Simulating physics for voxel constructions (Minecraft, Dwarf Fortress, etc)?

Question

I'm hoping to prototype some very basic physics/statics simulations for "voxel-based" games like Minecraft and Dwarf Fortress, so that the game can detect when a player has constructed a structure that should not be able to stand up on its own.. Obviously this is a very fuzzy definition -- whether a structure is impossible depends upon multitude of material and environmental properties -- but the general idea is to motivate players to build structures that resemble the buildings we see in the real world. I'll describe what I mean in a bit more detail below, but I generally want to know if anyone could suggest either an potential approach to the problem or a resource that I could use.

Here's some examples of buildings that could be impossible if the material was not strong enough. Here's some example situations. My understanding of this subject is not great but bear with me.

If this structure were to be made of concrete with dimensions of, say, 4m by 200m, it would probably not be able to stand up. Because the center of mass is not over its connection to the ground, I think it would either tip over or crack at the base.

The center of gravity of this arch lies between the columns holding it up, but if it was very big and made of a weak, heavy material, it would crumble under its own weight.

This tower has its center of gravity right over its base, but if it is sufficiently tall then it only takes a bit of force for the wind to topple it over.

Now, I expect that a full-scale real-time simulation of these physics isn't really possible... but there's a lot of ways that I could simplify the simulation. For example:

• Tests for physics-defying structures could be infrequently and randomly performed, so a bad building doesn't crumble right as soon as it is built, but as much as a few minutes later.
• Minecraft and Dwarf Fortress hardly perform rigid- or soft-body physics. For this reason, any piece of a building that is deemed to be physically impossible can simple "pop" into rubble instead of spawning a bunch of accurate physics props.

Answer 1

Have you considered taking an existing 3d environment physics engine and "rounding off" orientations of objects? In the case of your first object (the L-shaped thing), you could run a simulation of a continuous, non-voxelized object of similar shape behind the scenes and then monitor that object for orientation changes. In a simple case, if the object's representation of the continuous hits the ground, the object in the voxelized gameplay world could move its blocks to the ground.

Answer 2

I don't think there is a feasible way to do this. Minecraft has no notion of physical structure. So you will have to look at each block individually to determine if it should fall (there are other considerations but this is minimum). You would therefore need a way to distinguish between ground and "not ground". This is modeling problem first and foremost, not a programming problem (not even simulation design). I think this question is out of scope for SO.

For instance consider the following model, that may give you an indication of the complexities involved:

• each block above height = 0 experiences a "down pull" = P, P may be any of the following:
  • 0 if the box is supported by another box
  • m*g (where m is its mass which depends on material density * voxel volume) otherwise if it is free
• F represents some "friction" or "glue" between vertical faces of boxes, it counteracts P.
  • This friction should have a threshold beyond which it "breaks" and the block then has a net pull downwards.
  • if m*g < sum F, box stays where it is. Otherwise, box falls.
  • F depends on the pairs of materials in contact
  • for n=2, so you can form a line of blocks between two towers
• F is what causes the net pull of a box to be larger than m*g. For instance if you have two blocks a-b-c with c being on d, then a pulls on b, so b should be "heavier" than m*g where it contacts c. If this net is > F, then the pair a-b should fall.

You might be able to simulate the above and get interesting results, but you will find it really challenging to handle the case where there are two towsers with a line of blocks between them: the towers are coupled together by line of blocks, there is no longer a "tip" to the line of blocks. At this stage you might as well get out your physics books to create a system of boxes and springs and come up with equations that you might be able to solve numerically, but in a full 3D system you will have a 3D mesh of springs to navigate iteratively to converge to force values on each box and determine which ones move.

Answer 3

A professor of mine suggested that I look at this paper.

Additionally, I found the keyword for what it is I'm looking for. "Structural Analysis." I bought a textbook and I have a long road ahead of me.