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This is just a short note to highlight the visual impact that mip map generation and texture filtering methods can have on a final rendered result. It’s not rocket science and will be common knowledge to many, but I felt this was a nice clear example of how significant the effects can be and worth sharing.
I’ve recently been playing around with procedural city and road generation which has of course led to rendering of road surfaces for which I am using a trivially simple programmer art texture:
Even though I knew that find detail on textures viewed at extreme angles are always troublesome, feeding this through the normal mip map generation code with the existing trilinear texture filtering however produced a surprisingly disappointing result:
As you can see, the white lines in the road vanish very quickly with distance as their light coloured texels are swamped by the dark road surface around them during mip map down sampling – not at all realistic and bad enough for me to take a second look. The first thing was to look at the mip map generation code to see if it could be persuaded to keep more of the detail that I cared about. Current each mip map level was being generated using a naive 2×2 box filter with uniform weights:
lower_mip_texel = (higher_mip_texel1+higher_mip_texel2+higher_mip_texel3+higher_mip_texel4)/4;
very easy, very fast but also very bad at keeping detail. There are many better filters out there with varying quality/performance tradeoffs but I thought it worth trying a quick and simple change to weight the pixels by their approximate luminosity, calculated by simply averaging each source texel’s red, green and blue channels clamped to a chosen range:
higher_mip_texel_weight = Clamp((higher_mip_texel_red+higher_mip_texel_green+higher_mip_texel_blue)/3, 50, 255) lower_mip_texel = ( (higher_mip_texel1*higher_mip_texel_weight1)+ (higher_mip_texel2*higher_mip_texel_weight2)+ (higher_mip_texel3*higher_mip_texel_weight3)+ (higher_mip_texel4*higher_mip_texel_weight4)/ (higher_mip_texel_weight1+higher_mip_texel_weight2+ higher_mip_texel_weight3+higher_mip_texel_weight4);
This then favours brighter texels which will be more visible in the final render. Using this code to generate the mip maps instead of the uniformly weighted filter produced immediately better results:
While the white lines are now visible far more into the distance they become disproportionately fat as the lower mip level texels cover more and more screen space. There’s not much that can be done about this as however we filter the texture when making the mip maps we are either going to end up with no white lines or bit fat ones.
The next step then is to stop using trilinear filtering at runtime and instead switch to anisotropic filtering where the filter kernel shape effectively changes with the aspect of the textured surface on screen so the GPU can for example filter a wider area of the texture in the ‘u’ axis than it does in the ‘v’ and has more information for choosing the mip level to read each filter sample from. Returning to the original uniformly weighted mip maps where the lines disappeared so early but switching to anisotropic filtering produces noticible better results than either attempt so far:
and finally for good measure using the weighted mip maps with anisotropic filtering:
Not as dramatic effect as when switching to weighted mips with trilinear filtering but still an improvement and the best result of all.
So why not use anisotropic filtering all the time? well it comes down to compatibility and performance, not all legacy GPUs can support it although most modern cards can and even on cards that do there is a performance cost as the GPU is having to do significantly more work – the effects speak for themselves though and going forward I expect it will become the default setting for most games to avoid over-blurry textures as objects move away from the near plane.
Last post I talked about the perhaps not so interesting topic of data generation and caching, not a subject many people can get very excited about, but this time I want to talk about something I think is far more interesting. City Generation.
I’ve been interested in procedural landscape/planet generation for at least ten years, and over that time have seen at least dozens if not hundreds of landscape projects produced by other people out there who share this interest. One thing many of these projects have in common however is their landscapes however pretty tend to be fairly devoid of human infrastructure. One reason is it’s generally easier due to their inherent fractal nature to generate decent looking mountains, valleys and even trees and grass than it is to produce realistic roads, railways, towns and cities. Heightfield generation for landscapes is also a well covered topic with many professional and amateur research papers and articles on the subject – not so much on infrastructure simulation.
I’m as guilty of this as anyone else – none of the several landscape projects I’ve created in the past could boast anything particularly man made, no roads, no bridges, no buildings or at least none that were arranged in a manner more sophisticated than randomly dotted around on flat bits of ground.
So I thought it about time I got stuck in to what I consider to be a very interesting problem – that of procedural city generation. A tricky problem to be sure but that is of course what makes it interesting.
