How To Make A Random World Generator In Game Maker

Table of Contents • • • • • • • • • • • • • I wanted to generate interesting game maps that weren’t constrained to be realistic, and I wanted to try some techniques I hadn’t tried before. I usually make tile maps but instead used a different structure. What could I do with 1,000 polygons instead of 1,000,000 tiles? The distinct player-recognizable areas might be useful for gameplay: locations of towns, places to quest, territory to conquer or settle, landmarks, pathfinding waypoints, difficulty zones, etc. I generated maps with polygons, then rasterized them into tile maps that looked like this: Most procedural map generators, including some of my own previous projects, use noise functions (midpoint displacement, fractal, diamond-square, perlin noise, etc.) to generate a height map. I did not do that here.

Instead, I used a graph structure to model the things directed by gameplay constraints (elevation, roads, river flow, quest locations, monster types) and noise functions to model the variety not constrained by gameplay (coastline shape, river placement, tree placement). There were three main things I wanted for this project: good coastlines, mountains, and rivers. For the coastline, I wanted to make island maps that are surrounded by ocean, so that I don’t have to deal with people walking to the edge of the map. For the mountains, I started with something simple: mountains are whatever’s farthest from the coastline, so that you can always walk uphill to reach the top. For the rivers, I started with something simple: draw rivers from the coast to the mountains, so that you can always follow rivers down to the beach.

First, (2010) or an (2017). Read on to learn how it works, or get the. Here’s the overview of the process: Every project will have its own gameplay constraints. For this project, the gameplay constraints were partially taken from, a multiplayer RPG in which players start on the beach playing alone and then later join together on the mountaintop to fight bosses. Elevation directly corresponds to difficulty, and must monotonically increase, so that was a key constraint in the design.

I made this tutorial showing how you can create top down terrain in game maker using 2D perlin noise.

Elevation in Minecraft on the other hand isn’t constrained the same way, so the noise function they use works for that game. In multiplayer Age of Empires, the location of resources is constrained by the need to be somewhat balanced among the players; in Minecraft the distribution of resources is not constrained. When writing your own map generator, think about what which aspects of your map are set by the design and which can vary from map to map. Each of the ideas on this page can be used separately or together in your own map generator project. Polygons The first step is to generate some polygons. The simplest approach would be to use a hexagonal grid and perturb it a bit to make it look irregular.

This works (and the techniques on this page will work if you use a perturbed grid), but I wanted something even less regular than that, so I picked random points and generated, which are used for, including maps. The is incomplete but has some useful background.

I’m using nodename’s, which has an implementation of. Here’s an example of random dots (red) and the polygons that result: The polygon shapes and sizes are a bit irregular. Random numbers are more “clumpy” than what people expect. I want something closer to semi-random “blue noise”, or, not random points.

I approximate that by using a variant of, which is a fairly simple tweak to the random point locations to make them more evenly distributed. Lloyd relaxation replaces each point by the of the polygon. In my code I merely average the corners (see improveRandomPoints).

Here’s the result after running approximate Lloyd relaxation twice: Compare it to running. The more iterations, the more regular the polygons get. Running it twice gives me good results but every game will vary in its needs. Polygon sizes are improved by moving polygon centers.

The same approach works to improve edge lengths. Moving corners by averaging the nearby centers produces more uniform edge lengths, although it occasionally worsens the polygon sizes. In the code, see the improveCorners function. However, moving corners changes it from a Voronoi diagram to a. The algorithms for this map generator work with either style. Voronoi polygons are more uniformly sized, with varying shapes; barycentric dual polygons are more uniformly shaped, and the corners are more uniformly spaced. In the rest of the article I still call them Voronoi polygons and use screenshots of Voronoi, but the final demo uses the barycentric dual instead.

Using Voronoi adds some complexity so if you want to start with something simpler, try a square or hexagonal grid (you can see this in the demo). The rest of the techniques in this article will work with a grid. Optionally, randomly perturb the vertices of the grid to make it a little more natural looking. Map Representation I’m representing the map as two related: nodes and edges. The first graph has nodes for each polygon and edges between adjacent polygons.

It represents the, which is useful for anything involving adjacency (such as pathfinding). The second graph has nodes for each polygon corner and edges between corners. It contains the shapes of the polygons. It’s useful for anything involving the shapes (such as rendering borders). The two graphs are related. Every triangle in the Delaunay triangulation corresponds to a polygon corner in the Voronoi diagram. Every polygon in the Voronoi diagram corresponds to a corner of a Delaunay triangle.

Every edge in the Delaunay graph corresponds to an edge in the Voronoi graph. You can see this in the following diagram: Polygon A and B are adjacent to each other, so there is a (red) edge between A and B in the adjacency graph. For them to be adjacent there must be a polygon edge between them. The (blue) polygon edge connects corners 1 and 2 in the Voronoi shape graph.

Every edge in the adjacency graph corresponds to exactly one edge in the shape graph. In the Delaunay triangulation, triangle A- B- C connects the three polygons, and can be represented by corner 2. Thus, corners in the Delaunay triangulation are polygons in the Voronoi diagram, and vice versa. Here’s a larger example showing the relationship, with Voronoi polygon centers in red and corners in blue, and the Voronoi edges in white and the Delaunay triangulation in black: This duality means that I can represent the two graphs together. There are for combining the data from the two graphs.

In particular,. Each edge in a normal graph points to two nodes.

