Planetary Rings

What feels like a logical progression after my recent experiments with gas giant rendering, I thought I would next take a look a adding some rings to my planet, turning it into more of a Saturn than a Jupiter.  Reading up on them, Saturn's rings are a pretty complex structure the formation of which is not completely understood - as ever Wikipedia is a good starting point for information about them. Although they extend from 7,000 to 80,000 Km above the planet's equator they are only a handful of metres thick, being made up of countless particles of mainly water ice (plus a few other elements) from the truly tiny to around ten metres across.

Gas giant with rings as seen at dusk from a nearby planet

My approach for rendering such a complex system is similar in many ways to that for the gas giant itself, rather than ray-tracing though I opted for a more conventional geometric representation of the rings and used a single strip of geometry encircling the planet.  For now the rings are fixed in the XZ plane around the planet’s origin but as the planet itself can have an arbitrary axis in my solar simulation that doesn’t feel like too much of a limitation to be going on with.

Rendering the basic geometry produces this:

Basic ring geometry - a single tri-strip

What’s immediately apparent is once again we fall foul straight away of the polygonal nature of our graphics – although the tri-strip here is a pretty coarse approximation to a circle, no matter how many triangles we add to it we are still going to be able to see straight edges if we get close enough.  Fortunately the solution is simple and by adding a check to the pixel shader to reject pixels that are more than our maximum radius from the planet origin or less than our minimum we immediately get a nice smooth circular ring:

Clipping pixels by distance in pixel shader to produce smooth ring shape

The only trick here is to ensure the vertices of the ring geometry are far enough away from the planet origin that the closest distance of the edges of the triangles is at least the maximum ring radius rather than the vertices themselves being that distance otherwise the outer edges of the ring will be clipped by the geometry:

Vertices (in black) need to be further away than the ring radius to
prevent the ring (in red) being clipped by the triangle edges

A little trig shows this simply to be:


    vertRadius = ringRadius/cos(PI/numSides)


This only applies to the outer edge of the ring as on the inner edge by definition the triangle edges are closer to the centre than the vertices.


Another point to watch is the rings have to of course go both in front and behind the planet itself.  This sounds simple but is made slightly more complex that it first appears as I don't have a Z-buffer available when rendering at the planetary scale due to each planet being rendered in it's own co-ordinate space - they are simply rendered back to front - so they don't share a common Z space that could be used for a Z buffer.  The range of depths would be massive anyway and likely to cause flimmering artifacts.  Add on top of this the fact that planetary atmospheres need to alpha blend on top of whatever is behind them (including the far side of the rings) and a Z buffer isn't really an option.


Instead I render the rings in two passes, the first pass drawn before the encircled planet to provide the bulk of the rings and to allow the planet's atmosphere to alpha blend onto them.  The second pass is drawn after the planet has been rendered and uses an additional ray-sphere and stencil test to only render to the portion of the screen covered by the planet and only where the rings are in front of the planet surface.

Of course one great big slab isn’t very convincing so to get something a bit more realistic I again opted for a similar technique to the gas giant, I took a nice high resolution image of Saturn from the internet and cut out a slice of it’s rings, filtering the result down to a 1x2048 colour ramp texture.

Mapping this texture onto the ring geometry immediately produces something far more pleasing:

Colour ramp mapped onto ring geometry

The colour ramp doesn’t have any alpha information so looks wrong but with a little experimentation it turns out that calculating an alpha value in the pixel shader from the intensity of the colour works pretty well and also softens the inner and outer extremities of the ring:

Colour ramp mapped onto ring geometry with alpha from intensity

As the ring geometry has no thickness however, viewing it from acute angles produces some unsightly single pixel artifacts.  Although in no way scientific, pulling the Fresnel hammer out of the toolbox however makes the effect far less objectionable:

Rings edge-on without Fresnel term showing unsightly aliasing

Rings edge-on with acute Fresnel term - aliasing is reduced at the
expense of increased transparency

Note I’m using a pretty narrow Fresnel band for this purpose otherwise the ring tends to fade out too much of the time.  The number of rings in the effect can be varied with a simple scale value just like for the gas giant.

Changing the scale of the texture look-up to provide fewer, wider rings

More Noise

Although the rings here are pretty decent (largely due to stealing them from a real image I suspect), there is a distinct lack of detail when viewed from anything resembling close up.

Ultimately it would be cool to be able to fade in large numbers of actual meshes to represent the larger ice chunks that make up the rings when the view is near to or actually within the rings, but even without that I thought there was something that could be done to help represent the higher frequency detail these ice particles and ‘ice-asteroids’ present.