As with embarking upon any other problem, Google is your friend and after a little digging and reading I turned up a number of resources full of ideas on how cities can be generated. I’ve listed a few here that I have found interesting here which should provide an introduction to anyone wishing to take this subject further:
- Procedural Modeling of CitiesYoav I H Parish, Pascal Müllerhttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.92.5961&rep=rep1&type=pdf
- A Survey of Procedural Techniques for City GenerationGeorge Kelly, Hugh McCabehttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.91.8713&rep=rep1&type=pdf
- Real-time Procedural Generation of `Pseudo Infinite’ CitiesStefan Greuter, Jeremy Parker, Nigel Stewart, Geoff Leachhttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.88.7296&rep=rep1&type=pdf
- Procedural City ModelingThomas Lechner, Ben Watson, Uri Wilensky, Martin Felsenhttp://ccl.northwestern.edu/papers/ProceduralCityMod.pdf
There are also various commercial, open source and experimental projects to be found on the net, probably the best known commercial product is the heavyweight City Engine (http://www.procedural.com/cityengine/features.html) while independent projects such as http://www.synekism.com are also worth a look (a city simulation video game focused on dynamically generated content. The project was started is currently maintained by three university students in Canada)
First Things First
Of course before a city can be generated I need to know where to put it in the world – I do have an entire planet to play with here. Eventually I would like to have a system something along the lines of:
- Select a number of random points on the planet’s landmasses that are at least a given distance from each other
- Group clumps of nearby city points into political entities – these will form the countries
- Create Voronoi cells around these point groups – add a little noise and hopefully we have political boundaries for countries
- Use A* or other pathing algorithm to form primary road routes between each city point and it’s neighbours
- Generate cities
However that’s all still on the drawing board so for now I’m just picking points at random that aren’t too close to each other and not too close to water. Simples.
Laying Out The City
The approach I’m taking is to first generate a road network for the city, then to find all the bounded areas enclosed by the roads (I am calling these “charts”) before subdividing these charts into convex “lots” each of which will ultimately receive a building type chosen based upon city parameters and lot placement.
The road network is made up of two types of entity, “road segments” and “junctions”. The starting point for generation is a set of one or more junctions placed randomly within the central area of the city, each of which has between two and five connection points onto which road segments can be added. A loop then continually looks at any junctions in the road network that have connection points without roads attached and tries to add a road segments onto each of them. In addition to adding road segments onto junctions it also looks at any road segments that are only connected at one end – either to a junction or to a preceding road segment – and tries to add another road segment or junction on to that segment.
Make sense? Effectively each iteration of the loop causes the road network to grow by one step, each step either adding a road segment onto a previous one, adding a junction onto a previous road segment or adding a road segment onto a previous junction. Each road segment is given a “generation” number, the ones created from the initially placed junctions are generation zero and then every time a junction is added on to the end of a road segment which then spawns further road segments that aren’t continuations of the original road these child segments are given a higher generation number, 1, 2, 3, etc. This generation number can then be used later when deciding on the type of road geometry to create – generation #0 could be dual carriageway for example, generation #1 main roads and generation #2 narrower secondary streets.
Proximity constraints are applied at each step to prevent roads being created that would be too close to existing roads or junctions, and connection tests are made to see if an open road end is close enough to a junction with an open connection point to allow the two to be connected. The amount of variation in road heading also changes with generation and distance from the centre of the city – so low generation roads tend to be straighter while high generation (i.e. minor roads) tend to wriggle around more creating the suburbs. The amount of variation also increases as roads are further from the city centre.
To illustrate the process, these three images are sequential representations of the generation of one city’s road network:
In these images the Green roads are generation zero, Yellow is one, Blue is two, Magenta is three and Red is four. You will see that at certain points it appears to skip a generation (a red road directly from a blue one for example) – this is a result of a road segment from the intermediate generation being created then removed due to a proximity constraint violation but then the cause of the violation in turn being later removed due to a violation of it’s own allowing a new road of a later generation to replace the original.
Once no more roads or junctions can be created due to proximity constraints or distance from city centre checks the process terminates.
Charting it up
Once the entire road network has been created the next step is to find all the enclosed areas (which I call “charts”) which will eventually provide the lots for buildings to be placed on. To do this I first use Andrew’s Monotone Chain Algorithm to find the convex hull that encloses the entire road network, tracing around from any exterior road vertex with this then produces one big chart enclosing the outskirts of the city. Tracing around from all other uncharted vertices in turn then adds a number of additional charts each representing an enclosed area of the city.
The charts produced from the above road network look like this:
As you can see each chart represents a connected area of the city entirely enclosed by roads or the city boundary. They are pretty much all concave though and hard to work with further due to this complexity, so the next step is to break these charts down into convex “lots” onto which individual buildings can be placed. There are several ways this can be done, and I tried a few of them to see which worked best.
