OpenTTD: src/tgp.cpp Source File

OpenTTD

- Main Page
- Related Pages
- Modules
- Namespaces
- Data Structures
- Files

- File List
- Globals

tgp.cpp
Go to the documentation of this file.
1 /* $Id: tgp.cpp 27232 2015-04-11 18:46:01Z alberth $ */
2
3 /*
4 * This file is part of OpenTTD.
5 * 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.
6 * 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.
7 * 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/>.
8 */
9
12 #include "stdafx.h"
13 #include <math.h>
14 #include "clear_map.h"
15 #include "void_map.h"
16 #include "genworld.h"
17 #include "core/random_func.hpp"
18 #include "landscape_type.h"
19
20 #include "safeguards.h"
21
22 /*
23 *
24 * Quickie guide to Perlin Noise
25 * Perlin noise is a predictable pseudo random number sequence. By generating
26 * it in 2 dimensions, it becomes a useful random map that, for a given seed
27 * and starting X & Y, is entirely predictable. On the face of it, that may not
28 * be useful. However, it means that if you want to replay a map in a different
29 * terrain, or just vary the sea level, you just re-run the generator with the
30 * same seed. The seed is an int32, and is randomised on each run of New Game.
31 * The Scenario Generator does not randomise the value, so that you can
32 * experiment with one terrain until you are happy, or click "Random" for a new
33 * random seed.
34 *
35 * Perlin Noise is a series of "octaves" of random noise added together. By
36 * reducing the amplitude of the noise with each octave, the first octave of
37 * noise defines the main terrain sweep, the next the ripples on that, and the
38 * next the ripples on that. I use 6 octaves, with the amplitude controlled by
39 * a power ratio, usually known as a persistence or p value. This I vary by the
40 * smoothness selection, as can be seen in the table below. The closer to 1,
41 * the more of that octave is added. Each octave is however raised to the power
42 * of its position in the list, so the last entry in the "smooth" row, 0.35, is
43 * raised to the power of 6, so can only add 0.001838... of the amplitude to
44 * the running total.
45 *
46 * In other words; the first p value sets the general shape of the terrain, the
47 * second sets the major variations to that, ... until finally the smallest
48 * bumps are added.
49 *
50 * Usefully, this routine is totally scaleable; so when 32bpp comes along, the
51 * terrain can be as bumpy as you like! It is also infinitely expandable; a
52 * single random seed terrain continues in X & Y as far as you care to
53 * calculate. In theory, we could use just one seed value, but randomly select
54 * where in the Perlin XY space we use for the terrain. Personally I prefer
55 * using a simple (0, 0) to (X, Y), with a varying seed.
56 *
57 *
58 * Other things i have had to do: mountainous wasn't mountainous enough, and
59 * since we only have 0..15 heights available, I add a second generated map
60 * (with a modified seed), onto the original. This generally raises the
61 * terrain, which then needs scaling back down. Overall effect is a general
62 * uplift.
63 *
64 * However, the values on the top of mountains are then almost guaranteed to go
65 * too high, so large flat plateaus appeared at height 15. To counter this, I
66 * scale all heights above 12 to proportion up to 15. It still makes the
67 * mountains have flattish tops, rather than craggy peaks, but at least they
68 * aren't smooth as glass.
69 *
70 *
71 * For a full discussion of Perlin Noise, please visit:
72 * http://freespace.virgin.net/hugo.elias/models/m_perlin.htm
73 *
74 *
75 * Evolution II
76 *
77 * The algorithm as described in the above link suggests to compute each tile height
78 * as composition of several noise waves. Some of them are computed directly by
79 * noise(x, y) function, some are calculated using linear approximation. Our
80 * first implementation of perlin_noise_2D() used 4 noise(x, y) calls plus
81 * 3 linear interpolations. It was called 6 times for each tile. This was a bit
82 * CPU expensive.
83 *
84 * The following implementation uses optimized algorithm that should produce
85 * the same quality result with much less computations, but more memory accesses.
86 * The overall speedup should be 300% to 800% depending on CPU and memory speed.
