Creating maps of the noise functions

3r33838. 3r3-31. One of the most popular articles on my site is dedicated to 3r3828. generating polygonal maps
( Translation 3r33858. On Habré). Creating such cards requires a lot of effort. But I did not begin with this, but with
much
a simpler task that I will describe here. This simple technique allows you to create such cards in less than 50 lines of code:
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Creating maps of the noise functions draw 3r33856. such maps: it depends on the language, graphics library, platform, etc. I'll just explain how
Fill array
map data. 3r33853. 3r33838. 3r33853. 3r33838. [h2] Noise 3r3808. 3r33853. 3r33838. The standard way to generate 2D maps is to use a limited band noise function, such as a Perlin noise or simplex noise, as a building block. Here's what the noise function looks like:
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3r3334. 3r33866. 3r33853. 3r33838. We assign each point of the map a number from 0.0 to 1.0. In this image, 0.0 is black and 1.0 is white. 3r3338. 3r33858. Here's how to set the color of each grid point in the syntax of a language similar to C:
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3r3737. for (int y = 0; y < height; y++) {
for (int x = 0; x < width; x++) {
double nx = x /width - 0.? ny = y /height - 0.5;
value[y] [x]= noise (nx, ny ) 3r3-3870.} 3r3-3870.} 3r3-3765. 3r3-3666. 3r33838. The loop will work the same in jаvascript, Python, Haxe, C ++, C #, Java, and most other popular languages, so I will show it in a C-like syntax so that you can convert it to the language you need. In the remaining part of the tutorial, I will show how the body of the loop changes (line Value[y]W2w2w231. = ) When adding new functions. The demo will show the complete example. 3r33853. 3r33838. 3r33853. 3r33838. Some libraries will need to shift or multiply the values obtained, to recover them in the interval from 0.0 to 1.0. 3r33853. 3r33838. 3r33853. 3r33838.

Height 3r3808. 3r33853. 3r33838. The noise itself is just a collection of numbers. We need to give it meaning . The first thing you might think - to tie the noise value to the height (this is called a "height map"). Let's take the noise shown above and draw it as a height: 3r33853. 3r33838. 3r33853. 3r33838.

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  3r3737. elevation[y] [x]= noise (nx, ny); 3r33737. 3r33766. 3r33853.  3r33838. Yes, that's all. These cards have remained the same, but now I will call them    elevation    (tall), not    value    . 3r33853.  3r33838. 3r33853.  3r33838. We got a lot of hills, but nothing more. What's wrong? 3r33853.  3r33838. 3r33853.  3r33838. 3r3192. Frequency    3r33853.  3r33838. Noise can be generated at any    frequency 3r33856. . So far I have chosen only one frequency. Let's see how it affects. 3r33853.  3r33838. 3r33853.  3r33838. 3r33585. Try changing the value of the slider    (in original) and see what happens at different frequencies: 3r35353.  3r33838. 3r33853.  3r33838.

3r3124. 3r33866. 3r33853. 3r33838. Here the scale just changes. At first it seems not very useful, but it is not. I have another tutorial (3r3-33130. Translation of 3r33858. On Habré), which explains 3r3-3555. theory 3r3r56. : concepts such as frequency, amplitude, octaves, pink and blue noise, and so on. 3r33853. 3r33838. 3r33853. 3r33838.

  3r3737. elevation[y] [x]= noise (freq * nx, freq * ny); 3r33737. 3r33766. 3r33853.  3r33838. It is also sometimes useful to recall    wavelength    which is the inverse of frequency. With frequency doubling, the size is only halved. The doubling of the wavelength all doubles. The wavelength - the distance measured in pixels /tile /meters, or any other units that you have selected for the cards. It is associated with the frequency:    wavelength = map_size /frequency    . 3r33853.  3r33838. 3r33853.  3r33838. 3r3192. Octaves 3r3193. 3r33853.  3r33838. To make the elevation map more interesting, we have    add noise with different frequencies 3r3r566. : 3r33853.  3r33838. 3r33853.  3r33838.

