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openttd/src/tgp.cpp

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/* $Id$ */
/*
* 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/>.
*/
/** @file tgp.cpp OTTD Perlin Noise Landscape Generator, aka TerraGenesis Perlin */
#include "stdafx.h"
#include <math.h>
#include "clear_map.h"
#include "void_map.h"
#include "genworld.h"
#include "core/alloc_func.hpp"
#include "core/random_func.hpp"
#include "landscape_type.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, 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 scaleable; 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 wasnt 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 flatish tops, rather than craggy peaks, but at least they
* arent 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 overal 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 simplifiead noise generator produces only two
* values -1 and +1, use 3 octaves with wave lenght 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.
*
*/
#ifndef M_PI_2
#define M_PI_2 1.57079632679489661923
#define M_PI 3.14159265358979323846
#endif /* M_PI_2 */
/** Fixed point type for heights */
typedef int16 height_t;
static const int height_decimal_bits = 4;
static const height_t _invalid_height = -32768;
/** Fixed point array for amplitudes (and percent values) */
typedef int amplitude_t;
static const int amplitude_decimal_bits = 10;
/** Height map - allocated array of heights (MapSizeX() + 1) x (MapSizeY() + 1) */
struct HeightMap
{
height_t *h; //< array of heights
uint dim_x; //< height map size_x MapSizeX() + 1
uint total_size; //< height map total size
uint size_x; //< MapSizeX()
uint size_y; //< MapSizeY()
/**
* Height map accessor
* @param x X position
* @param y Y position
* @return height as fixed point number
*/
inline height_t &height(uint x, uint y)
{
return h[x + y * dim_x];
}
};
/** Global height map instance */
static HeightMap _height_map = {NULL, 0, 0, 0, 0};
/** Conversion: int to height_t */
#define I2H(i) ((i) << height_decimal_bits)
/** Conversion: height_t to int */
#define H2I(i) ((i) >> height_decimal_bits)
/** Conversion: int to amplitude_t */
#define I2A(i) ((i) << amplitude_decimal_bits)
/** Conversion: amplitude_t to int */
#define A2I(i) ((i) >> amplitude_decimal_bits)
/** Conversion: amplitude_t to height_t */
#define A2H(a) ((a) >> (amplitude_decimal_bits - height_decimal_bits))
/** Walk through all items of _height_map.h */
#define FOR_ALL_TILES_IN_HEIGHT(h) for (h = _height_map.h; h < &_height_map.h[_height_map.total_size]; h++)
/** Maximum index into array of noise amplitudes */
static const int TGP_FREQUENCY_MAX = 6;
/** Noise amplitudes (multiplied by 1024)
* - indexed by "smoothness setting" and log2(frequency) */
static const amplitude_t _amplitudes_by_smoothness_and_frequency[4][TGP_FREQUENCY_MAX + 1] = {
/* lowest frequncy.... ...highest (every corner) */
/* Very smooth */
{16000, 5600, 1968, 688, 240, 16, 16},
/* Smooth */
{16000, 16000, 6448, 3200, 1024, 128, 16},
/* Rough */
{16000, 19200, 12800, 8000, 3200, 256, 64},
/* Very Rough */
{24000, 16000, 19200, 16000, 8000, 512, 320},
};
/** Desired water percentage (100% == 1024) - indexed by _settings_game.difficulty.quantity_sea_lakes */
static const amplitude_t _water_percent[4] = {20, 80, 250, 400};