Instead of representing two edges in the two graph separately, I made edges point to four nodes: two polygon centers and two corners. It turns out to be quite useful to connect the two graphs together. With the combined representation, I can now use the Relationships Between Grid Parts sections of my.

They’re not grids so I’m not assigning grid coordinates, but many of the algorithms that work on grids also work here, and the algorithms that work on graphs also work here (on either of the two graphs). In the code, the graph/ directory has three classes: Center, Corner, and Edge: • Center.neighbors is a set of adjacent polygons • Center.borders is a set of bordering edges • Center.corners is a set of polygon corners • Edge.d0 and Edge.d1 are the polygons connected by the Delaunay edge • Edge.v0 and Edge.v1 are the corners connected by the Voronoi edge • Corner.touches is a set of polygons touching this corner • Corner.protrudes is a set of edges touching the corner • Corner.adjacent is a set of corners connected to this one Islands The second step is to draw the coastline. The borders of the map need to be water, but you can mark the other polygons as either water or land, using any approach you want. The coastline is then all the edges where land and water meet. Here’s an example that divides the world into land and water: In the code, Map.as contains the core map generation code. The IslandFunction returns True if a position is land, and False for water. There are four island functions included in the demo: • Radial uses sine waves to produce a round island • Perlin uses Perlin noise to control the shape • Square fills the entire map with land • Blob draws my You can use any shape, (including or or a ).

Or let the game designer draw their own shape. The code assigns water/land to both polygon centers and corners: • Assign water/land to the corners by setting Corner.water based on the IslandFunction.

• Assign water/land to the polygons by setting Center.water if some fraction of the corners have water set. A simple flood fill starting from the border of the map can determine which water areas are oceans (connected to the border) and lakes (surrounded by land): In the code, the flood fill runs on the polygon centers, and then we can decide what happens to corners: • Set Center.ocean for any polygon connected to the borders of the map through water polygons. Nfs Pro Street No Dvd Crack Download there.

If Center.water is set but.ocean is not, then it’s a lake. • Set Center.coast if the polygon is land but has an ocean border. Coastal areas will later get drawn as beaches. • Set Corner.ocean if the corner is surrounded by ocean polygons. • Set Corner.coast if the corner touches ocean and land polygons. • Reset Corner.water to be consistent with the surrounding area.

Elevation The most realistic approach would have been to define elevation first, and then define the coastline to be where the elevation reaches sea level. Instead, I’m starting with the goal, which is a good coastline, and working backwards from there. I set elevation to be the distance from the coast.

I originally tried elevations at polygon centers but setting elevations at corners worked out better. Corner-to-corner edges can serve as ridges and valleys. After calculating the elevation of corners ( Corner.elevation), the polygon elevation ( Center.elevation) is the average of the elevation at the corners. See the functions Map.assignCornerElevations and Map.assignPolygonElevations. Water polygons don’t count towards the distance. This is both because I expect lakes to be flat instead of sloped, and because this tends to build valleys around lakes, which helps guide rivers towards lakes.

One problem with the simple definition is that some islands have too many mountains and others have too few. To fix this, I redistribute the elevations to match a desired distribution, which has more low elevation land (coastline) than high elevation land (mountains). First, I sort the corners by elevation, and then I reset the elevation x of each to match the inverse of the desired cumulative distribution: y(x) = 1 - (1-x)^2. In the Map.redistributeElevations function, y is the position in the sorted list, and x is the desired elevation.

Using the quadratic formula, I can solve for x. This preserves ordering so that elevations always increase from the coast to the mountains. For any location, going downhill will eventually lead to the ocean. This diagram shows the steepest downhill direction from every corner, stored in Corner.downslope: By following the downhill arrows from any location, we eventually reach the ocean.

This will be useful for rivers but may also be useful for calculating and other features. I had two main goals for elevation: • Biome types: high elevations get snow, rock, tundra; medium elevations get shrubs, deserts, forests, and grassland; low elevations get rain forests, grassland, and beaches. • Rivers flow from high elevations down to the coast. Having elevations that always increase away from the coast means that there’s no local minima that complicate river generation. In addition, games may define their own use of elevation data. For example, uses elevation to distribute monsters.

This elevation calculation works for simple islands, which is what I needed for Realm of the Mad God. For continent generation, you’ll want to change this step to generate one or more mountain ranges that aren’t necessarily in the center, as well as isolated volcanos. Rivers Rivers and lakes are the two fresh water features I wanted. The most realistic approach would be to define moisture with wind, clouds, humidity, and rainfall, and then define the rivers and lakes based on where it rains.

Instead, I’m starting with the goal, which is good rivers, and working backwards from there. The island shape determines which areas are water and which are land. Lakes are water polygons that aren’t oceans. Rivers use the downhill directions shown earlier. I choose random corner locations in the mountains, and then follow the Corner.downslope path down to the ocean. The rivers flow from corner to corner: I tried both polygon centers and corners, but found that the corner graph made for much nicer looking rivers. Also, by keeping lakes flat, elevation tends to be lower near lakes, so rivers naturally flow into and out of lakes.

Multiple rivers can share the lower portion of their path. Every time a river flows through an edge, I increase the water volume stored in Edge.river by 1. At rendering time, the river width is the square root of the volume.

This approach is simple and works well. Moisture Since I’m working backwards, I don’t need moisture to form rivers. However, moisture would be useful for defining biomes (deserts, swamps, forests, etc.). Since rivers and lakes should form in areas with high moisture, I defined moisture to decrease as distance from fresh water increases. Corner.moisture is set to a^k for some a.

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