if a X/Y set are within the map.
* @param x coordinate x
* @param y coordinate y
* @return true if within the map
*/
static inline bool IsValidXY(int x, int y)
{
return x >= 0 && x < _height_map.size_x && y >= 0 && y < _height_map.size_y;
}
/**
* Allocate array of (Map::SizeX() + 1) * (Map::SizeY() + 1) heights and init the _height_map structure members
*/
static inline void 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);
}
/** Free height map */
static inline void FreeHeightMap()
{
_height_map.h.clear();
}
/**
* Generates new random height in given amplitude (generated numbers will range from - amplitude to + amplitude)
* @param r_max Limit of result
* @return generated height
*/
static inline Height RandomHeight(Amplitude r_max)
{
/* Spread height into range -r_max..+r_max */
return A2H(RandomRange(2 * r_max + 1) - r_max);
}
/**
* Base Perlin noise generator - fills height map with raw Perlin noise.
*
* This runs several iterations with increasing precision; the last iteration looks at areas
* of 1 by 1 tiles, the second to last at 2 by 2 tiles and the initial 2**MAX_TGP_FREQUENCIES
* by 2**MAX_TGP_FREQUENCIES tiles.
*/
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);
}
}
}
}
/**
* Create histogram and return pointer to its base point - to the count of zero heights.
* @param h_min The minimum height for the histogram.
* @param h_max The maximum height of the map.
* @param hist_buf The buffer of the histogram.
* @return Pointer to the base of the histogram.
*/
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;
}
/**
* Adjust the landscape to create lowlands on average (tropic landscape).
* @param fheight The height to adjust.
* @return The adjusted height.
*/
static double SineTransformLowlands(double fheight)
{
double height = fheight;
/* Half of tiles should be at lowest (0..25%) heights */
double sine_lower_limit = 0.5;
double linear_compression = 2;
if (height <= sine_lower_limit) {
/* Under the limit we do linear compression down */
height = height / linear_compression;
} else {
double m = sine_lower_limit / linear_compression;
/* Get sine_lower_limit..1 into -1..1 */
height = 2.0 * ((height - sine_lower_limit) / (1.0 - sine_lower_limit)) - 1.0;
/* Sine wave transform */
height = sin(height * M_PI_2);
/* Get -1..1 back to (sine_lower_limit / linear_compression)..1.0 */
height = 0.5 * ((1.0 - m) * height + (1.0 + m));
}
return height;
}
/**
* Adjust the landscape to create normal average height (temperate and toyland landscapes).
* @param fheight The height to adjust.
* @return The adjusted height.
*/
static double SineTransformNormal(double &fheight)
{
double height = fheight;
/* Move and scale 0..1 into -1..+1 */
height = 2 * height - 1;
/* Sine transform */
height = sin(height * M_PI_2);
/* Transform it back from -1..1 into 0..1 space */
height = 0.5 * (height + 1);
return height;
}
/**
* Adjust the landscape to create plateaus on average (arctic landscape).
* @param fheight The height to adjust.
* @return The adjusted height.
*/
static double SineTransformPlateaus(double &fheight)
{
double height = fheight;
/* Redistribute heights to have more tiles at highest (75%..100%) range */
double sine_upper_limit = 0.75;
double linear_compression = 2;
if (height >= sine_upper_limit) {
/* Over the limit we do linear compression up */
height = 1.0 - (1.0 - height) / linear_compression;
} else {
double m = 1.0 - (1.0 - sine_upper_limit) / linear_compression;
/* Get 0..sine_upper_limit into -1..1 */
height = 2.0 * height / sine_upper_limit - 1.0;
/* Sine wave transform */
height = sin(height * M_PI_2);
/* Get -1..1 back to 0..(1 - (1 - sine_upper_limit) / linear_compression) == 0.0..m */
height = 0.5 * (height + 1.0) * m;
}
return height;
}
/**
* Applies sine wave redistribution onto height map.
* @param h_min The minimum height for the map.
* @param h_max The maximum height for the map.