/** Desired maximum height - indexed by _settings_game.difficulty.terrain_type */
static const int8 _max_height[4] = {
6, ///< Very flat
9, ///< Flat
12, ///< Hilly
15 ///< Mountainous
};
/** 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(uint x, uint y)
{
return ((int)x) >= 0 && x < _height_map.size_x && ((int)y) >= 0 && y < _height_map.size_y;
}
/**
* Allocate array of (MapSizeX()+1)*(MapSizeY()+1) heights and init the _height_map structure members
* @return true on success
*/
static inline bool AllocHeightMap()
{
height_t *h;
_height_map.size_x = MapSizeX();
_height_map.size_y = MapSizeY();
/* Allocate memory block for height map row pointers */
_height_map.total_size = (_height_map.size_x + 1) * (_height_map.size_y + 1);
_height_map.dim_x = _height_map.size_x + 1;
_height_map.h = CallocT<height_t>(_height_map.total_size);
/* Iterate through height map initialize values */
FOR_ALL_TILES_IN_HEIGHT(h) *h = _invalid_height;
return true;
}
/** Free height map */
static inline void FreeHeightMap()
{
if (_height_map.h == NULL) return;
free(_height_map.h);
_height_map.h = NULL;
}
/**
* Generates new random height in given amplitude (generated numbers will range from - amplitude to + amplitude)
* @param rMax Limit of result
* @return generated height
*/
static inline height_t RandomHeight(amplitude_t rMax)
{
amplitude_t ra = (Random() << 16) | (Random() & 0x0000FFFF);
height_t rh;
/* Spread height into range -rMax..+rMax */
rh = A2H(ra % (2 * rMax + 1) - rMax);
return rh;
}
/**
* One interpolation and noise round
*
* The heights on the map are generated in an iterative process.
* We start off with a frequency of 1 (log_frequency == 0), and generate heights only for corners on the most coarsly mesh
* (i.e. only for x/y coordinates which are multiples of the minimum edge length).
*
* After this initial step the frequency is doubled (log_frequency incremented) each iteration to generate corners on the next finer mesh.
* The heights of the newly added corners are first set by interpolating the heights from the previous iteration.
* Finally noise with the given amplitude is applied to all corners of the new mesh.
*
* Generation terminates, when the frequency has reached the map size. I.e. the mesh is as fine as the map, and every corner height
* has been set.
*
* @param log_frequency frequency (logarithmic) to apply noise for
* @param amplitude Amplitude for the noise
* @return false if we are finished (reached the minimal step size / highest frequency)
*/
static bool ApplyNoise(uint log_frequency, amplitude_t amplitude)
{
uint size_min = min(_height_map.size_x, _height_map.size_y);
uint step = size_min >> log_frequency;
uint x, y;
/* Trying to apply noise to uninitialized height map */
assert(_height_map.h != NULL);
/* Are we finished? */
if (step == 0) return false;
if (log_frequency == 0) {
/* This is first round, we need to establish base heights with step = size_min */
for (y = 0; y <= _height_map.size_y; y += step) {
for (x = 0; x <= _height_map.size_x; x += step) {
height_t height = (amplitude > 0) ? RandomHeight(amplitude) : 0;
_height_map.height(x, y) = height;
}
}
return true;
}
/* It is regular iteration round.
* Interpolate height values at odd x, even y tiles */
for (y = 0; y <= _height_map.size_y; y += 2 * step) {
for (x = 0; x < _height_map.size_x; x += 2 * step) {
height_t h00 = _height_map.height(x + 0 * step, y);
