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/* $Id$ */

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/** @file tgp.cpp OTTD Perlin Noise Landscape Generator, aka TerraGenesis Perlin */

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#include "stdafx.h"

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#include <math.h>

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#include "openttd.h"

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#include "clear_map.h"

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#include "clear_map.h"

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#include "variables.h"

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#include "void_map.h"

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#include "tgp.h"

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#include "genworld.h"

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#include "core/alloc_func.hpp"

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#include "core/random_func.hpp"

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#include "settings_type.h"

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#include "landscape_type.h"

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#include "table/strings.h"

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/*

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 *

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 * Quickie guide to Perlin Noise

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 * Perlin noise is a predictable pseudo random number sequence. By generating

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 * it in 2 dimensions, it becomes a useful random map, that for a given seed

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 * and starting X & Y is entirely predictable. On the face of it, that may not

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 * be useful. However, it means that if you want to replay a map in a different

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 * terrain, or just vary the sea level, you just re-run the generator with the

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 * same seed. The seed is an int32, and is randomised on each run of New Game.

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 * The Scenario Generator does not randomise the value, so that you can

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 * experiment with one terrain until you are happy, or click "Random" for a new

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 * random seed.

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 *

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 * Perlin Noise is a series of "octaves" of random noise added together. By

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 * reducing the amplitude of the noise with each octave, the first octave of

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 * noise defines the main terrain sweep, the next the ripples on that, and the

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 * next the ripples on that. I use 6 octaves, with the amplitude controlled by

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 * a power ratio, usually known as a persistence or p value. This I vary by the

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 * smoothness selection, as can be seen in the table below. The closer to 1,

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 * the more of that octave is added. Each octave is however raised to the power

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 * of its position in the list, so the last entry in the "smooth" row, 0.35, is

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 * raised to the power of 6, so can only add 0.001838...  of the amplitude to

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 * the running total.

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 *

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 * In other words; the first p value sets the general shape of the terrain, the

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 * second sets the major variations to that, ... until finally the smallest

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 * bumps are added.

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 *

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 * Usefully, this routine is totally scaleable; so when 32bpp comes along, the

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 * terrain can be as bumpy as you like! It is also infinitely expandable; a

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 * single random seed terrain continues in X & Y as far as you care to

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 * calculate. In theory, we could use just one seed value, but randomly select

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 * where in the Perlin XY space we use for the terrain. Personally I prefer

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 * using a simple (0, 0) to (X, Y), with a varying seed.

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 *

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 *

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 * Other things i have had to do: mountainous wasnt mountainous enough, and

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 * since we only have 0..15 heights available, I add a second generated map

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 * (with a modified seed), onto the original. This generally raises the

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 * terrain, which then needs scaling back down. Overall effect is a general

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 * uplift.

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 *

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 * However, the values on the top of mountains are then almost guaranteed to go

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 * too high, so large flat plateaus appeared at height 15. To counter this, I

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 * scale all heights above 12 to proportion up to 15. It still makes the

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 * mountains have flatish tops, rather than craggy peaks, but at least they

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 * arent smooth as glass.

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 *

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 *

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 * For a full discussion of Perlin Noise, please visit:

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 * http://freespace.virgin.net/hugo.elias/models/m_perlin.htm

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 *

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 *

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 * Evolution II

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 *

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 * The algorithm as described in the above link suggests to compute each tile height

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 * as composition of several noise waves. Some of them are computed directly by

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 * noise(x, y) function, some are calculated using linear approximation. Our

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 * first implementation of perlin_noise_2D() used 4 noise(x, y) calls plus

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 * 3 linear interpolations. It was called 6 times for each tile. This was a bit

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 * CPU expensive.

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 *

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 * The following implementation uses optimized algorithm that should produce

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 * the same quality result with much less computations, but more memory accesses.

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 * The overal speedup should be 300% to 800% depending on CPU and memory speed.