As with so many other procedural effects, I decided that a bit of noise would probably add some interest, so I added some code to sample the same noise texture I used for previous effects.  The problem here though is that the particle detail in the rings is very high frequency in the cosmic scale of things but from a purely visual basis I wanted to show variety in the rings from all ranges.

To do this I re-used a trick from the terrain texturing shader where the scale of the texture co-ordinates is calculated on the fly using the partial derivative of the actual texture co-ordinates from the pixel - in this case from the position of the point being shaded on the plane of the rings.  The texture co-ordinates are scaled up or down in powers of two to produce as close to screen size texels as possible - in fact two scales are used by rounding the perfect scale up and down to the closest power of two then blending between these two texture samples to produce a smooth transition.

Ring noise sampled at uniform texel density produces aliasing and tiling at distance

Ring noise sampled at adaptive density to provide more uniform screen coverage without tiling

The texture co-ordinate effect you can see here is somewhat akin to mip-mapping but instead of using a lower resolution version of the texture to represent the same area of surface at a larger distance, I am instead using the same resolution texture to represent a larger area at that distance thereby eliminating the tiling effect often seen with high frequency textures at range.  Unlike mip-mapping it also works in the opposite direction, using the same resolution texture to represent smaller and smaller surface areas as it gets closer to the camera and each texel covers more than one pixel.

Using this signed noise value to lighten or darken each shaded point produces a nice fine grain effect in the rings I hope is vaguely representative of the countless millions of icy particles that in fact make them up.

Rings without noise

Rings with noise to simulate particulate detail

Lighting

As with everything else in my little solar system the rings need to be illuminated by the Sun, this is done simply using standard dot product lighting but the little twist here is to use the noise value from the previous step to slightly perturb the normal uses for the calculation.  This is a gross simulation of the arbitrary facets of the lumps of ice making up the rings being illuminated by the Sun and simply adds a bit of randomisation to the lighting.

A more dramatic effect which adds solidity to the rings is the shadow of the planet cast on to them.  Rather than using shadow mapping techniques this is calculated by doing a ray intersection in the pixel shader from the pixel towards the sun.  To soften the ubiquitous hard edge produced by ray-traced shadows the distance the ray travels through the planet is used to provide a soft edge where the distance is small falling off quickly to solid shadow.  While not strictly physically accurate when classically treating sunlight as a parallel source, I feel it adds to the effect.

Shadow of the gas giant cast onto the rings

Close up of edge of shadow showing the simulated penumbra

Finally the colours in the rings can be remapped again using the same RGB vector system I used before so each final colour component is a dot product of the shader output and the modulation vector passed in to the shader for that channel

Colour re-mapped rings

More drastically colour re-mapped rings :-)

And that's about it.  Any planetary body in my simulation can now have rings of arbitrary radii although it's probably best to not go crazy with them to keep some sense of reality.  Future work for them might include the inclusion of a particle system to provide a sense of thickness as the camera passes through the ring and/or even better a mesh particle system so you can see individual large ice chunks spinning away in space.

For now though, I'll wrap up with another couple of views of my gas giant's rings, comments as always are welcome!

Gas giant with rings from orbit of nearby planet

The same gas giant from nearer the surface of the planet

Gas Giants

Moving on from star rendering in my continuing tour of celestial bodies, I thought it would be interesting to have a go at trying to procedurally render a different type of entity – Gas Giants. 

There are four Gas Giants in our own Solar System, Jupiter, Saturn, Uranus and Neptune each very different from the other, but for my first go at rendering one I decided on the largest of these – namely Jupiter – to see how close to it’s distinctive appearance I could manage at real-time rates.

There is a lot of information available about Jupiter (http://en.wikipedia.org/wiki/Jupiter) and Gas Giants in general (http://en.wikipedia.org/wiki/Gas_giant) on sites such as Wikipedia, again the more I found out about the subject the more interesting it became and I strongly recommend a little background reading if it’s a subject that has any more than a passing interest for you.

Procedural Gas Giant generated and rendered with Osiris

Composite Jupiter image from the Cassini-Huygens probe
(NASA/JPL/Arizona University)

Like stars Gas Giants are conveniently smooth for rendering so I decided to use the same ray-tracing approach that I used for stars described in my previous posts.  This is not only efficient in terms of geometry but also produces lovely smooth spherical surfaces at all screen sizes which is important as I want to be able to fly right down near to the surface of my planets.