*/
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);
switch (_settings_game.game_creation.average_height) {
case GenworldAverageHeight::Auto:
/* Apply sine transform depending on landscape type */
switch (_settings_game.game_creation.landscape) {
case LandscapeType::Temperate: fheight = SineTransformNormal(fheight); break;
case LandscapeType::Tropic: fheight = SineTransformLowlands(fheight); break;
case LandscapeType::Arctic: fheight = SineTransformPlateaus(fheight); break;
case LandscapeType::Toyland: fheight = SineTransformNormal(fheight); break;
default: NOT_REACHED();
}
break;
case GenworldAverageHeight::Lowlands: fheight = SineTransformLowlands(fheight); break;
case GenworldAverageHeight::Normal: fheight = SineTransformNormal(fheight); break;
case GenworldAverageHeight::Plateaus: fheight = SineTransformPlateaus(fheight); break;
default: NOT_REACHED();
}
/* Transform it back into h_min..h_max space */
h = static_cast<Height>(fheight * (h_max - h_min) + h_min);
if (h < 0) h = I2H(0);
if (h >= h_max) h = h_max - 1;
}
}
/**
* Additional map variety is provided by applying different curve maps
* to different parts of the map. A randomized low resolution grid contains
* which curve map to use on each part of the make. This filtered non-linearly
* to smooth out transitions between curves, so each tile could have between
* 100% of one map applied or 25% of four maps.
*
* The curve maps define different land styles, i.e. lakes, low-lands, hills
* and mountain ranges, although these are dependent on the landscape style
* chosen as well.
*
* The level parameter dictates the resolution of the grid. A low resolution
* grid will result in larger continuous areas of a land style, a higher
* resolution grid splits the style into smaller areas.
* @param level Rough indication of the size of the grid sections to style. Small level means large grid sections.
*/
static void HeightMapCurves(uint level)
{
Height mh = TGPGetMaxHeight() - I2H(1); // height levels above sea level only
/** Basically scale height X to height Y. Everything in between is interpolated. */
struct ControlPoint {
Height x; ///< The height to scale from.
Height y; ///< The height to scale to.
};
/** 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);
/* Re-add sea level */
*h += I2H(1);
}
}
}
/**
* Adjusts heights in height map to contain required amount of water tiles.
* @param water_percent Fixed point water percentage on the map.
* @param h_max_new The new maximum height.
*/
static void HeightMapAdjustWaterLevel(int64_t water_percent, Height h_max_new)
{
Height h_water_level;
int64_t water_tiles, desired_water_tiles;
int *hist;
auto [h_min, h_max] = std::ranges::minmax(_height_map.h);
/* 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 = water_percent * _height_map.size_x * _height_map.size_y / WATER_PERCENT_FACTOR;
/* 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 PerlinCoastNoise2D(const double x, const double y, const double p, const int prime);
/**
* This routine sculpts in from the edge a random amount, again from Perlin
* sequences, to avoid rigid flat-edge slopes and add an irregular edge to the
* land. The smoothing routines makes it legal, gradually increasing up from
* the edge to the original terrain.
*
* More varied coastlines on large maps require coastal features that would
* turn small maps into tiny islands. To avoid this, multiple perlin sequences
* with different persistence values are scaled based on the map dimensions.
*
* The constants used are based on what looks right. If you're changing the
* limits or the persistence values you'll want to experiment with various map
* sizes.
* @param water_borders The sides with water borders.
*/
static void HeightMapCoastLines(BorderFlags water_borders)
{
/* Both map dimensions are powers of 2. Division by smaller powers of 2 will always result in an integer. */
const int smallest_size = std::min(_height_map.size_x, _height_map.size_y);
const int map_ratio = std::max(_height_map.size_x, _height_map.size_y) / smallest_size;
/* More jagged perlin noise is used to create inlets and craggier features. It scales with map size and ratio and quickly
* reaches the limit of 64. It scales both by the shortest side and the map ratio to try and balance variation in the
* coastline and the amount of water on the map.
*/
const int jagged_distance = std::min(12 + (smallest_size * smallest_size / 4096) + std::min(map_ratio, 16), 64);
/* Smoother perlin noise is used to add more depth to the coastline as the smallest edge increases in length */
const int smooth_distance = std::min(smallest_size / 32, 32);
/* Function to get the distance from the edge at x (the coastline is actually 1D noise).
