Planet 4 - Part 01 - Making a Mesh

Introduction to this series is here.

Phase 1 is initiated.  I will adhere to a keep-it-simple approach during development.  So setting up the window went very quickly; no config files, no nothing.

The first step was to create the nodes in a spherical arrangement.  I divided the space into unit cubes and looped through them.  Where the innermost and outermost vertices of the cube was on opposite sides of the surface, I placed a node.

Each node represents a surface of about 128m×128m.  Since they're neither square nor uniform the area differs from node to node.  I experimented with different sized planets a bit and decided that radius 60 makes a medium-sized planet.  The circumference is about 48km, which is definitely much further than I have ever traveled in Minecraft.  What's the point of an infinite world, then?

Fig. 1: Radius 60 Sphere - Each node represents a 128m×128m area

Next I move the nodes so that they are no longer on the sphere, but rather arranged in a grid.  This will make noticing and understanding bugs much easier.

Fig. 2: Nodes are now aligned to a grid for debugging visualization

I reduce the size of the planet to radius 5, implement an algorithm for finding their nearest neighbours and link them up.  Ideally, I would have used Delaunay triangulation, but I decided to keep it simple instead; I have never done Delaunay triangulation before.  So I looped through the nodes and checked adjacent grid points for neighbours to link to.  The first time I only checked in the positive directions.  Figure 3 shows the inadequacy of this optimization:

Fig. 3: Added node-to-node links - My first bug is apparent

A simple fix is to just check the negative directions as well.  This does slow it down a bit though.  There is a faster way, but it is complicated, so I stuck to the simple way.

Fig. 4: Fixed the links bug

While my current algorithm does find every node that will contain a part of the sphere's surface, this causes some foreseeable problems, in that the double layer in some regions will stop the erosion algorithm from working correctly.  I take a cross section to see what it looks like (Fig.5) and see two possible solutions.  I could get rid of all diagonal links, or I could remove the extra layer before linking up the nodes.

Fig. 5: Cross section shows double layering

I decided to implement the node removal method, since this will simplify the eventual creation of the zones.  Each node that has three axis-aligned neighbours that are closer to the center is removed.  The cross section looks okay, so I switch back to the full sphere view:

Fig. 6: Removing the extra layer is not working as intended

That's no sphere!  I tried a few different techniques, with no positive results.  Eventually I realize the problem:  When I remove a node I change the circumstances of the surrounding nodes.  Near the axis-aligned planes that pass through the sphere's origin this causes that some nodes will no longer be removed.  The solution is to keep a set of nodes that need to be removed, and only remove them after all have been found.

Fig. 7: It works now

And finally I put the nodes back into their original spherical arrangement.

Fig. 8: Off the grid and back to a sphere

Planet 4 - Part 00 - Introduction

Suddenly, I'm working on making a planet.  Again.

The first attempt was based on an article I read about a R.O.A.M.-based level-of-detail algorithm.  I focused so much on the data structures that I never got to the graphics, and so I lost interest.

The second attempt was to take a square grid, stretch and fold it into an octahedron and tesselate it into a sphere.  Though I managed to create an undistorted heightmap with continents, when I got to erosion I decided that distortion is too complicated.

The third attempt was to create a Minecraft-like flat world of cubes that wrap around at the edges, instead of being infinite.  At the time I was planning on adding "seamless" space travel.  I spent a lot of time working on finding a transformation that would allow the planet to be flat when you are close, but round when you are flying through space.  All the possible transformations had the flaw that the space-space had a two-to-one mapping to the planet-space; I.e, when you take off from a planet you end up in two locations in space.  What a mess!

In this new attempt, the fourth, the planet will be round and made up of voxels, using a technique called dual-contouring to allow diagonal and curved shapes.  The same technique was used by Miguel Cepero in his Voxel Farm engine, which is a component of the ForgeLight Engine being used in the EverQuest Next games.

My plan of action for Phase 1:

1. Get the basic framework up and running, so that I can debug right from the beginning.
2. Make a spherical mesh with reasonably evenly distributed vertices/nodes.  Each node represents a cuboid zone of voxels (a.k.a. a chunk).  Each edge represents a connection between adjacent zones.
3. Implement large-scale emulation and simulation procedures to generate the zone generation parameters.  E.g. continents, plate tectonics, water erosion, formation of rivers, lakes and oceans, temperature, prevailing winds, rainfall, and seasonal effects.
4. Serialization and deserialization of the zone generation parameter mesh.
5. Implement generation of zone voxel data from parameters using emulation and simulation of small-scale processes.  This is only triggered when the camera comes close enough to the zone.
6. Alteration of the voxels.  E.g. digging, building, explosions, eruptions, fluids.
7. Serialization of differences between the current zone voxel data and the procedural voxel data.
8. Automatic loading and unloading of zones.
9. Phase 2: Fancy graphics.

Next post: Part 01