3r3163. 3r33866. 3r33853. 3r33838. 3r33853. 3r33838.

  3r3737. elevation[y] [x]= 1 * noise (1 * nx, 1 * ny); 3r33838. + 0.5 * noise (2 * nx, 2 * ny); 3r33838. + ??? * noise (4 * nx, 2 * ny); 3r33737. 3r33766. 3r33853.  3r33838. Let's mix in a large low-frequency card hills with small high-hills. 3r33585. Move the slider    (original) to add small hills to the mix:
 3r33838. 3r33853.  3r33838.

3r3184. 3r33866. 3r33853. 3r33838. Now it is much more like the fractal relief we need! We can get hills and uneven mountains, but we still have no flat plains. For this you need something else. 3r33853. 3r33838. 3r33853. 3r33838. 3r3192. Redistribution 3r33853. 3r33838. The noise function gives us values between 0 and 1 (or -1 to +? depending on the library). To create flat plains, we can raise the height to the power of . 3r33585. Move the slider (in the original of the article) to receive different degrees. 3r33853. 3r33838. 3r33853. 3r33838.

3r3737. e = 1 * noise (1 * nx, 1 * ny); 3r33838. + 0.5 * noise (2 * nx, 2 * ny); 3r33838. + ??? * noise (4 * nx, 4 * ny); 3r33838. elevation[y] [x]= Math.pow (e, exponent); 3r33737. 3r33766. 3r33853. 3r33838. High values of 3r33855. lower average heights into plains , and low values raise average heights towards mountain peaks. We need to lower them. I use power functions because they are simpler, but you can use any curve; I have a more complicated [leech=https://www.redblobgames.com/articles/noise/2d/#spectrum] demo 3r33858. . 3r33853. 3r33838. 3r33853. 3r33838. Now that we have a realistic elevation map, let's add biomes! 3r33853. 3r33838. 3r33853. 3r33838.

Biomes 3r3808. 3r33853. 3r33838. Noise gives numbers, but we need a map with forests, deserts and oceans. The first thing you can do is turn small heights into water:
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3r3737. function biome (e) {
if (e < waterlevel) return WATER;
else return LAND;
} 3rr3766.
3r33838. Wow, this is already becoming a procedurally generated world! We have water, grass and snow. But what if we need more? Let's make a sequence of water, sand, grass, forest, savannah, desert, and snow:
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Relief based on elevation [/i] 3r33853. 3r33838. 3r33853. 3r33838.

  3r3737. function biome (e) {
if (e 3r37532. else if (e  < 0.2) return BEACH;
else if (e  < 0.3) return FOREST;
else if (e  < 0.5) return JUNGLE;
else if (e  < 0.7) return SAVANNAH;
else if e  < 0.9) return DESERT;
else return SNOW;
)  3r33838. Wow, that looks great! For your game you can change the values and biomes. There will be much more jungle in Crysis; Skyrim has a lot more ice and snow. But no matter how you change the numbers, this approach is rather limited. The types of relief correspond to heights, therefore they form stripes. To make them more interesting, we need to choose biomes based on something else. Let's create    the second is 3r33856. noise map for humidity. 3r33853.  3r33838. 3r33853.  3r33838.