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 *

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 * I will try to explain it on the example below:

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 *

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 * Have a map of 4 x 4 tiles, our simplifiead noise generator produces only two

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 * values -1 and +1, use 3 octaves with wave lenght 1, 2 and 4, with amplitudes

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 * 3, 2, 1. Original algorithm produces:

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 *

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 * 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

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 * 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

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 * 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

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 * 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

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 *

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 * 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

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 * 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

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 * 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

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 * 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

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 *

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 *

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 * Optimization 1:

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 *

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 * 1) we need to allocate a bit more tiles: (size_x + 1) * (size_y + 1) = (5 * 5):

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 *

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 * 2) setup corner values using amplitude 3

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 * {    -3.0        X          X          X          3.0   }

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 * {     X          X          X          X          X     }

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 * {     X          X          X          X          X     }

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 * {     X          X          X          X          X     }

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 * {     3.0        X          X          X         -3.0   }

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 *

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 * 3a) interpolate values in the middle

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 * {    -3.0        X          0.0        X          3.0   }

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 * {     X          X          X          X          X     }

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 * {     0.0        X          0.0        X          0.0   }

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 * {     X          X          X          X          X     }

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 * {     3.0        X          0.0        X         -3.0   }

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 *

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 * 3b) add patches with amplitude 2 to them

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 * {    -5.0        X          2.0        X          1.0   }

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 * {     X          X          X          X          X     }

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 * {     2.0        X         -2.0        X          2.0   }

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 * {     X          X          X          X          X     }

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 * {     1.0        X          2.0        X         -5.0   }

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 *

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 * 4a) interpolate values in the middle

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 * {    -5.0       -1.5        2.0        1.5        1.0   }

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 * {    -1.5       -0.75       0.0        0.75       1.5   }

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 * {     2.0        0.0       -2.0        0.0        2.0   }

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 * {     1.5        0.75       0.0       -0.75      -1.5   }

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 * {     1.0        1.5        2.0       -1.5       -5.0   }

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 *

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 * 4b) add patches with amplitude 1 to them

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 * {    -6.0       -0.5        1.0        2.5        0.0   }

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 * {    -0.5       -1.75       1.0       -0.25       2.5   }

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 * {     1.0        1.0       -3.0        1.0        1.0   }

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 * {     2.5       -0.25       1.0       -1.75      -0.5   }

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 * {     0.0        2.5        1.0       -0.5       -6.0   }

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 *

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 *

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 *

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 * Optimization 2:

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 *

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 * As you can see above, each noise function was called just once. Therefore

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 * we don't need to use noise function that calculates the noise from x, y and

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 * some prime. The same quality result we can obtain using standard Random()

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 * function instead.

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 *

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 */

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#ifndef M_PI_2

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#define M_PI_2 1.57079632679489661923

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#define M_PI   3.14159265358979323846

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#endif /* M_PI_2 */

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/** Fixed point type for heights */

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typedef int16 height_t;

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static const int height_decimal_bits = 4;

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static const height_t _invalid_height = -32768;

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/** Fixed point array for amplitudes (and percent values) */

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typedef int amplitude_t;

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static const int amplitude_decimal_bits = 10;

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/** Height map - allocated array of heights (MapSizeX() + 1) x (MapSizeY() + 1) */

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struct HeightMap

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{

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	height_t *h;         //< array of heights

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	uint     dim_x;      //< height map size_x MapSizeX() + 1

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	uint     total_size; //< height map total size

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	uint     size_x;     //< MapSizeX()

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	uint     size_y;     //< MapSizeY()

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};

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/** Global height map instance */

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static HeightMap _height_map = {NULL, 0, 0, 0, 0};

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/** Conversion: int to height_t */

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#define I2H(i) ((i) << height_decimal_bits)

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/** Conversion: height_t to int */

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#define H2I(i) ((i) >> height_decimal_bits)

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/** Conversion: int to amplitude_t */

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#define I2A(i) ((i) << amplitude_decimal_bits)

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/** Conversion: amplitude_t to int */

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#define A2I(i) ((i) >> amplitude_decimal_bits)

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/** Conversion: amplitude_t to height_t */

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#define A2H(a) ((a) >> (amplitude_decimal_bits - height_decimal_bits))

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/** Walk through all items of _height_map.h */

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#define FOR_ALL_TILES_IN_HEIGHT(h) for (h = _height_map.h; h < &_height_map.h[_height_map.total_size]; h++)

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/** Noise amplitudes (multiplied by 1024)

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 * - indexed by "smoothness setting" and log2(frequency) */

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static const amplitude_t _amplitudes_by_smoothness_and_frequency[4][12] = {

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	/* Very smooth */

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	{1000,  350,  123,   43,   15,    1,     1,    0,    0,    0,    0,    0},