I also wanted to be able to produce a wide variety of gas giant effects with only a few input parameters so needed a system that could make interesting visual surfaces with more variation than just their colour.

As seen in the images above, gas giants tend to follow a basic structure of having bands of different coloured material at differing latitudes; these are counter-circulating streams of material called zones and belts and trying to simulate such a major feature seemed like a good starting point.  Using the planet space ‘y’ co-ordinate of the pixel being shaded (essentially the latitude) as a lookup into a colour ramp texture is a nice simple starting point for this effect.  In this case I generated the (1 x 2048) sized look up texture by taking a slice out of the above cassini image of Jupiter and filtering it down to the correct size – this gave me a genuine Jovian colour palette straight off-bat, support for other colours is described below.

Basic colour bands from look-up texture

Using Noise

Already there is a basic sense of a Jupiter like planet but of course it’s way too regular and ordered to give a proper idea of the thick turbulent gaseous atmosphere that makes up so much of this type of world.  Adding some degree of noise to the choice of colour from the ramp texture is an obvious choice in this situation, using the same volume noise texture that I used for the star rendering and combining two weighted channels of two octaves gives a far more interesting result

Noise channel #1

Noise channel #2

Noise channel #3

Noise channel #4

Combined noise

Colour ramp rendered with noise

This looks pretty decent from this fairly distant viewpoint but as the camera moves in towards the surface the pattern loses detail as it’s stretched out over more screen space.  Although the naturally soft nature of the surface detail makes this far less unsightly than it would be on a planet surface with more innate contrast, I thought it could be improved by adding additional octaves of progressively higher frequency noise.

The problem with adding higher frequencies however is that you start to get under-sampling artifacts showing up as sparkly noise in the effect when viewed from too large a distance for that frequency - an almost classic example of shader aliasing.  To avoid this two blend weights are calculated based upon a combination of the distance of the planet from the camera and it’s radius.  These two blend weights are passed to the gas giant pixel shader and used to control the contribution of the upper two bands of noise frequencies.  In this way the higher frequency noise blends in smoothly as the camera nears the surface and fades out as it moves further away.  By choosing the blend distances appropriately the transition is essentially invisible.

Close in to gas giant surface without high frequency noise

Close in to gas giant surface with high frequency noise

Silhouette Edges

The interior of the planet is now looking far more interesting but the silhouette edges are letting it down a bit.  Even at 1280x720 resolution the hard edges are unsightly and without any other anti-aliasing currently in use they jar against the smooth colour graduations of the surface.

While the plan is to add anti-aliasing in the future (either MSAA if performance allows or possibly FXAA) I realised there is something that can be done in the shader itself to improve matters and provide some other desirable effects.  Rather than having a hard edge around the sphere it would be far nicer to have a thin band of alpha pixels fading off around the edge to smooth things out.

Fortunately this is quite simple to do, by using a Fresnel term calculated with a dot product of the surface normal and the ray from the camera to the pixel being shaded the alpha value of the pixel can tend to zero as the surface becomes tangential to the view direction.  The only trick required is to control the amount of Fresnel to use to give a consistent on-screen width of just a couple of pixels for the fall off zone – without this the alpha zone would grow and shrink in size as the camera changed distance.  The Fresnel zone is calculated once in C++ and passed to the shader as a constant.

Planet silhouette edges without Fresnel based alpha - aliasing very evident

Planet silhouette edges with Fresnel based alpha - much smoother

A handy side effect is that by clamping the distance factor a larger fade out zone can be used when the camera nears the planet surface producing a completely non-scientific but rather nice atmosphere effect to soften the horizon at these close-up ranges - this can be seen in the high frequency noise planet close up images above.

Cyclones

Adding noise certainly made the surface of my gas giant more interesting but I wasn’t satisfied, it still wasn’t quite what I had hoped for.  Reading about gas giants and looking at the Cassini image at the top of this post it’s quickly becomes obvious that a primary feature of these planets are large numbers of cyclones and anti-cyclones ranging in size from barely perceptible to ones such as the “Great Red Spot” on Jupiter several times larger than the Earth itself combining to make for a highly turbulent surface.


Modelling planet scale cyclones accurately is a computationally expensive proposition beyond the capabilities of a real time system but there is something that can be done on a purely visual level to give at least a nod towards their presence.  To do this I decided to model a system where a potentially large number of cyclones could be represented as a set of cones emanating from the centre of the planet each with their own radius and rotational strength.  In the pixel shader the point being shaded is tested against this set of cones and should it fall within one is then rotated around that cone’s axis by the cone’s rotational strength scaled by the points distance from the cone’s central axis.