First I tried combining “ears” of the charts into convex regions. Ear clipping is a common algorithm for triangulating complex polygons and involves finding sets of three adjacent vertices where the vector between the first and third vertex doesn’t cross any other edge of the polygon, effectively forming a corner or “ear” – you keep doing this until you have no polygon left which as long as there aren’t any holes is guaranteed to occur. The downside of this approach is that you end up with all sorts of random shapes many of which are narrow slivers or shards not very well suited to building lot usage.
Next I tried finding pairs of vertices in the polygon that were as diametrically opposite as possible while having a vector between them that didn’t intersect any other polygon edge. The thought was that this would continually chop the polygon roughly in half producing more even lot distribution but in practice the shapes produced were no more regular and still not suitable.
Finally the solution I settled on was to find the convex hull of each chart (again using Andrew’s Monotone Chain) and from this find the vector representing the hull’s longest axis. This was done by summing the length of each edge into buckets each representing an angle range (10 degrees in my case) then taking the angle from the bucket with the longest total edge length accumulated. The chart was then rotated by this angle to align this longest axis with the Y axis before finally clipping the chart into two pieces across the middle in the X axis to form two new charts. Repeatedly doing this until the individual charts are small enough to count as lots produces a set of output charts many but not all of which are convex – I decided to classify the convex ones as building lots and the remaining concave ones as greenfield lots for parks, car parks or other non-building purposes.
The results of this lot subdivision on the above city looks like this:
Here the green lots are suitable for building, the red lots are concave and thus classified for parks or similar and the blue lots are isolated from the road network and not suitable for use at all. Removing the isolated lots and tweaking the colours produces this:
Here the grey charts are suitable for building with the green ones representing parks – the red charts have been classified as being too small to be considered further – in practice these would probably end up being simple tarmac areas suitable for street furniture. Although it’s far from perfect I’m not too unhappy with the result – it could be better, I would like to see more consistently useful lot shapes for example but it may be good enough to be getting on with.
The final step is taking the road network and lots and generating renderable geometry from them, after that’s it’s building selection and construction which I haven’t got to yet. This is how the road and lot network looks in the engine for now anyway:
And that’s it as it stands. The city generator is deterministic and seeded from the city’s world position (and in the future it’s physical/political parameters) so I’ve many cities all around my planet of varying sizes and complexity, the next step is building generation and placement. Procedural architectural generation is a whole new bag, so it’s back to Google for me…
In my previous post I introduced the Osiris project that I’ve started working on and outlined the basic construction system for the planet I’m trying to procedurally build. With that set up, the next step was to create a system for generating and storing the multitude of data that is required to represent an entire planet.
Now planets are pretty large things and the diversity and quantity of data that is required to represent one at even fairly low fidelity gets very large very quickly. A requirement of this system though is that I want to be able to run my demo and immediately fly down near to the surface to see what’s there – I don’t want to have to sit waiting for minutes or hours while it churns away in the background building everything up.
For this to work I obviously need some form of asynchronous data generation system that can run in the background spitting out bits and pieces of data as quickly as possible while the main foreground thread is dealing with the user interface, camera movement and most importantly rendering the view.
This fits quite well with modern CPUs where the number of logical cores and hardware threads is continuing to rise providing increasing scope for such background operations, but that does also mean that the data generation system needs to be able to run on an arbitrary number of threads rather than just a single background one. An added bonus of such scalability is that time can even be stolen from the primary rendering thread when not much else is going on – for example when the view is stationary or when the application is minimised.
Ultimately this work should be able to be farmed off to secondary PCs in some form of distributed computing system or even out into the cloud – but to support that data generation has to be completely decoupled from the rendering and able to operate in isolation. Even if such distribution never happens though designing in such separation and isolation is still a valuable architectural design goal.
So I need to be able to generate data in the background, but to achieve my interactive experience I also need it to be generating the correct data in the background, which in this case means that at any given moment I want it to be generating data for the most significant features that are closest to the viewpoint. This determination of what to generate also needs to be highly dynamic as the viewpoint can move around very quickly – thousands or even tens of thousands of miles per hour at times – so it’s no good queuing up thousands of jobs, the current set of what’s required needs to be generated and maintained on the fly.