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	/* Smooth */

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	{1000, 1000,  403,  200,   64,    8,     1,    0,    0,    0,    0,    0},

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	/* Rough */

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	{1000, 1200,  800,  500,  200,   16,     4,    0,    0,    0,    0,    0},

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	/* Very Rough */

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	{1500, 1000, 1200, 1000,  500,   32,    20,    0,    0,    0,    0,    0},

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};

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/** Desired water percentage (100% == 1024) - indexed by _settings_game.difficulty.quantity_sea_lakes */

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static const amplitude_t _water_percent[4] = {20, 80, 250, 400};

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/** Desired maximum height - indexed by _settings_game.difficulty.terrain_type */

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static const int8 _max_height[4] = {

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	6,       ///< Very flat

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	9,       ///< Flat

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	12,      ///< Hilly

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	15       ///< Mountainous

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};

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/** Check if a X/Y set are within the map.

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 * @param x coordinate x

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 * @param y coordinate y

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 * @return true if within the map

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 */

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static inline bool IsValidXY(uint x, uint y)

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{

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	return ((int)x) >= 0 && x < _height_map.size_x && ((int)y) >= 0 && y < _height_map.size_y;

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}

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/** Allocate array of (MapSizeX()+1)*(MapSizeY()+1) heights and init the _height_map structure members */

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static inline bool AllocHeightMap()

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{

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	height_t *h;

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	_height_map.size_x = MapSizeX();

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	_height_map.size_y = MapSizeY();

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	/* Allocate memory block for height map row pointers */

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	_height_map.total_size = (_height_map.size_x + 1) * (_height_map.size_y + 1);

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	_height_map.dim_x = _height_map.size_x + 1;

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	_height_map.h = CallocT<height_t>(_height_map.total_size);

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	if (_height_map.h == NULL) return false;

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	/* Iterate through height map initialize values */

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	FOR_ALL_TILES_IN_HEIGHT(h) *h = _invalid_height;

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	return true;

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}

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/** Free height map */

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static inline void FreeHeightMap()

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{

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	if (_height_map.h == NULL) return;

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	free(_height_map.h);

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	_height_map.h = NULL;

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}

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/** RandomHeight() generator */

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static inline height_t RandomHeight(amplitude_t rMax)

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{

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	amplitude_t ra = (Random() << 16) | (Random() & 0x0000FFFF);

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	height_t rh;

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	/* Scale the amplitude for better resolution */

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	rMax *= 16;

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	/* Spread height into range -rMax..+rMax */

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	rh = A2H(ra % (2 * rMax + 1) - rMax);

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	return rh;

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}

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/** One interpolation and noise round */

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static bool ApplyNoise(uint log_frequency, amplitude_t amplitude)

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{

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	uint size_min = min(_height_map.size_x, _height_map.size_y);

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	uint step = size_min >> log_frequency;

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	uint x, y;

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	assert(_height_map.h != NULL);

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	/* Are we finished? */

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	if (step == 0) return false;

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	if (log_frequency == 0) {

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		/* This is first round, we need to establish base heights with step = size_min */

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		for (y = 0; y <= _height_map.size_y; y += step) {

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			for (x = 0; x <= _height_map.size_x; x += step) {

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				height_t height = (amplitude > 0) ? RandomHeight(amplitude) : 0;

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			}

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		}

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		return true;

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	}

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	/* It is regular iteration round.

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	 * Interpolate height values at odd x, even y tiles */

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	for (y = 0; y <= _height_map.size_y; y += 2 * step) {

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		for (x = 0; x < _height_map.size_x; x += 2 * step) {

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			height_t h01 = (h00 + h02) / 2;

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		}

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	}

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	/* Interpolate height values at odd y tiles */

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	for (y = 0; y < _height_map.size_y; y += 2 * step) {

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		for (x = 0; x <= _height_map.size_x; x += step) {

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			height_t h10 = (h00 + h20) / 2;

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		}

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	}

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	for (y = 0; y <= _height_map.size_y; y += step) {

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		for (x = 0; x <= _height_map.size_x; x += step) {

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		}

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	}

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	return (step > 1);

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}

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/** Base Perlin noise generator - fills height map with raw Perlin noise */

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static void HeightMapGenerate()

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{

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	uint size_min = min(_height_map.size_x, _height_map.size_y);

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	uint iteration_round = 0;