87 *
88 * I will try to explain it on the example below:
89 *
90 * Have a map of 4 x 4 tiles, our simplified noise generator produces only two
91 * values -1 and +1, use 3 octaves with wave length 1, 2 and 4, with amplitudes
92 * 3, 2, 1. Original algorithm produces:
93 *
94 * 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
95 * 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
96 * 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
97 * 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
98 *
99 * 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
100 * 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
101 * 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
102 * 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
103 *
104 *
105 * Optimization 1:
106 *
107 * 1) we need to allocate a bit more tiles: (size_x + 1) * (size_y + 1) = (5 * 5):
108 *
109 * 2) setup corner values using amplitude 3
110 * { -3.0 X X X 3.0 }
111 * { X X X X X }
112 * { X X X X X }
113 * { X X X X X }
114 * { 3.0 X X X -3.0 }
115 *
116 * 3a) interpolate values in the middle
117 * { -3.0 X 0.0 X 3.0 }
118 * { X X X X X }
119 * { 0.0 X 0.0 X 0.0 }
120 * { X X X X X }
121 * { 3.0 X 0.0 X -3.0 }
122 *
123 * 3b) add patches with amplitude 2 to them
124 * { -5.0 X 2.0 X 1.0 }
125 * { X X X X X }
126 * { 2.0 X -2.0 X 2.0 }
127 * { X X X X X }
128 * { 1.0 X 2.0 X -5.0 }
129 *
130 * 4a) interpolate values in the middle
131 * { -5.0 -1.5 2.0 1.5 1.0 }
132 * { -1.5 -0.75 0.0 0.75 1.5 }
133 * { 2.0 0.0 -2.0 0.0 2.0 }
134 * { 1.5 0.75 0.0 -0.75 -1.5 }
135 * { 1.0 1.5 2.0 -1.5 -5.0 }
136 *
137 * 4b) add patches with amplitude 1 to them
138 * { -6.0 -0.5 1.0 2.5 0.0 }
139 * { -0.5 -1.75 1.0 -0.25 2.5 }
140 * { 1.0 1.0 -3.0 1.0 1.0 }
141 * { 2.5 -0.25 1.0 -1.75 -0.5 }
142 * { 0.0 2.5 1.0 -0.5 -6.0 }
143 *
144 *
145 *
146 * Optimization 2:
147 *
148 * As you can see above, each noise function was called just once. Therefore
149 * we don't need to use noise function that calculates the noise from x, y and
150 * some prime. The same quality result we can obtain using standard Random()
151 * function instead.
152 *
153 */
154
156 typedef int16 height_t;
157 static const int height_decimal_bits = 4;
158
160 typedef int amplitude_t;
161 static const int amplitude_decimal_bits = 10;
162
164 struct HeightMap
165 {
166 height_t *h; //< array of heights
167 /* Even though the sizes are always positive, there are many cases where
168 * X and Y need to be signed integers due to subtractions. */
169 int dim_x; //< height map size_x MapSizeX() + 1
170 int total_size; //< height map total size
171 int size_x; //< MapSizeX()
172 int size_y; //< MapSizeY()
173
180 inline height_t &height(uint x, uint y)
181 {
182 return h[x + y * dim_x];
183 }
184 };
185
187 static HeightMap _height_map = {NULL, 0, 0, 0, 0};
188
190 #define I2H(i) ((i) << height_decimal_bits)
191
192 #define H2I(i) ((i) >> height_decimal_bits)
193
195 #define I2A(i) ((i) << amplitude_decimal_bits)
196
197 #define A2I(i) ((i) >> amplitude_decimal_bits)
198
200 #define A2H(a) ((a) >> (amplitude_decimal_bits - height_decimal_bits))
201
202
204 #define FOR_ALL_TILES_IN_HEIGHT(h) for (h = _height_map.h; h < &_height_map.h[_height_map.total_size]; h++)
205
207 static const int MAX_TGP_FREQUENCIES = 10;
208
210 static const amplitude_t _water_percent[4] = {70, 170, 270, 420};
211
218 static height_t TGPGetMaxHeight()
219 {
230 static const int max_height[5][MAX_MAP_SIZE_BITS - MIN_MAP_SIZE_BITS + 1] = {
231 /* 64 128 256 512 1024 2048 4096 */
232 { 3, 3, 3, 3, 4, 5, 7 },
233 { 5, 7, 8, 9, 14, 19, 31 },
234 { 8, 9, 10, 15, 23, 37, 61 },
235 { 10, 11, 17, 19, 49, 63, 73 },
236 { 12, 19, 25, 31, 67, 75, 87 },
237 };
238
239 int max_height_from_table = max_height[_settings_game.difficulty.terrain_type][min(MapLogX(), MapLogY()) - MIN_MAP_SIZE_BITS];
240 return I2H(min(max_height_from_table, _settings_game.construction.max_heightlevel));
241 }
242
249 static amplitude_t GetAmplitude(int frequency)
250 {
251 /* Base noise amplitudes (multiplied by 1024) and indexed by "smoothness setting" and log2(frequency).
252 * Used for maps that have their smallest side smaller than 512. */
253 static const amplitude_t amplitudes_small[][10] = {
254 /* lowest frequency ...... highest (every corner) */
255 {60000, 2273, 4142, 2253, 421, 213, 137, 177, 37, 16},
256 {50000, 2273, 4142, 2253, 421, 213, 137, 177, 37, 61},
257 {40000, 2273, 4142, 2253, 421, 213, 137, 177, 37, 91},
258 {30000, 2273, 4142, 2253, 421, 213, 137, 177, 37, 161},
259 };
260
261 /* Base noise amplitudes (multiplied by 1024) and indexed by "smoothness setting" and log2(frequency).
