Orbit Tessellation developer diary for Kerbal Space Program 2

Orbit Tessellation developer diary for Kerbal Space Program 2(kerbalspaceprogram.com)

192 points by bmease 5 years ago | 82 comments

modeless 5 years ago |

Space rendering is full of interesting problems like this. Another one is that single precision floating point doesn't have enough precision to represent both planet scale and human scale in the same coordinate system (let alone solar system scale or galaxy scale), yet GPUs don't support double precision well. So you have to make sure that you do calculations needing high precision on the CPU in double precision and only send the GPU coordinates it can handle, or your 3D models will get crunched by precision errors.

Another one is that a planet sphere renderer will often tesselate the sphere into quads in lat-lon space. Of course the quads are split into two triangles for rendering. However, at the poles, one of the triangles has zero area because two of its vertices are the same, the pole. Then when you texture map that "quad" with a square texture, half of the texture is not shown, and you get visible seams (Google Earth suffers from this artifact, or at least it did in the past). What's less obvious is that this problem is present to a lesser extent in every quad on the sphere, because the triangle with the horizontal edge nearer the pole is smaller than the other, so half of the texture is stretched and half is shrunk. The fix is to use homogeneous texture coordinates.

skykooler 5 years ago | |

KSP's approach to the precision problem is surprisingly simple: whenever you get more than two kilometers away from the origin, move the entire universe two kilometers so that the location of your craft, and all the physics-relevant computations on it, have small numbers as coordinates.

(This fix was known as Krakensbane: it solved a bug known as the Deep-Space Kraken, which was essentially that floating-point physics inaccuracies would tear your ship apart when you got much further than the moon or so, before it was implemented.)

lamontcg 5 years ago | | |

Pretty sure that the floating origin moves with the craft now every frame. The entire universe also orbits around the craft when it is below the inverse rotation altitude threshold, which means that PhysX is doing physics in the co-rotating reference frame. That means that the "First point of Ares" -- normally (1,0,0) -- rotates around the z-axis as the craft moves and you have to query Planitarium.right to determine what its current orientation is. That means that tick-to-tick coordinates change, which makes trajectory optimization hard because values in the future won't match at all. You have to remove that rotation to get something like actual inertial coordinates (after also removing the offset origin to the vessel as well).

They've also recently fixed issues with single precision calculation in KSP1 and used a double-precision QuaternionD.LookRotation in the maneuver nodes to keep interplanetary trajectories from hopping around a lot.

[ oh it also uses left handed coordinates, which is terrible which means (0,1,0) is the north pole and the left handed cross product gets used so dual vectors like angular momentum point south for east-going orbits -- except the Orbit class uses normal right handed vectors and when you forget to .xzy swizzle a vector for one reason or another you can wind up debugging an issue all day long ]

modeless 5 years ago | | |

That's interesting. It doesn't sound that simple though, I imagine there are some gotchas with that. They are probably constrained by what Unity allows.

In my custom engine I did the world to camera transform for each object on the CPU in double precision, essentially making the camera the origin for all subsequent single precision computations on the GPU. That works for small objects and even large objects that are split into small parts, like a planet split into LOD terrain tiles. But it didn't work for orbit lines because they are a single object at planet scale that you can zoom in on to see at human scale (I didn't have an adaptive tesselation system like the one in the article).

It also wouldn't have worked for galaxy scale, where even double precision wouldn't be enough. I don't know exactly what Celestia and similar "entire universe" apps do. Emulated quad precision floating point?

Edit: I just realized that you are talking about precision issues with the physics engine, while I'm talking about precision issues in the rendering engine. Related but slightly different. Physics engines aren't constrained by GPUs and can use double precision throughout. But they often have stability issues even in normal circumstances so I can certainly imagine that solar system scales would be a problem even in double precision.

gorgoiler 5 years ago | |

An interesting piece of industry-insider information, at least as far as I recall from the Sony pub regulars I knew back in the day: the colloquial term for the polar artefact you describe is the cat’s bumhole.