* p1, p2, p3 are small prime numbers so the sequences aren't identical.
*/
auto get_depth = [&](int x, int p1, int p2, int p3) {
return 2 // we ensure a margin of two water tiles at the edge of the map
+ smooth_distance * (1 + PerlinCoastNoise2D(x, x, 0.2, p1)) // +1 rather than abs reduces the number of V shaped inlets
+ jagged_distance * abs(PerlinCoastNoise2D(x, x, 0.5, p2))
+ 8 * abs(PerlinCoastNoise2D(x, x, 0.8, p3)); // Some unscaled jaggedness to breakup anything smoothed by scaling
};
int y, x;
/* Lower to sea level */
for (y = 0; y <= _height_map.size_y; y++) {
if (water_borders.Test(BorderFlag::NorthEast)) {
/* Top right */
for (x = 0; x < get_depth(y, 67, 179, 53); x++) {
_height_map.height(x, y) = 0;
}
}
if (water_borders.Test(BorderFlag::SouthWest)) {
/* Bottom left */
for (x = _height_map.size_x; x > (_height_map.size_x - 1 - get_depth(y, 199, 67, 101)); x--) {
_height_map.height(x, y) = 0;
}
}
}
/* Lower to sea level */
for (x = 0; x <= _height_map.size_x; x++) {
if (water_borders.Test(BorderFlag::NorthWest)) {
/* Top left */
for (y = 0; y < get_depth(x, 179, 211, 167); y++) {
_height_map.height(x, y) = 0;
}
}
if (water_borders.Test(BorderFlag::SouthEast)) {
/* Bottom right */
for (y = _height_map.size_y; y > (_height_map.size_y - 1 - get_depth(x, 101, 193, 71)); y--) {
_height_map.height(x, y) = 0;
}
}
}
}
/**
* Start at given point, move in given direction, find and Smooth coast in that direction.
* @param org_x The X-coordinate to start at.
* @param org_y The Y-coordinate to start at.
* @param dir_x The direction along the X-axis.
* @param dir_y The direction along the Y-axis.
*/
static void HeightMapSmoothCoastInDirection(int org_x, int org_y, int dir_x, int dir_y)
{
const int max_coast_dist_from_edge = 100;
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 neighbourhood? */
if (IsValidXY(x + dir_y, y + dir_x) && _height_map.height(x + dir_y, y + dir_x) > 0) break;
/* Coast found in the neighbourhood 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;
}
}
/**
* Smooth coasts by modulating height of tiles close to map edges with cosine of distance from edge.
* @param water_borders The sides where the borders are water.
*/
static void HeightMapSmoothCoasts(BorderFlags 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 (water_borders.Test(BorderFlag::NorthWest)) HeightMapSmoothCoastInDirection(x, 0, 0, 1);
if (water_borders.Test(BorderFlag::SouthEast)) 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 (water_borders.Test(BorderFlag::NorthEast)) HeightMapSmoothCoastInDirection(0, y, 1, 0);
if (water_borders.Test(BorderFlag::SouthWest)) HeightMapSmoothCoastInDirection(_height_map.size_x - 1, y, -1, 0);
}
}
/**
* This routine provides the essential cleanup necessary before OTTD can
* display the terrain. When generated, the terrain heights can jump more than
* one level between tiles. This routine smooths out those differences so that
* the most it can change is one level. When OTTD can support cliffs, this
* routine may not be necessary.
* @param dh_max The maximum height different between two adjacent tiles.
