/* $Id$ */ /* * 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. * */ /** 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; int64 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 = A2I(((int64)water_percent) * (int64)(_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 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() { int sea_level_setting = _settings_game.difficulty.quantity_sea_lakes; const amplitude_t 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_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; } /** * 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 = 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); } /** * 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); }