smcameron 5 years ago | | |

One way around this is cube-mapping. You construct a cube then normalize all the vertices to "over-inflate" it until it's a sphere. Then you have six textures mapped to the faces of the cube, and no cat's bumhole, and no international date-line zipper. If you subdivide the faces of the cube into rectangles via equal angles instead of naively into a grid, then cut each of the rectangles into two triangles by the shortest diagonal, then you get a very nice tessellation with triangles that are nice and fat (nearly equilateral) with no thin sliver triangles and they're all of approximately equal size. The other thing you can do is double the vertices along the cube face edges, so that no two cube faces share any vertices. In that way you can avoid some "hairy ball theorem" related problems when it comes time to do normal mapping, which involves constructing tangent and bitangent vectors for each vertex. Each face of the cube can have a field of tangents and bitangents with no discontinuities, and since no texture or normal map crosses any boundary between faces, you avoid problems that come up with such discontinuities. (Hairy ball theorem says it's impossible to construct a field of tangents and bitangents covering a sphere that does not contain some discontinuity, so one solution is to stuff the discontinuities between cube map faces where they cannot bother any texture or normal map.)

Tessellated sphere looks like this: https://imgur.com/l3GmWq3

nuclearsugar 5 years ago | |

Creating astronomy visualizations often involves all sorts of fun tricks. I work in a planetarium as a 3D animator and each day has interesting unique challenges. Indeed we have to remain mindful of not pushing Maya too hard when it comes to series of scale.

We use fluids as a way to create 3D nebulae that can be flown through. https://thefulldomeblog.com/2013/08/20/the-nebula-challenge/

Or if you constrain the fluid into a sphere, then you have a dynamic volumetric sun. https://thefulldomeblog.com/2013/07/30/customizing-a-close-u...

When needing to fly through a star field, relying on particle sprites is an easy way to quickly render thousands of stars. https://thefulldomeblog.com/2013/07/03/creating-a-star-field...

Background stars are achieved by point-constraining a poly sphere to the camera. Having a poly sphere allows for easy manipulation to create realistic diurnal motion. https://thefulldomeblog.com/2013/11/13/background-stars-v2/

Flying through a galaxy field can be achieved with loads of galaxy images mapped to poly planes. For galaxies that are seen edge on, we sometimes add more detail by emitting fluid from the image colors. https://thefulldomeblog.com/2013/07/16/flying-through-a-gala...

Simulating the bands of Jupiter is tricky but I've done some experiments with 2D fluids. https://thefulldomeblog.com/2014/01/30/jupiter-bands-simulat...

And of course since the visuals are rendered for a planetarium dome, we gotta render using a fisheye camera. These days all render engines support fisheye, but 10 years ago it was a different story. https://thefulldomeblog.com/2019/09/07/exploring-render-engi... https://thefulldomeblog.com/2013/06/28/fisheye-lens-shader-o... https://thefulldomeblog.com/2013/07/23/stitching-hemicube-re...

zlsa 5 years ago | | |

I'm sure you've heard this before, but have you checked out Space Engine[0]? It has some pretty advanced features, like path animations and cubemap rendering. I'm not sure how well it'd integrate into existing workflows, but I've used it for creating high dynamic range skyboxes for spacecraft renders.

[0]: http://spaceengine.org/

smcameron 5 years ago | | |

> Simulating the bands of Jupiter is tricky but I've done some experiments with 2D fluids.

Nice! I've always wanted to do some fluid dynamics on the surface of a sphere, but the math is too hard for me. I found a video on youtube where someone has done some interesting things a few years ago: https://www.youtube.com/watch?v=Lzagndcx8go&t=1s but there's very little information about it. Then there was what was done for the film 2010: The year we make contact" http://2010odysseyarchive.blogspot.com/2014/12/

I've had to resort to simpler means myself, which means faking it. I use OpenSimplex noise on the surface of a sphere, and from this I can find the gradient of the noise field tangent to the surface of the sphere, rotate this vector 90 degrees about an axis passing through the center of the sphere -- which is equivalent to some kind of spherical curl of the noise field -- which gives me a non-divergent velocity field. Because incompressible fluid flows are also non-divergent, there's a strong but superficial resemblance -- it looks like fluid flow, even though it is just an arbitrary process. Into this field, I dump a bunch of colored particles and let them flow around, painting alpha blended, slowly fading trails behind them onto the surface of a cube to be used later as textures of a cubemapped sphere.