height_t h02 = _height_map.height(x + 2 * step, y);
height_t h01 = (h00 + h02) / 2;
_height_map.height(x + 1 * step, y) = h01;
}
}
/* Interpolate height values at odd y tiles */
for (y = 0; y < _height_map.size_y; y += 2 * step) {
for (x = 0; x <= _height_map.size_x; x += step) {
height_t h00 = _height_map.height(x, y + 0 * step);
height_t h20 = _height_map.height(x, y + 2 * step);
height_t h10 = (h00 + h20) / 2;
_height_map.height(x, y + 1 * step) = h10;
}
}
/* Add noise for next higher frequency (smaller steps) */
for (y = 0; y <= _height_map.size_y; y += step) {
for (x = 0; x <= _height_map.size_x; x += step) {
_height_map.height(x, y) += RandomHeight(amplitude);
}
}
return (step > 1);
}
/** Base Perlin noise generator - fills height map with raw Perlin noise */
static void HeightMapGenerate()
{
uint size_min = min(_height_map.size_x, _height_map.size_y);
uint iteration_round = 0;
amplitude_t amplitude;
bool continue_iteration;
int log_size_min, log_frequency_min;
int log_frequency;
/* Find first power of two that fits, so that later log_frequency == TGP_FREQUENCY_MAX in the last iteration */
for (log_size_min = TGP_FREQUENCY_MAX; (1U << log_size_min) < size_min; log_size_min++) { }
log_frequency_min = log_size_min - TGP_FREQUENCY_MAX;
/* Zero must be part of the iteration, else initialization will fail. */
assert(log_frequency_min >= 0);
/* Keep increasing the frequency until we reach the step size equal to one tile */
do {
log_frequency = iteration_round - log_frequency_min;
if (log_frequency >= 0) {
/* Apply noise for the next frequency */
assert(log_frequency <= TGP_FREQUENCY_MAX);
amplitude = _amplitudes_by_smoothness_and_frequency[_settings_game.game_creation.tgen_smoothness][log_frequency];
} else {
/* Amplitude for the low frequencies on big maps is 0, i.e. initialise with zero height */
amplitude = 0;
}
continue_iteration = ApplyNoise(iteration_round, amplitude);
iteration_round++;
} while (continue_iteration);
assert(log_frequency == TGP_FREQUENCY_MAX);
}
/** Returns min, max and average height from height map */
static void HeightMapGetMinMaxAvg(height_t *min_ptr, height_t *max_ptr, height_t *avg_ptr)
{
height_t h_min, h_max, h_avg, *h;
int64 h_accu = 0;
h_min = h_max = _height_map.height(0, 0);
/* Get h_min, h_max and accumulate heights into h_accu */
FOR_ALL_TILES_IN_HEIGHT(h) {
if (*h < h_min) h_min = *h;
if (*h > h_max) h_max = *h;
h_accu += *h;
}
/* Get average height */
h_avg = (height_t)(h_accu / (_height_map.size_x * _height_map.size_y));
/* Return required results */
if (min_ptr != NULL) *min_ptr = h_min;
if (max_ptr != NULL) *max_ptr = h_max;
if (avg_ptr != NULL) *avg_ptr = h_avg;
}
/** Dill histogram and return pointer to its base point - to the count of zero heights */
static int *HeightMapMakeHistogram(height_t h_min, height_t h_max, int *hist_buf)
{
int *hist = hist_buf - h_min;
height_t *h;
/* Count the heights and fill the histogram */
FOR_ALL_TILES_IN_HEIGHT(h) {
assert(*h >= h_min);
assert(*h <= h_max);
hist[*h]++;
}
return hist;
}
/** Applies sine wave redistribution onto height map */
static void HeightMapSineTransform(height_t h_min, height_t h_max)
{
height_t *h;
FOR_ALL_TILES_IN_HEIGHT(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_t)(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.
*
* At this point in map generation, all height data has been normalized to 0
* to 239.