*/
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;
}
}
}
/**
* Height map terraform post processing:
* - water level adjusting
* - coast Smoothing
* - slope Smoothing
* - height histogram redistribution by sine wave transform
*/
static void HeightMapNormalize()
{
const int64_t water_percent = _settings_game.difficulty.quantity_sea_lakes != CUSTOM_SEA_LEVEL_NUMBER_DIFFICULTY ? _water_percent[_settings_game.difficulty.quantity_sea_lakes] : _settings_game.game_creation.custom_sea_level * WATER_PERCENT_FACTOR / 100;
const Height h_max_new = TGPGetMaxHeight();
const Height roughness = 7 + 3 * _settings_game.game_creation.tgen_smoothness;
HeightMapAdjustWaterLevel(water_percent, h_max_new);
BorderFlags water_borders = _settings_game.construction.freeform_edges ? _settings_game.game_creation.water_borders : BORDERFLAGS_ALL;
if (water_borders == BorderFlag::Random) water_borders = static_cast<BorderFlags>(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);
}
}
/**
* The Perlin Noise calculation using large primes
* The initial number is adjusted by two values; the generation_seed, and the
* passed parameter; prime.
* prime is used to allow the perlin noise generator to create useful random
* numbers from slightly different series.
* @param x The X-coordinate.
* @param y The Y-coordinate.
* @param prime The prime for the generation.
* @return The Perlin noise.
*/
static double IntNoise(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;
}
/**
* This routine determines the interpolated value between a and b
* @param a The first value.
* @param b The second value.
* @param x The fraction between the two values to get the value for.
* @return The interpolated value.
*/
static inline double LinearInterpolate(const double a, const double b, const double x)
{
return a + x * (b - a);
}
/**
* This routine returns the smoothed interpolated noise for an x and y, using
* the values from the surrounding positions.
* @param x The X-coordinate.
* @param y The Y-coordinate.
* @param prime The prime for the generation.
* @return The smoothed Perlin noise.
*/
static double InterpolatedNoise(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 = IntNoise(integer_x, integer_y, prime);
const double v2 = IntNoise(integer_x + 1, integer_y, prime);
const double v3 = IntNoise(integer_x, integer_y + 1, prime);
const double v4 = IntNoise(integer_x + 1, integer_y + 1, prime);
const double i1 = LinearInterpolate(v1, v2, fractional_x);
const double i2 = LinearInterpolate(v3, v4, fractional_x);
return LinearInterpolate(i1, i2, fractional_y);
}
/**
* This is a similar function to the main perlin noise calculation, but uses
* the value p passed as a parameter rather than selected from the predefined
* sequences. as you can guess by its title, i use this to create the indented
* coastline, which is just another perlin sequence.
* @param x The X-coordinate.
* @param y The Y-coordinate.
* @param p Scaling factor for the noise.
* @param prime The prime for the generation.
* @return The smoothed Perlin noise.
*/
static double PerlinCoastNoise2D(const double x, const double y, const double p, const int prime)
{
constexpr int OCTAVES = 6;
constexpr double INITIAL_FREQUENCY = 1 << OCTAVES;
double total = 0.0;
double max_value = 0.0;
double frequency = 1.0 / INITIAL_FREQUENCY;
double amplitude = 1.0;
for (int i = 0; i < OCTAVES; i++) {
total += InterpolatedNoise(x * frequency, y * frequency, prime) * amplitude;
max_value += amplitude;
frequency *= 2.0;
amplitude *= p;
}
/* Bringing the output range into [-1, 1] makes it much easier to reason with */
return total / max_value;
}
/**
* A small helper function to initialize the terrain.
* @param tile The tile to set the height for.
* @param height The new height of the tile.
*/
static void TgenSetTileHeight(TileIndex tile, int height)
{
SetTileHeight(tile, height);
/* Only clear the tiles within the map area. */
if (IsInnerTile(tile)) {
MakeClear(tile, ClearGround::Grass, 3);
}
}
/**
* The main new land generator using Perlin noise. Desert landscape is handled
* different to all others to give a desert valley between two high mountains.
* Clearly if a low height terrain (flat/very flat) is chosen, then the tropic
* areas won't be high enough, and there will be very little tropic on the map.
* Thus Tropic works best on Hilly or Mountainous.
*/
void GenerateTerrainPerlin()
{
AllocHeightMap();
GenerateWorldSetAbortCallback(FreeHeightMap);
HeightMapGenerate();
IncreaseGeneratingWorldProgress(GenWorldProgress::Landscape);
HeightMapNormalize();
IncreaseGeneratingWorldProgress(GenWorldProgress::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));
}
}
FreeHeightMap();
GenerateWorldSetAbortCallback(nullptr);
}
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