262 * Used for maps that have their smallest side equal to 512. */
263 static const amplitude_t amplitudes_middle[][10] = {
264 {55000, 2273, 5142, 253, 2421, 213, 137, 177, 37, 16},
265 {45000, 2273, 5142, 253, 2421, 213, 137, 177, 37, 61},
266 {35000, 2273, 5142, 253, 2421, 213, 137, 177, 37, 91},
267 {25000, 2273, 5142, 253, 2421, 213, 137, 177, 37, 161},
268 };
269
270 /* Base noise amplitudes (multiplied by 1024) and indexed by "smoothness setting" and log2(frequency).
271 * Used for maps that have their smallest side bigger than 512. */
272 static const amplitude_t amplitudes_large[][10] = {
273 /* lowest frequency ...... highest (every corner) */
274 {55000, 2273, 5142, 253, 421, 2213, 137, 177, 37, 16},
275 {45000, 2273, 5142, 253, 421, 2213, 137, 177, 37, 61},
276 {35000, 2273, 5142, 253, 421, 2213, 137, 177, 37, 91},
277 {25000, 2273, 5142, 253, 421, 2213, 137, 177, 37, 161},
278 };
279
280 /* Make sure arrays cover all smoothness settings. */
281 assert_compile(lengthof(amplitudes_small) == TGEN_SMOOTHNESS_END);
282 assert_compile(lengthof(amplitudes_middle) == TGEN_SMOOTHNESS_END);
283 assert_compile(lengthof(amplitudes_large) == TGEN_SMOOTHNESS_END);
284
285 /* Extrapolation factors for ranges before the table.
286 * The extrapolation is needed to account for the higher map heights. They need larger
287 * areas with a particular gradient so that we are able to create maps without too
288 * many steep slopes up to the wanted height level. It's definitely not perfect since
289 * it will bring larger rectangles with similar slopes which makes the rectangular
290 * behaviour of TGP more noticable. However, these height differentiations cannot
291 * happen over much smaller areas; we basically double the "range" to give a similar
292 * slope for every doubling of map height.
293 */
294 static const double extrapolation_factors[] = { 3.3, 2.8, 2.3, 1.8 };
295
296 int smoothness = _settings_game.game_creation.tgen_smoothness;
297 int smallest_size = min(_settings_game.game_creation.map_x, _settings_game.game_creation.map_y);
298
299 int index;
300 amplitude_t amplitude;
301 if (smallest_size < 9) { // Smallest map side is less than 2^9 == 512.
302 index = frequency - MAX_TGP_FREQUENCIES + lengthof(amplitudes_small[0]);
303 amplitude = amplitudes_small[smoothness][max(0, index)];
304 } else if (smallest_size == 9) {
305 index = frequency - MAX_TGP_FREQUENCIES + lengthof(amplitudes_middle[0]);
306 amplitude = amplitudes_middle[smoothness][max(0, index)];
307 } else {
308 index = frequency - MAX_TGP_FREQUENCIES + lengthof(amplitudes_large[0]);
309 amplitude = amplitudes_large[smoothness][max(0, index)];
310 }
311 if (index >= 0) return amplitude;
312
313 /* We need to extrapolate the amplitude. */
314 double extrapolation_factor = extrapolation_factors[smoothness];
315 int height_range = I2H(16);
316 do {
317 amplitude = (amplitude_t)(extrapolation_factor * (double)amplitude);
318 height_range <<= 1;
319 index++;
320 } while (index < 0);
321
322 return Clamp((TGPGetMaxHeight() - height_range) / height_range, 0, 1) * amplitude;
323 }
324
331 static inline bool IsValidXY(int x, int y)
332 {
333 return x >= 0 && x < _height_map.size_x && y >= 0 && y < _height_map.size_y;
334 }
335
336
341 static inline bool AllocHeightMap()
342 {
343 height_t *h;
344
345 _height_map.size_x = MapSizeX();
346 _height_map.size_y = MapSizeY();
347
348 /* Allocate memory block for height map row pointers */
349 _height_map.total_size = (_height_map.size_x + 1) * (_height_map.size_y + 1);
350 _height_map.dim_x = _height_map.size_x + 1;
351 _height_map.h = CallocT<height_t>(_height_map.total_size);
352
353 /* Iterate through height map and initialise values. */
354 FOR_ALL_TILES_IN_HEIGHT(h) *h = 0;
355
356 return true;
357 }
358
360 static inline void FreeHeightMap()
361 {
362 free(_height_map.h);
363 _height_map.h = NULL;
364 }
365
371 static inline height_t RandomHeight(amplitude_t rMax)
372 {
373 /* Spread height into range -rMax..+rMax */
374 return A2H(RandomRange(2 * rMax + 1) - rMax);
375 }
376
384 static void HeightMapGenerate()
385 {
386 /* Trying to apply noise to uninitialized height map */
387 assert(_height_map.h != NULL);
388
389 int start = max(MAX_TGP_FREQUENCIES - (int)min(MapLogX(), MapLogY()), 0);
390 bool first = true;
391
392 for (int frequency = start; frequency < MAX_TGP_FREQUENCIES; frequency++) {
393 const amplitude_t amplitude = GetAmplitude(frequency);
394
395 /* Ignore zero amplitudes; it means our map isn't height enough for this
396 * amplitude, so ignore it and continue with the next set of amplitude. */
397 if (amplitude == 0) continue;
398
399 const int step = 1 << (MAX_TGP_FREQUENCIES - frequency - 1);
400
401 if (first) {
402 /* This is first round, we need to establish base heights with step = size_min */
403 for (int y = 0; y <= _height_map.size_y; y += step) {
404 for (int x = 0; x <= _height_map.size_x; x += step) {
405 height_t height = (amplitude > 0) ? RandomHeight(amplitude) : 0;
406 _height_map.height(x, y) = height;
407 }
408 }
409 first = false;
410 continue;
411 }
412
413 /* It is regular iteration round.