*/
struct control_point_t {
height_t x;
height_t y;
};
struct control_point_list_t {
size_t length;
const control_point_t *list;
};
static const control_point_t _curve_map_1[] = {
{ 0, 0 }, { 48, 24 }, { 192, 32 }, { 240, 96 }
};
static const control_point_t _curve_map_2[] = {
{ 0, 0 }, { 16, 24 }, { 128, 32 }, { 192, 64 }, { 240, 144 }
};
static const control_point_t _curve_map_3[] = {
{ 0, 0 }, { 16, 24 }, { 128, 64 }, { 192, 144 }, { 240, 192 }
};
static const control_point_t _curve_map_4[] = {
{ 0, 0 }, { 16, 24 }, { 96, 72 }, { 160, 192 }, { 220, 239 }, { 240, 239 }
};
static const control_point_list_t _curve_maps[] = {
{ lengthof(_curve_map_1), _curve_map_1 },
{ lengthof(_curve_map_2), _curve_map_2 },
{ lengthof(_curve_map_3), _curve_map_3 },
{ lengthof(_curve_map_4), _curve_map_4 },
};
static void HeightMapCurves(uint level)
{
height_t ht[lengthof(_curve_maps)];
/* Set up a grid to choose curve maps based on location */
uint sx = Clamp(1 << level, 2, 32);
uint sy = Clamp(1 << level, 2, 32);
byte *c = (byte *)alloca(sx * sy);
for (uint i = 0; i < sx * sy; i++) {
c[i] = Random() % lengthof(_curve_maps);
}
/* Apply curves */
for (uint 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 + 0.5f;
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 (uint 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 + 0.5f;
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_t *h = &_height_map.height(x, y);
/* Apply all curve maps that are used on this tile. */
for (uint t = 0; t < lengthof(_curve_maps); t++) {
if (!HasBit(corner_bits, t)) continue;
const control_point_t *cm = _curve_maps[t].list;
for (uint i = 0; i < _curve_maps[t].length - 1; i++) {
const control_point_t &p1 = cm[i];
const control_point_t &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);
break;
}
}
}
/* Apply interpolation of curve map results. */
*h = (height_t)((ht[corner_a] * yri + ht[corner_b] * yr) * xri + (ht[corner_c] * yri + ht[corner_d] * yr) * xr);
}
}
}
/** Adjusts heights in height map to contain required amount of water tiles */
static void HeightMapAdjustWaterLevel(amplitude_t water_percent, height_t h_max_new)
{
height_t h_min, h_max, h_avg, h_water_level;
int water_tiles, desired_water_tiles;
height_t *h;
int *hist;
HeightMapGetMinMaxAvg(&h_min, &h_max, &h_avg);
/* Allocate histogram buffer and clear its cells */
int *hist_buf = CallocT<int>(h_max - h_min + 1);
/* Fill histogram */
hist = HeightMapMakeHistogram(h_min, h_max, hist_buf);
/* How many water tiles do we want? */
desired_water_tiles = (int)(((int64)water_percent) * (int64)(_height_map.size_x * _height_map.size_y)) >> amplitude_decimal_bits;
/* 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 4, 8, 12 or 16 depending on terrain type (very flat, flat, hilly, mountains)
*/
FOR_ALL_TILES_IN_HEIGHT(h) {
/* Transform height from range h_water_level..h_max into 0..h_max_new range */
*h = (height_t)(((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;
}
free(hist_buf);
}
static double perlin_coast_noise_2D(const double x, const double y, const double p, const int prime);
/**
* This routine sculpts in from the edge a random amount, again a Perlin
* sequence, to avoid the rigid flat-edge slopes that were present before. The
* Perlin noise map doesnt know where we are going to slice across, and so we
* often cut straight through high terrain. the smoothing routine makes it
* legal, gradually increasing up from the edge to the original terrain height.
* By cutting parts of this away, it gives a far more irregular edge to the
* map-edge. Sometimes it works beautifully with the existing sea & lakes, and
* creates a very realistic coastline. Other times the variation is less, and
* the map-edge shows its cliff-like roots.
*
* This routine may be extended to randomly sculpt the height of the terrain
* near the edge. This will have the coast edge at low level (1-3), rising in
* smoothed steps inland to about 15 tiles in. This should make it look as
* though the map has been built for the map size, rather than a slice through
* a larger map.
*
* Please note that all the small numbers; 53, 101, 167, etc. are small primes
* to help give the perlin noise a bit more of a random feel.
*/
static void HeightMapCoastLines(uint8 water_borders)
{
int smallest_size = min(_settings_game.game_creation.map_x, _settings_game.game_creation.map_y);
const int margin = 4;
uint 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 = max((smallest_size * smallest_size / 16) + max_x, (smallest_size * smallest_size / 16) + 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 = max((smallest_size * smallest_size / 16) + max_x, (smallest_size * smallest_size / 16) + 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 = max((smallest_size * smallest_size / 16) + max_y, (smallest_size * smallest_size / 16) + 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 = max((smallest_size * smallest_size / 16) + max_y, (smallest_size * smallest_size / 16) + 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;
}
}
}
}
/** Start at given point, move in given direction, find and Smooth coast in that direction */
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_t h_prev = 16;
height_t 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) > 15) 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 = min(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 */
static void HeightMapSmoothCoasts(uint8 water_borders)
{
uint 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);
}
}
/**
* 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.