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	amplitude_t amplitude;

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	bool continue_iteration;

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	uint log_size_min, log_frequency_min;

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	int log_frequency;

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	/* Find first power of two that fits */

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	for (log_size_min = 6; (1U << log_size_min) < size_min; log_size_min++) { }

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	log_frequency_min = log_size_min - 6;

   342

   343

	do {

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		log_frequency = iteration_round - log_frequency_min;

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		if (log_frequency >= 0) {

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			amplitude = _amplitudes_by_smoothness_and_frequency[_settings_game.game_creation.tgen_smoothness][log_frequency];

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		} else {

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			amplitude = 0;

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		}

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		continue_iteration = ApplyNoise(iteration_round, amplitude);

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		iteration_round++;

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	} while(continue_iteration);

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}

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/** Returns min, max and average height from height map */

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static void HeightMapGetMinMaxAvg(height_t *min_ptr, height_t *max_ptr, height_t *avg_ptr)

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{

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	height_t h_min, h_max, h_avg, *h;

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	int64 h_accu = 0;

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	/* Get h_min, h_max and accumulate heights into h_accu */

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	FOR_ALL_TILES_IN_HEIGHT(h) {

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		if (*h < h_min) h_min = *h;

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		if (*h > h_max) h_max = *h;

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		h_accu += *h;

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	}

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	/* Get average height */

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	h_avg = (height_t)(h_accu / (_height_map.size_x * _height_map.size_y));

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   372

	/* Return required results */

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	if (min_ptr != NULL) *min_ptr = h_min;

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	if (max_ptr != NULL) *max_ptr = h_max;

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	if (avg_ptr != NULL) *avg_ptr = h_avg;

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}

   377

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/** Dill histogram and return pointer to its base point - to the count of zero heights */

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static int *HeightMapMakeHistogram(height_t h_min, height_t h_max, int *hist_buf)

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{

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	int *hist = hist_buf - h_min;

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	height_t *h;

   383

   384

	/* Fill histogram */

   385

	FOR_ALL_TILES_IN_HEIGHT(h) {

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		assert(*h >= h_min);

   387

		assert(*h <= h_max);

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		hist[*h]++;

   389

	}

   390

	return hist;

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}

   392

   393

/** Applies sine wave redistribution onto height map */

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static void HeightMapSineTransform(height_t h_min, height_t h_max)

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{

   396

	height_t *h;

   397

   398

	FOR_ALL_TILES_IN_HEIGHT(h) {

   399

		double fheight;

   400

   401

		if (*h < h_min) continue;

   402

   403

		/* Transform height into 0..1 space */

   404

		fheight = (double)(*h - h_min) / (double)(h_max - h_min);

   405

		/* Apply sine transform depending on landscape type */

   406

		switch(_settings_game.game_creation.landscape) {

   407

			case LT_TOYLAND:

   408

			case LT_TEMPERATE:

   409

				/* Move and scale 0..1 into -1..+1 */

   410

				fheight = 2 * fheight - 1;

   411

				/* Sine transform */

   412

				fheight = sin(fheight * M_PI_2);

   413

				/* Transform it back from -1..1 into 0..1 space */

   414

				fheight = 0.5 * (fheight + 1);

   415

				break;

   416

   417

			case LT_ARCTIC:

   418

				{

   419

					/* Arctic terrain needs special height distribution.

   420

					 * Redistribute heights to have more tiles at highest (75%..100%) range */

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					double sine_upper_limit = 0.75;

   422

					double linear_compression = 2;

   423

					if (fheight >= sine_upper_limit) {

   424

						/* Over the limit we do linear compression up */

   425

						fheight = 1.0 - (1.0 - fheight) / linear_compression;

   426

					} else {

   427

						double m = 1.0 - (1.0 - sine_upper_limit) / linear_compression;

   428

						/* Get 0..sine_upper_limit into -1..1 */

   429

						fheight = 2.0 * fheight / sine_upper_limit - 1.0;

   430

						/* Sine wave transform */

   431

						fheight = sin(fheight * M_PI_2);

   432

						/* Get -1..1 back to 0..(1 - (1 - sine_upper_limit) / linear_compression) == 0.0..m */

   433

						fheight = 0.5 * (fheight + 1.0) * m;

   434

					}

   435

				}

   436

				break;

   437

   438

			case LT_TROPIC:

   439

				{

   440

					/* Desert terrain needs special height distribution.