414 * Interpolate height values at odd x, even y tiles */
415 for (int y = 0; y <= _height_map.size_y; y += 2 * step) {
416 for (int x = 0; x <= _height_map.size_x - 2 * step; x += 2 * step) {
417 height_t h00 = _height_map.height(x + 0 * step, y);
418 height_t h02 = _height_map.height(x + 2 * step, y);
419 height_t h01 = (h00 + h02) / 2;
420 _height_map.height(x + 1 * step, y) = h01;
421 }
422 }
423
424 /* Interpolate height values at odd y tiles */
425 for (int y = 0; y <= _height_map.size_y - 2 * step; y += 2 * step) {
426 for (int x = 0; x <= _height_map.size_x; x += step) {
427 height_t h00 = _height_map.height(x, y + 0 * step);
428 height_t h20 = _height_map.height(x, y + 2 * step);
429 height_t h10 = (h00 + h20) / 2;
430 _height_map.height(x, y + 1 * step) = h10;
431 }
432 }
433
434 /* Add noise for next higher frequency (smaller steps) */
435 for (int y = 0; y <= _height_map.size_y; y += step) {
436 for (int x = 0; x <= _height_map.size_x; x += step) {
437 _height_map.height(x, y) += RandomHeight(amplitude);
438 }
439 }
440 }
441 }
442
444 static void HeightMapGetMinMaxAvg(height_t *min_ptr, height_t *max_ptr, height_t *avg_ptr)
445 {
446 height_t h_min, h_max, h_avg, *h;
447 int64 h_accu = 0;
448 h_min = h_max = _height_map.height(0, 0);
449
450 /* Get h_min, h_max and accumulate heights into h_accu */
451 FOR_ALL_TILES_IN_HEIGHT(h) {
452 if (*h < h_min) h_min = *h;
453 if (*h > h_max) h_max = *h;
454 h_accu += *h;
455 }
456
457 /* Get average height */
458 h_avg = (height_t)(h_accu / (_height_map.size_x * _height_map.size_y));
459
460 /* Return required results */
461 if (min_ptr != NULL) *min_ptr = h_min;
462 if (max_ptr != NULL) *max_ptr = h_max;
463 if (avg_ptr != NULL) *avg_ptr = h_avg;
464 }
465
467 static int *HeightMapMakeHistogram(height_t h_min, height_t h_max, int *hist_buf)
468 {
469 int *hist = hist_buf - h_min;
470 height_t *h;
471
472 /* Count the heights and fill the histogram */
473 FOR_ALL_TILES_IN_HEIGHT(h) {
474 assert(*h >= h_min);
475 assert(*h <= h_max);
476 hist[*h]++;
477 }
478 return hist;
479 }
480
482 static void HeightMapSineTransform(height_t h_min, height_t h_max)
483 {
484 height_t *h;
485
486 FOR_ALL_TILES_IN_HEIGHT(h) {
487 double fheight;
488
489 if (*h < h_min) continue;
490
491 /* Transform height into 0..1 space */
492 fheight = (double)(*h - h_min) / (double)(h_max - h_min);
493 /* Apply sine transform depending on landscape type */
494 switch (_settings_game.game_creation.landscape) {
495 case LT_TOYLAND:
496 case LT_TEMPERATE:
497 /* Move and scale 0..1 into -1..+1 */
498 fheight = 2 * fheight - 1;
499 /* Sine transform */
500 fheight = sin(fheight * M_PI_2);
501 /* Transform it back from -1..1 into 0..1 space */
502 fheight = 0.5 * (fheight + 1);
503 break;
504
505 case LT_ARCTIC:
506 {
507 /* Arctic terrain needs special height distribution.