Above - the noise of heights; below - the noise of humidity [/i] 3r33853. 3r33838. 3r33853. 3r33838. Now let's use the height and humidity of together r3r3856. . In the first image illustrated below axis y - is the height (image taken from above), and the x axis - the humidity (second picture above). This gives us a convincing map:
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3r33320. 3r33866. 3r33853. 3r33838. Relief based on two noise values  3r33853. 3r33838. 3r33853. 3r33838. Low heights are the oceans and coasts. Great heights are rocky and snowy. In between, we get a wide range of biomes. The code looks like this:
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  3r3737. function biome (e, m) {
if (e 3r3333337. if (e  < 0.12) return BEACH;
if (e> 0.8) {
if (m  < 0.1) return SCORCHED;
if (m  < 0.2) return BARE;
if (m 3r34343. return SNOW; 3r33838.}
3r3433870. mr.333384. return SNOW; 3r33838.}
3r3433870. re 3) 0.6) {
If (m 3r33348. If (m 3r33349. Return TAIGA; 3r33870.} 3r3-3870. 3r3-33870. If (e> 0.3) {
If (m 3r333544. If (m 3r33355. If (e3r) TEMPERATE_RAIN_FOREST; 3r3-3870.} 3r3-3870. 3r3-3870. If (m  < 0.16) return SUBTROPICAL_DESERT;
If (m  < 0.33) return GRASSLAND;
If (m  < 0.66) return TROPICAL_SEASONAL_FOREST;
Return TROPICAL_RAIN_FOREST;
}

66. 3r33838. If necessary, you can change all these values in accordance with the requirements of your game. 3r33853. 3r33838. 3r33853. 3r33838. If we do not need biomes, then smooth gradients (see 3-333372. This article 3r33858.) Can create colors: 3r35353. 3r33838. 3r33853. 3r33838.

Climate 3r3808. 3r33853. 3r33838. In the previous section, I used height 3r33856. as a replacement r3r3855. temperature . The greater the height, the lower the temperature. However, temperatures are also influenced by geographic latitude. Let's use for temperature control and altitude, and latitude:
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3r3405. 3r33866. 3r33853. 3r33838. Near the poles (higher latitudes), the climate is cold, and on the tops of mountains (high altitude) is also colder climate. While I worked for it is not very much: for the right approach to these parameters need a lot of fine tuning. 3r33853. 3r33838. 3r33853. 3r33838. There is also 3r33855. Seasonal 3r33856. changing of the climate. In summer and winter the northern and southern hemisphere are becoming warmer and colder, but at the equator, the situation is not particularly changed. Here, too, much can be done, for example, one can model the prevailing winds and ocean currents, the influence of biomes on climate and the averaging effect of oceans on temperature. 3r33853. 3r33838. 3r33853. 3r33838.

Islands 3r3808. 3r33853. 3r33838. In some projects I needed the borders of the map to be water. This turns the world into one or more islands. There are many ways to do this, but in my polygon map generator I used a fairly simple solution: I changed the height as `e = e + a - b * d ^ c` where `d` - distance from the center (on a scale of 0-1). Another option is to change `e = (e + a) * (1 - b * d ^ c)` . Constant `a` raises everything up, `b` lowers the edges down, and `c 3r3373765. controls the rate of decline. 3r33853. 3r33838. 3r33853. 3r33838.`

3r33440. 3r33866. 3r33853. 3r33838. 3r33855. I'm not quite happy with this and there is still much to explore. Should it be Manhattan or Euclidean distance? Should it depend on the distance to the center or from the distance to the edge? Should the distance be squared, or be linear, or have some other degree? Should it be the addition /subtraction or multiplication /division, or something else? Original article try Add, a = 0.? b = 0.? c = 2.0 or try Multiply, a = 0.0? b = 1.0? c = 1.5. The options that suit you are dependent on your project. 3r33853. 3r33838. 3r33853. 3r33838. Why even stick to standard math functions? As I told in my

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24-11-2018, 15:18

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Biomes 3r3808. 3r33853. 3r33838. Noise gives numbers, but we need a map with forests, deserts and oceans. The first thing you can do is turn small heights into water: 3r33838. 3r33853. 3r33838.

weber

24-11-2018, 15:18

Algorithms / Mathematics / Game development

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Biomes 3r3808. 3r33853. 3r33838. Noise gives numbers, but we need a map with forests, deserts and oceans. The first thing you can do is turn small heights into water:
3r33838. 3r33853. 3r33838.