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hello and welcome to a new coding adventure today we're going to be
looking at marching cubes
I'm afraid that's what passes for humor on this channel now before I can get to
the actual marching cubes we'll need some function that takes in a point in
3d space and gives out a single value then if we have some region of space
that we're particularly interested in we could use that function to sample points
at regular intervals inside of it. The highest value I got with my particular
function was 16 which I've colored white and the lowest was negative 34 which
I've colored black. Now I need to add a little slider here called the surface
level. As I move it up you can see that the points with values below the surface
level will disappear so those points we can think of as being in empty space
while the points at or above the surface level are on the surface or inside of
some shape. The goal of the marching cubes algorithm is to construct the
surface of that shape from triangles so that we can display it as a mesh. To
think about how this works we can simplify the problem to just a single
cube. There are eight corner points each of which can be either inside or outside
of the shape, which gives us 2 to the power 8, or 256 different configurations.
For example with just one point inside the shape we get a single triangle over
here. If the point above it is also inside the shape we get a little
rectangle made from two triangles and so on. As you can see some of the
configurations get pretty wild but thankfully there are only 14 unique
cases, the rest are just symmetries of those but still figuring them all out is a
tremendous headache that I did not want to undertake so I took the easy way out
and downloaded a triangulation table like this from the internet. So let's
take this case for example corner points 7 5 and 1 are active which we can
interpret as configuration one zero one zero zero zero one zero, or in a more
familiar number system configuration 162. This is the code for calculating that
index just in case you're interested. Now I can take this index and
look up the corresponding entry in that triangulation table this tells me to
join edges five zero one and five four zero and seven six eleven to form three
triangles so in code I look up the triangulation info here and loop through
each edge index. I then look up in another little table the indices of the
two corner points that form that edge. With those I can calculate the position
at the center of the edge and add that to my list of vertices. All we need to do
now is march through the entire space and construct the mesh one cube at a
time. Behold, marching cubes! By the way in the
code I just showed I was creating a new vertex regardless of whether one
already existed in that position. A more sophisticated implementation could
share vertices between triangles but I just wanted to make it as simple as
possible for the example. The result here is also extra blocky looking
because i'm always placing vertices at the midpoint of the edge, but to be more
accurate we should try estimate where along the edge the surface actually is.
For example if the value at the bottom of an edge is negative two and at the
top it's three and the surface value was say zero we would estimate that the
surface is forty percent up from the bottom of the edge since that's where
zero would be if the value was changing linearly. All right so once I had kind of
wrapped my head around these ideas and convinced my triangles to behave
themselves, I started experimenting with a little terrain editor. This works
simply by adding or subtracting from the points under the brush. It's a little slow
and finicky at the moment but it's still kind of cool to play around with so I'd
definitely like to improve it at some point. I then began experimenting with
layering noise in increasing frequencies and decreasing amplitudes to generate
terrain. I didn't spend too long on this but I think in general the results are
more interesting looking than pure height map terrain, because you get some
overhangs and nice details like that... although sometimes the physical
feasibility is questionable. Anyway one effect that I found kind of cool is
terracing. So the value at each point in space is being calculated as
-position.y which creates a ground plane. Plus the
noise value at that position. To add terraces we just need to add position.y
mod the terrace height that we want. A small change to the calculation and we
have spherical welds instead. While I was playing with some more noise I created
something that looked a little like a fish tank and I thought it might be fun
to explore an infinite underwater world. To support an endless world I needed to
be able to break things up into chunks like so. Once I had that working I added
a little cylinder as a submarine so I could swim around and I also converted
my marching cube script to a compute shader, which sped it up a lot. This would be
great if it didn't also turn everything into spaghetti. The problem was that I
was adding vertices one at a time, and because this is multi-threaded vertices
from other threads were getting added in between and messing up the order of the
triangles. I have only recently started learning about compute shaders (two episodes
ago to be precise) so I'm not sure what the correct way to tackle this is, but my
crude fix was to create a triangle struct, assign three vertices to that, and
then append that to the buffer. Finally I upgraded the submarine from a cylinder
to a capsule plus some 'turn-y' bits and I was away.
So this brings us to the end of another coding adventure. I'd definitely like to
expand on the terraforming tool and experimenting with the erosion from the
first episode on the terrain from this episode would be pretty interesting as
well I think. Anyway until next time, cheers