508 * Redistribute heights to have more tiles at highest (75%..100%) range */
509 double sine_upper_limit = 0.75;
510 double linear_compression = 2;
511 if (fheight >= sine_upper_limit) {
512 /* Over the limit we do linear compression up */
513 fheight = 1.0 - (1.0 - fheight) / linear_compression;
514 } else {
515 double m = 1.0 - (1.0 - sine_upper_limit) / linear_compression;
516 /* Get 0..sine_upper_limit into -1..1 */
517 fheight = 2.0 * fheight / sine_upper_limit - 1.0;
518 /* Sine wave transform */
519 fheight = sin(fheight * M_PI_2);
520 /* Get -1..1 back to 0..(1 - (1 - sine_upper_limit) / linear_compression) == 0.0..m */
521 fheight = 0.5 * (fheight + 1.0) * m;
522 }
523 }
524 break;
525
526 case LT_TROPIC:
527 {
528 /* Desert terrain needs special height distribution.
529 * Half of tiles should be at lowest (0..25%) heights */
530 double sine_lower_limit = 0.5;
531 double linear_compression = 2;
532 if (fheight <= sine_lower_limit) {
533 /* Under the limit we do linear compression down */
534 fheight = fheight / linear_compression;
535 } else {
536 double m = sine_lower_limit / linear_compression;
537 /* Get sine_lower_limit..1 into -1..1 */
538 fheight = 2.0 * ((fheight - sine_lower_limit) / (1.0 - sine_lower_limit)) - 1.0;
539 /* Sine wave transform */
540 fheight = sin(fheight * M_PI_2);
541 /* Get -1..1 back to (sine_lower_limit / linear_compression)..1.0 */
542 fheight = 0.5 * ((1.0 - m) * fheight + (1.0 + m));
543 }
544 }
545 break;
546
547 default:
548 NOT_REACHED();
549 break;
550 }
551 /* Transform it back into h_min..h_max space */
552 *h = (height_t)(fheight * (h_max - h_min) + h_min);
553 if (*h < 0) *h = I2H(0);
554 if (*h >= h_max) *h = h_max - 1;
555 }
556 }
557
574 static void HeightMapCurves(uint level)
575 {
576 int mh = TGPGetMaxHeight();
577
579 struct control_point_t {
580 height_t x;
581 height_t y;
582 };
583 /* Scaled curve maps; value is in height_ts. */
584 #define F(fraction) ((height_t)(fraction * mh))
585 const control_point_t curve_map_1[] = { { F(0.0), F(0.0) }, { F(0.6 / 3), F(0.1) }, { F(2.4 / 3), F(0.4 / 3) }, { F(1.0), F(0.4) } };
586 const control_point_t curve_map_2[] = { { F(0.0), F(0.0) }, { F(0.2 / 3), F(0.1) }, { F(1.6 / 3), F(0.4 / 3) }, { F(2.4 / 3), F(0.8 / 3) }, { F(1.0), F(0.6) } };
587 const control_point_t curve_map_3[] = { { F(0.0), F(0.0) }, { F(0.2 / 3), F(0.1) }, { F(1.6 / 3), F(0.8 / 3) }, { F(2.4 / 3), F(1.8 / 3) }, { F(1.0), F(0.8) } };
588 const control_point_t curve_map_4[] = { { F(0.0), F(0.0) }, { F(0.2 / 3), F(0.1) }, { F(1.2 / 3), F(0.9 / 3) }, { F(2.0 / 3), F(2.4 / 3) } , { F(5.5 / 6), F(0.99) }, { F(1.0), F(0.99) } };
589 #undef F
590
592 struct control_point_list_t {
593 size_t length;
594 const control_point_t *list;
595 };
596 const control_point_list_t curve_maps[] = {
597 { lengthof(curve_map_1), curve_map_1 },
598 { lengthof(curve_map_2), curve_map_2 },
599 { lengthof(curve_map_3), curve_map_3 },
600 { lengthof(curve_map_4), curve_map_4 },
601 };
602
603 height_t ht[lengthof(curve_maps)];
604 MemSetT(ht, 0, lengthof(ht));
605
606 /* Set up a grid to choose curve maps based on location; attempt to get a somewhat square grid */
607 float factor = sqrt((float)_height_map.size_x / (float)_height_map.size_y);
608 uint sx = Clamp((int)(((1 << level) * factor) + 0.5), 1, 128);
609 uint sy = Clamp((int)(((1 << level) / factor) + 0.5), 1, 128);
610 byte *c = AllocaM(byte, sx * sy);
611