Finally as generation of data can be a non-trivial process the system needs to be able to cache data it’s already generated on disk for rapid reloading on subsequent runs or even for later on in the same run if the in-memory data had to be flushed to keep the total memory footprint down. I can’t simply cache everything however as for an entire planet the amount of data for the level of fidelity I want to reproduce can easily run into terabytes so it’s important to only cache up to a realistic point – say a few gigabytes worth – with the rest being always generated on demand.
To maximise the effectiveness of disk caching I also want to include compression in the caching system – the computation overhead of a standard compression library such as zlib shouldn’t be exorbitantly expensive compared to the potentially gigabytes of saved disk space.
This is quite a shopping list of requirements of course, which brings home the unavoidable complexity of generating high fidelity data on a planetary scale, but even non-optimal solutions to these primary requirements should allow me to build on top of such a generic data generation system and start to look at the planetary infrastructure generation and simulation work that I am primarily interested in.
Unfortunately of course data generation architecture lends itself only so well to pretty pictures so rather than some dull boxes and lines representation of data flow the images with this post show the atmospheric scattering shader that I’ve also recently added – it’s probably the single biggest improvement in both visual impact and fidelity and suddenly makes the terrain look like a planet rather than just a textured ball – more on this atmospheric shader in a later post.
The stats helper monkeys at WordPress.com mulled over how this blog did in 2010, and here’s a high level summary of its overall blog health:
The Blog-Health-o-Meter™ reads This blog is doing awesome!.
The Leaning Tower of Pisa has 296 steps to reach the top. This blog was viewed about 1,200 times in 2010. If those were steps, it would have climbed the Leaning Tower of Pisa 4 times
In 2010, there were 16 new posts, not bad for the first year! There were 87 pictures uploaded, taking up a total of 13mb. That’s about 2 pictures per week.
The busiest day of the year was November 10th with 66 views. The most popular post that day was A note on voxel cell LOD transitions.
Where did they come from?
The top referring sites in 2010 were
gamedev.net, wiftcoder.wordpress.com and wiki.blitzgamesstudios.com
Some visitors came searching, mostly for voxel lod, gpu clipmap, world lod solutions, nvidia gpu enerated landscapes, and octave isosurface sphere.
Attractions in 2010
These are the posts and pages that got the most views in 2010.
A note on voxel cell LOD transitions July 2010
Procedural News May 2010
Introduction to Geo May 2010
Planetary Basics May 2010
Links May 2010
Before delving deeper into terrain construction I thought a brief note on co-ordinate systems would be worthwhile. Stellar bodies come in all shapes and sizes but as I live on planet Earth like most people basing my virtual planet upon this well known baseline makes a lot of sense.
Now the Earth isn’t quite a perfect sphere so it’s radius varies but it’s volumetric mean radius is about 6371 Km so that’s a good enough figure to go on. Most computer graphics use single precision floating point numbers for their calculations as they are generally a bit faster for the computer to work with and are universally supported by recent graphics cards, but with only 23 bits for the significand they have only seven significant digits which can be a real problem when representing data on a planetary scale.
Simply using a single precision floating point vector to represent the position of something on the surface of our Earth sized planet for example would give an effective resolution of just a couple of meters, possibly good enough for a building but hardly useful for anything smaller and definitely insufficient for moving around at speeds lower than hundreds of kilometers per hour. Trying to naively use floats for the whole pipeline and we quickly see our world jiggling and snapping around in a truly horrible manner as we navigate.
Moving to the use of double precision floating point numbers is an obvious and easy solution to this problem however as with their 52 bit significand they can easily represent positions down to millionths of a millimetre at planetary scale which is more than enough for our needs. With modern CPUs their use is no longer as prohibitively expensive as they used to be in performance terms either with some rudimentary timings showing only a 10%-15% drop in speed when switching core routines from single to double precision. Also the large amounts of RAM available now make the increased memory requirement of doubles easily justified, the problem of modern GPUs using single precision however remains as somehow we have to pipe our double resolution data from the CPU through the single precision pipe to the GPU for rendering.
My solution for this is simply to have the single precision part of the process, namely the rendering, take place in a co-ordinate space centred upon the viewpoint rather than the centre of the planet. This ensures that the available resolution is being used as effectively as possible as when the precision falls off on distance objects these are by nature very small on screen where the numerical resolution issues won’t be visible.
To make this relocation of origin possible, I store with each tile it’s centre point in world space as a double precision vector then store the vertex positions for the tile’s geometry components as single precision floats relative to this centre. Before each tile is rendered, the vector from the viewpoint to the centre of the tile in double precision space is calculated and used to generate the single precision complete tile->world->view->projection space matrix used for rendering.