Testing a point against potentially hundreds of cones in the pixel shader is however a whole heap of processing so an efficient way to do so is required.  The method I decided upon was to store the cone information in a relatively low resolution cube map texture that could be sampled using the normal of the planet sphere at the point being shaded to determine which cone the point in question fell within, if any.  This way a single texture read provides all the information without having to iterate over each cone individually in the shader.


The cyclone cube map texture uses an uncompressed 32bit format encoded as follows:

• Red : X component of the unit length axis of the cone that encloses or is closest to this texel
• Green : Y component of the unit length axis of the cone that encloses or is closest to this texel
• Blue : Normalised rotational strength of the cyclone whos cone this texel is affected by
• Alpha : Normalised radius of the cyclone whos cone this texel is affected by, the sign of this value represents the sign of the Z component of the unit length cone axis that is computed in the shader

The format is set up so each byte is interpreted by the GPU as a signed normalised number so the values -128 to +127 are stored in the texture bytes which then arrive in the range [-1, +1] when the texture is sampled in the pixel shader.


The normalised rotational strength of the cyclone and normalised radius values encoded in the texture are scaled in the shader based upon minimum and maximum values passed to it in shader constants.


A little experimentation showed that between 100 and 200 cones of sensible radii could be effectively encoded using a cube map only 128x128 on each side, no two cones being allowed to be within one texel’s worth of angle to avoid filtering artifacts.  A benefit of storing axis and radius information in the cube map rather than actual per-texel offsets is that oversampling artifacts in the texture sampling are avoided as the distance calculations in the shader are operating on the same axial values for every pixel affected by that cone – the down side is that each pixel can only be affected by a single cyclone but I am happy to live with that for now.

Colour coding the pixels based upon the cone axis they are closest to and therefore affected by produces what is essentially a spherical Voronoi diagram of the points where the central axes of each cone penetrates the surface of the sphere

Voronoi diagram showing area of influence of each cyclone

Colour coding the pixels instead with a greyscale value indicating the distance from the central axis of their nearest cone produces the following effect

Position and strength of each cyclone

Clearly indicating the size and position of each cyclone.  Finally, using a combination of this distance value and a global maximum rotational strength supplied to the shader in a constant to rotate each sample point around it’s closest cone axis produces the final cyclone effect:

Final Gas Giant with cyclones

A number of cyclones of different size and strength are easily visible here – it’s not perfect but I think it’s a worthwhile addition that makes the overall effect more interesting.

Colours and Bands

The final step is to allow the shader to produce more varied effects for the potentially large number of gas giants I want my procedural universe to be able to contain.  There are two additional parameters that I’ve added to help support this increase in variety.

The first is a simple scale value that is used to control the mapping of latitude values onto the colour ramp texture.  By increasing the scale the width of the bands can be reduced and their number increased while decreasing the scale of course produces the opposite effect – fewer, wider  bands

Gas Giant with twice as many bands

Gas Giant with half as many bands

The second is a colour remapping post-process for taking the RGB generated by the shader and altering it to add variety.  The manner I thought simplest to do this was to pass three vectors to the shader that are multiplied by the red, green and blue shader colour values immediately before the shader returns.  For example passing (1, 0, 0), (0, 1, 0) and (0, 0, 1) would leave the colour unchanged as the red output is just the red input, the green output just the green input and so on.

Passing different values however completely changes the result allowing the final red, green and blue components that end up on the screen to be an arbitrary mix of those from the shader proper.  Although any range could be used some care needs to be taken to keep the general luminosity in a sensible range or we end up with completely black or pure white planets.  A degree of over-brightening can however produce some funky alien worlds.

Colour remapped gas giant

More dramatically colour remapped gas giant

Further variation could be achieved by using a different noise  texture, different noise octave scales and weights or a different colour ramp texture but for now I think this is sufficient.

Future work

Although the cyclone system was developed for gas giants, there is no reason it couldn't also be applied to other bodies with atmospheres.  The clouds on my Earth style planets for example are currently read from a fBm based cube map but it would be interesting to see how they look with cyclones applied – something else to put on my already lengthy TODO list I think.

This post is already in great danger of suffering from TL:DR so I’ll wrap it up there, my parting shot is this image from the surface of one of the Earth type planets in my solar system that shows the gas giant rising over the horizon.  Always more to do, but I’m quite pleased with the result so far.

Gas Giant viewed from the surface of a nearby Earth-like planet