For the bands, I superimpose a simple velocity field of counter rotating bands on top of this curl-noise generated velocity field. Something like: horizontal_velocity += K x sin(5 x latitude)

Results looks like this: https://duckduckgo.com/?q=gaseous-giganticus&t=h_&iax=images...

The idea for using the curl of a noise field to mimic fluid dynamics is from a paper by Robert Bridson, et al.: https://www.cs.ubc.ca/~rbridson/docs/bridson-siggraph2007-cu...

This program is open source, it's here: https://github.com/smcameron/gaseous-giganticus

gbrown_ 5 years ago | |

> yet GPUs don't support double precision well.

Are there GPUs without FP64 functionality at all? Or are you just referring to most consumer GPUs being built for FP32 performance over FP64?

Robadob 5 years ago | | |

It's not that GPUs don't support fp64, it's that for domestic gamer GPUs fp64 arithmetic is normally ~1:32 performance of fp32 arithmetic.

e.g. 1080gtx

    FP16 (half) performance
    138.6 GFLOPS (1:64)
    FP32 (float) performance
    8.873 TFLOPS
    FP64 (double) performance
    277.3 GFLOPS (1:32)

e.g. 3090rtx

    FP16 (half) performance
    35.58 TFLOPS (1:1)
    FP32 (float) performance
    35.58 TFLOPS
    FP64 (double) performance
    556.0 GFLOPS (1:64)

Only generally 'tesla' class cards targeted at super computers have a 1:2 ratio (e.g. v100, A100, Titan V). Note, I believe Titan V is the only Titan series GPU with good double performance, as the Volta architecture was never available to Geforce GPUs.

https://www.techpowerup.com/gpu-specs/geforce-gtx-1080.c2839

https://www.techpowerup.com/gpu-specs/geforce-rtx-3090.c3622

https://www.techpowerup.com/gpu-specs/tesla-v100-sxm3-32-gb....

https://www.techpowerup.com/gpu-specs/a100-sxm4-80-gb.c3746

https://www.techpowerup.com/gpu-specs/titan-v.c3051

modeless 5 years ago | | |

There are many GPUs with no double precision floating point support in hardware. Modern ones can probably emulate it. Older ones don't have any explicit support. Most real time 3D renderers do not use double precision at all.

91aintprime 5 years ago | |

    Some napkin/WolframAlpha math:
    if you wanted to use simple x,y,z coordinates,
    with the sun at the center
    and be able to represent locations at 30 AU (Neptune)
    with an accuracy of 1mm, e.g. 30AU vs 30.000...0001AU
    you'd need ~16 decimal digits of precision
    which is the same number of bits as a double (FP64)
    of course there's better ways to do this,
    in the surrounding smarter comments

jhgb 5 years ago | |

> Another one is that single precision floating point doesn't have enough precision to represent both planet scale and human scale in the same coordinate system (let alone solar system scale or galaxy scale), yet GPUs don't support double precision well.

Could you do double-single computations on a GPU? (By that I mean something like double-double arithmetic, only with two singles instead of two doubles.)

modeless 5 years ago | | |

Sure, with a performance penalty. Some GPUs do support double precision, though again at a performance penalty. You might run into issues with the fixed function parts of the GPU being single precision even on GPUs that support double precision types in shaders, depending on how you do things. Also, shading languages probably don't have nice libraries for double single precision so you'd have to roll your own, and probably without niceties like operator overloading.

It's not required for space rendering, as once everything is in camera coordinates you no longer have any visible precision issues (as long as you are using a float reverse Z buffer). You just have to be careful to make sure your world to camera transforms are done on the CPU, and you break large objects like planets into small LOD chunks with their own local coordinate systems, which you need to do anyway.

wwarren 5 years ago | |

Can’t we use an icosahedron for a better sphere?

modeless 5 years ago | | |

Yes, and there are many other tessellations you can use, if you texture it with a single texture. But you can't texture a whole planet with one texture if you allow zooming from planet to human scale, the texture would be terabytes. You must tile the sphere with textures that are loaded on demand, and textures are square, so it makes sense to divide the sphere into quads (actually a quadtree for zooming).

exDM69 5 years ago | | |

If you want to texture a sphere, the cubesphere is the best way to draw. It is what you get when you subdivide a cube using slerp instead of lerp for interpolation.

Icosahedron doesn't work well if you have textures. The triangle topology near the poles lead to bad texturing.