612 for (uint i = 0; i < sx * sy; i++) {
613 c[i] = Random() % lengthof(curve_maps);
614 }
615
616 /* Apply curves */
617 for (int x = 0; x < _height_map.size_x; x++) {
618
619 /* Get our X grid positions and bi-linear ratio */
620 float fx = (float)(sx * x) / _height_map.size_x + 1.0f;
621 uint x1 = (uint)fx;
622 uint x2 = x1;
623 float xr = 2.0f * (fx - x1) - 1.0f;
624 xr = sin(xr * M_PI_2);
625 xr = sin(xr * M_PI_2);
626 xr = 0.5f * (xr + 1.0f);
627 float xri = 1.0f - xr;
628
629 if (x1 > 0) {
630 x1--;
631 if (x2 >= sx) x2--;
632 }
633
634 for (int y = 0; y < _height_map.size_y; y++) {
635
636 /* Get our Y grid position and bi-linear ratio */
637 float fy = (float)(sy * y) / _height_map.size_y + 1.0f;
638 uint y1 = (uint)fy;
639 uint y2 = y1;
640 float yr = 2.0f * (fy - y1) - 1.0f;
641 yr = sin(yr * M_PI_2);
642 yr = sin(yr * M_PI_2);
643 yr = 0.5f * (yr + 1.0f);
644 float yri = 1.0f - yr;
645
646 if (y1 > 0) {
647 y1--;
648 if (y2 >= sy) y2--;
649 }
650
651 uint corner_a = c[x1 + sx * y1];
652 uint corner_b = c[x1 + sx * y2];
653 uint corner_c = c[x2 + sx * y1];
654 uint corner_d = c[x2 + sx * y2];
655
656 /* Bitmask of which curve maps are chosen, so that we do not bother
657 * calculating a curve which won't be used. */
658 uint corner_bits = 0;
659 corner_bits |= 1 << corner_a;
660 corner_bits |= 1 << corner_b;
661 corner_bits |= 1 << corner_c;
662 corner_bits |= 1 << corner_d;
663
664 height_t *h = &_height_map.height(x, y);
665
666 /* Apply all curve maps that are used on this tile. */
667 for (uint t = 0; t < lengthof(curve_maps); t++) {
668 if (!HasBit(corner_bits, t)) continue;
669
670 const control_point_t *cm = curve_maps[t].list;
671 for (uint i = 0; i < curve_maps[t].length - 1; i++) {
672 const control_point_t &p1 = cm[i];
673 const control_point_t &p2 = cm[i + 1];
674
675 if (*h >= p1.x && *h < p2.x) {
676 ht[t] = p1.y + (*h - p1.x) * (p2.y - p1.y) / (p2.x - p1.x);
677 break;
678 }
679 }
680 }
681
682 /* Apply interpolation of curve map results. */
683 *h = (height_t)((ht[corner_a] * yri + ht[corner_b] * yr) * xri + (ht[corner_c] * yri + ht[corner_d] * yr) * xr);
684 }
685 }
686 }
687
689 static void HeightMapAdjustWaterLevel(amplitude_t water_percent, height_t h_max_new)
690 {
691 height_t h_min, h_max, h_avg, h_water_level;
692 int64 water_tiles, desired_water_tiles;
693 height_t *h;
694 int *hist;
695
696 HeightMapGetMinMaxAvg(&h_min, &h_max, &h_avg);
697
698 /* Allocate histogram buffer and clear its cells */
699 int *hist_buf = CallocT<int>(h_max - h_min + 1);
700 /* Fill histogram */
701 hist = HeightMapMakeHistogram(h_min, h_max, hist_buf);
702
703 /* How many water tiles do we want? */
704 desired_water_tiles = A2I(((int64)water_percent) * (int64)(_height_map.size_x * _height_map.size_y));
705
706 /* Raise water_level and accumulate values from histogram until we reach required number of water tiles */
707 for (h_water_level = h_min, water_tiles = 0; h_water_level < h_max; h_water_level++) {
708 water_tiles += hist[h_water_level];
709 if (water_tiles >= desired_water_tiles) break;
710 }
711
712 /* We now have the proper water level value.
713 * Transform the height map into new (normalized) height map:
714 * values from range: h_min..h_water_level will become negative so it will be clamped to 0
715 * values from range: h_water_level..h_max are transformed into 0..h_max_new
716 * where h_max_new is depending on terrain type and map size.