*/
static void HeightMapSmoothSlopes(height_t dh_max)
{
int x, y;
for (y = 0; y <= (int)_height_map.size_y; y++) {
for (x = 0; x <= (int)_height_map.size_x; x++) {
height_t h_max = 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 (y = _height_map.size_y; y >= 0; y--) {
for (x = _height_map.size_x; x >= 0; x--) {
height_t h_max = min(_height_map.height((uint)x < _height_map.size_x ? x + 1 : x, y), _height_map.height(x, (uint)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 amplitude_t water_percent = _water_percent[_settings_game.difficulty.quantity_sea_lakes];
const height_t h_max_new = I2H(_max_height[_settings_game.difficulty.terrain_type]);
const height_t roughness = 7 + 3 * _settings_game.game_creation.tgen_smoothness;
HeightMapAdjustWaterLevel(water_percent, h_max_new);
byte 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(12, h_max_new);
if (_settings_game.game_creation.variety > 0) {
HeightMapCurves(_settings_game.game_creation.variety);
}
HeightMapSmoothSlopes(16);
}
/**
* 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.
*/
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;
}
/**
* Hj. Malthaner's routine included 2 different noise smoothing methods.
* We now use the "raw" int_noise one.
* However, it may be useful to move to the other routine in future.
* So it is included too.
*/
static double smoothed_noise(const int x, const int y, const int prime)
{
#if 0
/* A hilly world (four corner smooth) */
const double sides = int_noise(x - 1, y) + int_noise(x + 1, y) + int_noise(x, y - 1) + int_noise(x, y + 1);
const double center = int_noise(x, y);
return (sides + sides + center * 4) / 8.0;
#endif
/* This gives very hilly world */
return int_noise(x, y, prime);
}
/**
* This routine determines the interpolated value between a and b
*/
static inline double linear_interpolate(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.
*/
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 = smoothed_noise(integer_X, integer_Y, prime);
const double v2 = smoothed_noise(integer_X + 1, integer_Y, prime);
const double v3 = smoothed_noise(integer_X, integer_Y + 1, prime);
const double v4 = smoothed_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);
}
/**
* 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.
*/
static double perlin_coast_noise_2D(const double x, const double y, const double p, const int prime)
{
double total = 0.0;
int i;
for (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;
}
/** A small helper function to initialize the terrain */
static void TgenSetTileHeight(TileIndex tile, int height)
{
SetTileHeight(tile, height);
/* Only clear the tiles within the map area. */
if (TileX(tile) != MapMaxX() && TileY(tile) != MapMaxY() &&
(!_settings_game.construction.freeform_edges || (TileX(tile) != 0 && TileY(tile) != 0))) {
MakeClear(tile, CLEAR_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 wont be high enough, and there will be very little tropic on the map.
* Thus Tropic works best on Hilly or Mountainous.
*/
void GenerateTerrainPerlin()
{
uint x, y;
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 (y = 0; y < _height_map.size_y - 1; y++) MakeVoid(_height_map.size_x * y);
for (x = 0; x < _height_map.size_x; x++) MakeVoid(x);
}
/* Transfer height map into OTTD map */
for (y = 0; y < _height_map.size_y; y++) {
for (x = 0; x < _height_map.size_x; x++) {
int height = H2I(_height_map.height(x, y));
if (height < 0) height = 0;
if (height > 15) height = 15;
TgenSetTileHeight(TileXY(x, y), height);
}
}
IncreaseGeneratingWorldProgress(GWP_LANDSCAPE);
FreeHeightMap();
GenerateWorldSetAbortCallback(NULL);
}
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