In this way the single precision vertices are only ever transformed to be in the correct location relative to the viewpoint (essentially the origin for rendering) to ensure maximum precision. The end result is that I can fly from millions of miles out in space down to being inches from the surface of the terrain without any numerical precision problems.
There are of course other ways to achieve this, using nested co-ordinate spaces for example but selective use of doubles on the CPU is both simple and relatively efficient in performance and memory costs so feels like the best way.
Of course numerical precision issues are not limited to the positions of vertices, another example is easily found with the texture co-ordinates used to look up into the terrain textures. On the one hand I want a nice continuous texture space across the planet to avoid seams in the texture tiling but as the texture co-ordinates are only single precision floats there simply isn’t the precision for this. Instead different texture scales have to be used at different terrain LOD levels and the results somehow blended together to avoid seams – I’m not going to go to deeply in to my solution for that here as I think it’s probably worth a post of it’s own in due course.
Continuing the theme of procedurally generated planets, I’ve started a new project I’ve called Osiris (the Egyptian god usually identified as the god of the Afterlife, the underworld and the dead) which is a new experiment into seeing how far I can get having code create a living breathing world.
Although my previous projects Isis and Geo were both also in this vein, I felt that they each had such significant limitations in their underlying technology that it was better to start again with something fresh. The biggest difference between Geo and Osiris is that where the former used a completely arbitrary voxel based mesh structure for its terrain Osiris uses a more conventional essentially 2D tile based structure. I decided to do this as I was never able to achieve a satisfactory transition effect between the level of details in the voxel mesh leaving ugly artifacts and, worse, visible cracks between mesh sections – both of which made the terrain look essentially broken.
After spending so much time on the underlying terrain mesh systems in Isis and Geo I also wanted to implement something a little more straightforward so I could turn my attention more quickly to the procedural creation of a planetary scale infrastructure – cities, roads, railways and the like along with more interesting landscape features such as rivers or icebergs. This is an area that really interests me and is an immediately more appealing area for experimentation as it’s not an area I have attempted previously. Although a 2D tile mesh grid system is pretty basic in the terrain representation league table, there is still a degree of complexity to representing an entire planet using any technique so even that familiar ground should remain interesting.
The first version shown here is the basic planetary sphere rendered using mesh tiles of various LOD levels. I’ve chosen to represent the planet essentially as a distorted cube with each face represented by a 32×32 single tile at the lowest LOD level. While the image below on the left may be suitable as a base for Borg-world, I think the one on the right is the basis I want to persue…
While mapping a cube onto a sphere produces noticeable distortion as you approach the corners of each face, by generating terrain texturing and height co-ordinates from the sphere’s surface rather than the cube’s I hope to minimise how visible this distortion is and it feels like having what is essentially a regular 2D grid to build upon will make many of the interesting challenges to come more manageable. The generation and storage of data in particular becomes simpler when the surface of the planet can be broken up into square patches each of which provides a natural container for the data required to simulate and render that area.
At this lowest level of detail (LOD) each face of the planetary cube is represented by a single 32×32 polygon patch. At this resolution each patch covers about 10,000 km of an Earth sized planet’s equator with each polygon within it covering about 313 km. While that’s acceptable when viewing the planet from a reasonable distance in space as you get closer the polygon edges start to get pretty damn obvious so of course the patches have to be subdivided into higher detail representations.
I’ve chosen to do this in pretty much the simplest way possible to keep the code simple and make a nice robust association between sections of the planet’s surface and the data required to render them. As the view nears a patch it gets recursively divided into four smaller patches each of which is 32×32 polygons in it’s own right effectively halving the size of each polygon in world space and quadrupling the polygonal density.
Here you can see four stages of the subdivision illustrated – normally of course this would be happening as the view descended towards the planet but I’ve kept the view artificially high here to illustrate the change in the geometry. With such a basic system there is obviously a noticeably visible ‘pop’ when a tile is split into it’s four children – this could be improved by geo-morphing the vertices on the child tile from their equivalent positions on the parent tile to their actual child ones but as the texturing information is stored on the vertices there is going to be a pop as the higher frequency texturing information appears anyway . Another option might be to render both tiles during a transition and alpha-blend between them, a system I used in the Geo project with mixed results.
LOD transitions are a classic problem in landscape systems but I don’t really want to get bogged down in that at the moment so I’m prepared to live with this popping and look at other areas. It’s a good solid start anyway though I think and with some basic camera controls set up to let me fly down to and around my planet I reckon I’m pretty well set up for future developments.