   441

					 * Half of tiles should be at lowest (0..25%) heights */

   442

					double sine_lower_limit = 0.5;

   443

					double linear_compression = 2;

   444

					if (fheight <= sine_lower_limit) {

   445

						/* Under the limit we do linear compression down */

   446

						fheight = fheight / linear_compression;

   447

					} else {

   448

						double m = sine_lower_limit / linear_compression;

   449

						/* Get sine_lower_limit..1 into -1..1 */

   450

						fheight = 2.0 * ((fheight - sine_lower_limit) / (1.0 - sine_lower_limit)) - 1.0;

   451

						/* Sine wave transform */

   452

						fheight = sin(fheight * M_PI_2);

   453

						/* Get -1..1 back to (sine_lower_limit / linear_compression)..1.0 */

   454

						fheight = 0.5 * ((1.0 - m) * fheight + (1.0 + m));

   455

					}

   456

				}

   457

				break;

   458

   459

			default:

   460

				NOT_REACHED();

   461

				break;

   462

		}

   463

		/* Transform it back into h_min..h_max space */

   464

		*h = (height_t)(fheight * (h_max - h_min) + h_min);

   465

		if (*h < 0) *h = I2H(0);

   466

		if (*h >= h_max) *h = h_max - 1;

   467

	}

   468

}

   469

   470

/** Adjusts heights in height map to contain required amount of water tiles */

   471

static void HeightMapAdjustWaterLevel(amplitude_t water_percent, height_t h_max_new)

   472

{

   473

	height_t h_min, h_max, h_avg, h_water_level;

   474

	int water_tiles, desired_water_tiles;

   475

	height_t *h;

   476

	int *hist;

   477

   478

	HeightMapGetMinMaxAvg(&h_min, &h_max, &h_avg);

   479

   480

	/* Allocate histogram buffer and clear its cells */

   481

	int *hist_buf = CallocT<int>(h_max - h_min + 1);

   482

	/* Fill histogram */

   483

	hist = HeightMapMakeHistogram(h_min, h_max, hist_buf);

   484

   485

	/* How many water tiles do we want? */

   486

	desired_water_tiles = (int)(((int64)water_percent) * (int64)(_height_map.size_x * _height_map.size_y)) >> amplitude_decimal_bits;

   487

   488

	/* Raise water_level and accumulate values from histogram until we reach required number of water tiles */

   489

	for (h_water_level = h_min, water_tiles = 0; h_water_level < h_max; h_water_level++) {

   490

		water_tiles += hist[h_water_level];

   491

		if (water_tiles >= desired_water_tiles) break;

   492

	}

   493

   494

	/* We now have the proper water level value.

   495

	 * Transform the height map into new (normalized) height map:

   496

	 *   values from range: h_min..h_water_level will become negative so it will be clamped to 0

   497

	 *   values from range: h_water_level..h_max are transformed into 0..h_max_new

   498

	 * , where h_max_new is 4, 8, 12 or 16 depending on terrain type (very flat, flat, hilly, mountains)

   499

	 */

   500

	FOR_ALL_TILES_IN_HEIGHT(h) {

   501

		/* Transform height from range h_water_level..h_max into 0..h_max_new range */

   502

		*h = (height_t)(((int)h_max_new) * (*h - h_water_level) / (h_max - h_water_level)) + I2H(1);

   503

		/* Make sure all values are in the proper range (0..h_max_new) */

   504

		if (*h < 0) *h = I2H(0);

   505

		if (*h >= h_max_new) *h = h_max_new - 1;

   506

	}

   507

   508

	free(hist_buf);

   509

}

   510

   511

static double perlin_coast_noise_2D(const double x, const double y, const double p, const int prime);

   512

   513

/**

   514

 * This routine sculpts in from the edge a random amount, again a Perlin

   515

 * sequence, to avoid the rigid flat-edge slopes that were present before. The

   516

 * Perlin noise map doesnt know where we are going to slice across, and so we

   517

 * often cut straight through high terrain. the smoothing routine makes it

   518

 * legal, gradually increasing up from the edge to the original terrain height.

   519

 * By cutting parts of this away, it gives a far more irregular edge to the

   520

 * map-edge. Sometimes it works beautifully with the existing sea & lakes, and