717 */
718 FOR_ALL_TILES_IN_HEIGHT(h) {
719 /* Transform height from range h_water_level..h_max into 0..h_max_new range */
720 *h = (height_t)(((int)h_max_new) * (*h - h_water_level) / (h_max - h_water_level)) + I2H(1);
721 /* Make sure all values are in the proper range (0..h_max_new) */
722 if (*h < 0) *h = I2H(0);
723 if (*h >= h_max_new) *h = h_max_new - 1;
724 }
725
726 free(hist_buf);
727 }
728
729 static double perlin_coast_noise_2D(const double x, const double y, const double p, const int prime);
730
751 static void HeightMapCoastLines(uint8 water_borders)
752 {
753 int smallest_size = min(_settings_game.game_creation.map_x, _settings_game.game_creation.map_y);
754 const int margin = 4;
755 int y, x;
756 double max_x;
757 double max_y;
758
759 /* Lower to sea level */
760 for (y = 0; y <= _height_map.size_y; y++) {
761 if (HasBit(water_borders, BORDER_NE)) {
762 /* Top right */
763 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);
764 max_x = max((smallest_size * smallest_size / 64) + max_x, (smallest_size * smallest_size / 64) + margin - max_x);
765 if (smallest_size < 8 && max_x > 5) max_x /= 1.5;
766 for (x = 0; x < max_x; x++) {
767 _height_map.height(x, y) = 0;
768 }
769 }
770
771 if (HasBit(water_borders, BORDER_SW)) {
772 /* Bottom left */
773 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);
774 max_x = max((smallest_size * smallest_size / 64) + max_x, (smallest_size * smallest_size / 64) + margin - max_x);
775 if (smallest_size < 8 && max_x > 5) max_x /= 1.5;
776 for (x = _height_map.size_x; x > (_height_map.size_x - 1 - max_x); x--) {
777 _height_map.height(x, y) = 0;
778 }
779 }
780 }
781
782 /* Lower to sea level */
783 for (x = 0; x <= _height_map.size_x; x++) {
784 if (HasBit(water_borders, BORDER_NW)) {
785 /* Top left */
786 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);
787 max_y = max((smallest_size * smallest_size / 64) + max_y, (smallest_size * smallest_size / 64) + margin - max_y);
788 if (smallest_size < 8 && max_y > 5) max_y /= 1.5;
789 for (y = 0; y < max_y; y++) {
790 _height_map.height(x, y) = 0;
791 }
792 }
793
794 if (HasBit(water_borders, BORDER_SE)) {
795 /* Bottom right */
796 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);
797 max_y = max((smallest_size * smallest_size / 64) + max_y, (smallest_size * smallest_size / 64) + margin - max_y);
798 if (smallest_size < 8 && max_y > 5) max_y /= 1.5;
799 for (y = _height_map.size_y; y > (_height_map.size_y - 1 - max_y); y--) {
800 _height_map.height(x, y) = 0;
801 }
802 }
803 }
804 }
805
807 static void HeightMapSmoothCoastInDirection(int org_x, int org_y, int dir_x, int dir_y)
808 {
809 const int max_coast_dist_from_edge = 35;
810 const int max_coast_Smooth_depth = 35;
811
812 int x, y;
813 int ed; // coast distance from edge
814 int depth;
815
816 height_t h_prev = I2H(1);
817 height_t h;
818
819 assert(IsValidXY(org_x, org_y));
820
821 /* Search for the coast (first non-water tile) */
822 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++) {
823 /* Coast found? */
824 if (_height_map.height(x, y) >= I2H(1)) break;
825
826 /* Coast found in the neighborhood? */
827 if (IsValidXY(x + dir_y, y + dir_x) && _height_map.height(x + dir_y, y + dir_x) > 0) break;
828
829 /* Coast found in the neighborhood on the other side */
830 if (IsValidXY(x - dir_y, y - dir_x) && _height_map.height(x - dir_y, y - dir_x) > 0) break;
831 }
832
833 /* Coast found or max_coast_dist_from_edge has been reached.
834 * Soften the coast slope */
835 for (depth = 0; IsValidXY(x, y) && depth <= max_coast_Smooth_depth; depth++, x += dir_x, y += dir_y) {
836 h = _height_map.height(x, y);
837 h = min(h, h_prev + (4 + depth)); // coast softening formula
838 _height_map.height(x, y) = h;
839 h_prev = h;
840 }
841 }
842
844 static void HeightMapSmoothCoasts(uint8 water_borders)
845 {
846 int x, y;
847 /* First Smooth NW and SE coasts (y close to 0 and y close to size_y) */
848 for (x = 0; x < _height_map.size_x; x++) {
849 if (HasBit(water_borders, BORDER_NW)) HeightMapSmoothCoastInDirection(x, 0, 0, 1);
850 if (HasBit(water_borders, BORDER_SE)) HeightMapSmoothCoastInDirection(x, _height_map.size_y - 1, 0, -1);
851 }
852 /* First Smooth NE and SW coasts (x close to 0 and x close to size_x) */
853 for (y = 0; y < _height_map.size_y; y++) {
854 if (HasBit(water_borders, BORDER_NE)) HeightMapSmoothCoastInDirection(0, y, 1, 0);
855 if (HasBit(water_borders, BORDER_SW)) HeightMapSmoothCoastInDirection(_height_map.size_x - 1, y, -1, 0);
856 }
857 }
858