Icosahedron may work better if you have a fully procedural pipeline and don't need to worry about square textures.

fy20 5 years ago |

One of the things KSP taught me is that orbital mechanics aren't that complicated, but even so, pretty much all movies and TV shows about space were written by someone who doesn't even know the basics.

mypalmike 5 years ago |

I used a very similar approach to render airplane contrails in a flight sim back in the late 90s. The contrail had a binary tree representing the volume of space taken up by segments of the trail. Projecting this volume into screen space and comparing against a heuristic resulted in either rendering the segment or recursing down the tree for finer detail.

cas8 5 years ago |

KSP 2 has easily been my most anticipated game for a while now. It's a bummer that there's still a while to wait, but I'm hoping that it's worth it.

Toutouxc 5 years ago | |

You can give Simple Rockets 2 a try in the meantime. It uses fully customizable procedural parts (wings, fuel tanks, even engines) instead of premade parts like KSP, it looks a bit nicer and it includes a visual programming environment for your spacecraft (e.g. you can build a SpaceX-like autoland routine).

capableweb 5 years ago | | |

I've never tried Simple Rocket, could you compare it to KSP? At a glance, it seems more serious than KSP while KSP has a "fun" edge, but besides that they seem more similar than not.

Cthulhu_ 5 years ago | |

Same, so far they've mainly showed a lot of visual improvements, but I really hope the technical groundwork is being done as well.

deepsun 5 years ago |

My biggest problem with trajectories in KSP was that they flip non-continuously once the trajectory passes through a sphere of influence. I believe it would be much clearer and easier if trajectories were continuously changing but just marked once they pass through a SoI.

elil17 5 years ago |

My biggest question: who the hell plays KSP without the orbit map interface?

ranger207 5 years ago | |

Getting to the Mun manually isn't too hard once you know what you're doing. Get to a low orbit, then thrust prograde when the Mun comes over the horizon. Keep an eye on your remaining delta-v (or do the math beforehand and watch your stopwatch) and you should come pretty close. Make sure your Munar orbit is counterclockwise and returning is just prograde thrust again.

For a more immersive experience, install the RasterPropMonitor mod to get interactable IVA displays. Add a compatible camera mod and Docking Port Alignment Indicator and you can even do a multi-craft Apollo style mission entirely from the cockpit.

orbital-decay 5 years ago | |

Actually it can be a fun exercise flying purely in IVA with a slide rule and window- or periscope-based reticles, just like those on Apollo Lunar Module [1][2], or Russian space stations [3]. The Apollo descent and landing procedure included elaborate roll maneuvers to confirm everything visually with the landing point designator. You can measure the horizon curvature and use similar techniques to guess your altitude and attitude.

[1] https://apollo11space.com/apollo-11-windows/

[2] https://www.hq.nasa.gov/alsj/coas.htm

[3] (yes, ISS has an optical viewfinder called VShTV - it's installed in Zarya module. It was meant for emergencies and never been used to reorient the module manually, AFAIK)

esjeon 5 years ago |

I'm a bit puzzled here, after seeing the word "screen-space". I'm no game dev, but I know that there's tessellation shader for this very purpose. We can let the shader churn out more points on-demand in a separate step in the rendering pipeline. I think doing this in "screen-space" is a bit unnatural. (Just nitpicking.)

teraflop 5 years ago | |

"Screen space" refers to the coordinate system. Regardless of whether you were doing tessellation on the CPU or the GPU, you would want to use screen coordinates to make your decisions about which segments to subdivide, because what you care about is the deviation of the rendered curve from its "ideal" path. A large error in world coordinates doesn't matter if it's so far from the viewpoint that it looks tiny.

Tessellation shaders are useful for processing polygonal geometry with many thousands of polygons, but they have a fairly constrained programming model. And as you can see from the example images, rendering a high-quality orbit path only requires a few dozen vertices. The performance benefit from moving that computation into a tessellation shader is likely to be insignificant compared to the additional complexity and overhead.

esjeon 5 years ago | | |

Thanks for the reply. I've written graphics code only on more-or-less lab environments, and have read many papers mentioning screen-space algorithms which trades off accuracy for other characteristics. Maybe I'm triggered by that. lol

avereveard 5 years ago |

can't wait to see what they will be doing with multiplayer