866 static void HeightMapSmoothSlopes(height_t dh_max)
867 {
868 for (int y = 0; y <= (int)_height_map.size_y; y++) {
869 for (int x = 0; x <= (int)_height_map.size_x; x++) {
870 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;
871 if (_height_map.height(x, y) > h_max) _height_map.height(x, y) = h_max;
872 }
873 }
874 for (int y = _height_map.size_y; y >= 0; y--) {
875 for (int x = _height_map.size_x; x >= 0; x--) {
876 height_t h_max = 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;
877 if (_height_map.height(x, y) > h_max) _height_map.height(x, y) = h_max;
878 }
879 }
880 }
881
889 static void HeightMapNormalize()
890 {
891 int sea_level_setting = _settings_game.difficulty.quantity_sea_lakes;
892 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;
893 const height_t h_max_new = TGPGetMaxHeight();
894 const height_t roughness = 7 + 3 * _settings_game.game_creation.tgen_smoothness;
895
896 HeightMapAdjustWaterLevel(water_percent, h_max_new);
897
898 byte water_borders = _settings_game.construction.freeform_edges ? _settings_game.game_creation.water_borders : 0xF;
899 if (water_borders == BORDERS_RANDOM) water_borders = GB(Random(), 0, 4);
900
901 HeightMapCoastLines(water_borders);
902 HeightMapSmoothSlopes(roughness);
903
904 HeightMapSmoothCoasts(water_borders);
905 HeightMapSmoothSlopes(roughness);
906
907 HeightMapSineTransform(12, h_max_new);
908
909 if (_settings_game.game_creation.variety > 0) {
910 HeightMapCurves(_settings_game.game_creation.variety);
911 }
912
913 HeightMapSmoothSlopes(16);
914 }
915
923 static double int_noise(const long x, const long y, const int prime)
924 {
925 long n = x + y * prime + _settings_game.game_creation.generation_seed;
926
927 n = (n << 13) ^ n;
928
929 /* Pseudo-random number generator, using several large primes */
930 return 1.0 - (double)((n * (n * n * 15731 + 789221) + 1376312589) & 0x7fffffff) / 1073741824.0;
931 }
932
933
937 static inline double linear_interpolate(const double a, const double b, const double x)
938 {
939 return a + x * (b - a);
940 }
941
942
947 static double interpolated_noise(const double x, const double y, const int prime)
948 {
949 const int integer_X = (int)x;
950 const int integer_Y = (int)y;
951
952 const double fractional_X = x - (double)integer_X;
953 const double fractional_Y = y - (double)integer_Y;
954
955 const double v1 = int_noise(integer_X, integer_Y, prime);
956 const double v2 = int_noise(integer_X + 1, integer_Y, prime);
957 const double v3 = int_noise(integer_X, integer_Y + 1, prime);
958 const double v4 = int_noise(integer_X + 1, integer_Y + 1, prime);
959
960 const double i1 = linear_interpolate(v1, v2, fractional_X);
961 const double i2 = linear_interpolate(v3, v4, fractional_X);
962
963 return linear_interpolate(i1, i2, fractional_Y);
964 }
965
966
973 static double perlin_coast_noise_2D(const double x, const double y, const double p, const int prime)
974 {
975 double total = 0.0;
976
977 for (int i = 0; i < 6; i++) {
978 const double frequency = (double)(1 << i);
979 const double amplitude = pow(p, (double)i);
980
981 total += interpolated_noise((x * frequency) / 64.0, (y * frequency) / 64.0, prime) * amplitude;
982 }
983
984 return total;
985 }
986
987
989 static void TgenSetTileHeight(TileIndex tile, int height)
990 {
991 SetTileHeight(tile, height);
992
993 /* Only clear the tiles within the map area. */
994 if (IsInnerTile(tile)) {
995 MakeClear(tile, CLEAR_GRASS, 3);
996 }
997 }
998
1006 void GenerateTerrainPerlin()
1007 {
1008 if (!AllocHeightMap()) return;
1009 GenerateWorldSetAbortCallback(FreeHeightMap);
1010
1011 HeightMapGenerate();
1012
1013 IncreaseGeneratingWorldProgress(GWP_LANDSCAPE);
1014
1015 HeightMapNormalize();
1016
1017 IncreaseGeneratingWorldProgress(GWP_LANDSCAPE);
1018
1019 /* First make sure the tiles at the north border are void tiles if needed. */
1020 if (_settings_game.construction.freeform_edges) {
1021 for (int y = 0; y < _height_map.size_y - 1; y++) MakeVoid(_height_map.size_x * y);
1022 for (int x = 0; x < _height_map.size_x; x++) MakeVoid(x);
1023 }
1024
1025 int max_height = H2I(TGPGetMaxHeight());
1026
1027 /* Transfer height map into OTTD map */
1028 for (int y = 0; y < _height_map.size_y; y++) {
1029 for (int x = 0; x < _height_map.size_x; x++) {
1030 TgenSetTileHeight(TileXY(x, y), Clamp(H2I(_height_map.height(x, y)), 0, max_height));
1031 }
1032 }
1033
1034 IncreaseGeneratingWorldProgress(GWP_LANDSCAPE);
1035
1036 FreeHeightMap();
1037 GenerateWorldSetAbortCallback(NULL);
1038 }