Quad isn't the best?

While reading some articles over the internet I am deeply starting to thing, that the quad-based LoD algorithm wasn't the best idea. I think so mainly because using such technique on a rather flat surfaces I still will have a lot of unneeded detail.

To demonstrate what I mean, I have found some pictures on the internet.

The picture to the left illustrates something like a hill near the flat ground. The hill itself is more "extruded" from the surface, and it needs more vertexes to represent all it's slopes and caves. It's more logical to add extra detail to the hills, and do not extra detail where the area is completely flat. This is the algorithm I need to implement if I want more complex terrain look more natural. This algorithm is called Optimally Adapted Meshes (OAM).

Unlike previous picture, this one exactly represents the technique I use at the moment. It can be seen with naked eyes that there are way more vertexes used on the areas, where you actually do not need them.

The OAM algorithm, or it's implementation to visualize terrains in realtime (Real-time Optimally Adapted Meshes, or ROAM) uses a height map to determine for each vertex it's error value - the heights around it so see if the area around it is flat or it needs more detail. Based on error value it determines where the extra detail should be added and where it's ok to leave the same amount of vertexes at the moment.

I also need to think in parallel the scaling problem, and implement it inside.

Links

Roam info & papers: 1, 2, 3, 4

 

Glitches

I have realized, that something needs to be changed in my code. I did some tests trying to see how program responses to big numbers. I have created a planet with the size exact to Earth's, and tried to fly here and there to see the performance, and then I ran to some unpleasant glitches.

This is taken from the stationary orbit at 1100 km from the surface of the virtual Earth. Strange thing that this artifacts not always appears (maybe I should call them UFO? :) ). It seems that this happens when some other processes run in background and use CPU resources a lot. I haven't tested it on other computers, maybe it's hardware specific.

I also noticed, that memory allocation and garbage collection isn't quite good, because the project constantly drains memory while runs. The problem is in LoD code, definitely.

Scales again

I've been thinking a lot about scales recently, once again, and those thoughts driving me nuts slowly.

Space is a very very very large thing. Our planet is about 6'300 km in radius, that is 12'600 km in diameter, and that is 12'600'000 meters, 8 digits. Assuming one world unit in the close distance is 1 meter of the planet, I have only 100 more sized object to be able to handle in close distance. So if I will be crazy enough to fly close to the sun (so that is should be rendered in real scale), I would have an float overflow because the radius of the sun is abou 110 times bigger, that the Earth's radius. We can ask why do we need such big numbers to store if we are 10 meters from the surface? Well, even if the part of a surface if 10 meters from you, you still have to take in mind that the center point of an asteroidal body is way far away from you and it is needed to make a proper curvature of a planet. To solve this somehow I have only 3 options in my mind:

1. Store vertex coordinates in doubles and apply exponential space transformations before converting them to floats.
2. Store vertex coordinates in doubles and cull vertexes that are very far away.
3. Make up something else.

And in my opinion, the only reasonable option is the last one..

There are couple of planetary engine demos around the web, I wonder how they solve this problem.

When to split & when to combine

Today I have almost finished my LoD algorithm. For now I just use simple "divide to 4" technique, and later I will probably use some other, more efficient one, like true ROAM, but for now it's ok.

In the heart of it lies one big question - when to split node to add more detail, and when to combine 4 nodes to one, so to remove unneeded detail. My first thoughts were to make some kind of table with the dependency of distance to node to necessary LoD level, but it was rejected soon because of planet sizes, which varies a lot. For example, using this approach my big planets will be less detailed, rather than small ones because of node's size - it will be bigger for big planets.. like the side of a big cube is bigger that the side of a small one.

Then I tried to calculate the ratio between the distance to node and node's size, and this gave a better result. 

The idea is simple. First I calculate the factor (F) which equals to distance to node (actually the it's the distance to closest vertex of a node) divided by node's size. Then I analyze this like so:

1. If F is less than some number (Kmin), which means that camera is close to node, then extra detail should be added (the node should be split on 4 smaller nodes). Of course here the check should be added if the detail level is at it's maximum.
2. If F i greater than some number (Kmax), which means, that camera is far enough from the node, then extra detail should be removed. And of course here the check should be added if the detail level is at it's minimum.
3. And finally, if F is between Kmin and Kmax - do nothing.

Something like this. In this picture I have chosen Kmin to be 2, and Kmax to be 3, but it's obvious, that this is the place to experiment.

This logic needs to be integrated in the procedure that scans all the quadtree, and decides if the leaf should just be rendered, or divided/combined. 

Deciding what to render

For the last two days I was thinking about my quadtree of nodes. Quadtree-based structure is used to store terrain nodes at different level of detail, based on the camera distance to them - more closely is the camera, then more detailed should be terrain. I will later write some text about my quadtree implementation, but for now I want to be detailed in explaining the scheme, which is essential to selecting the quadtree nodes, that needs to be rendered.

The quadtree consists of 2 core elements - node(s) and leaf(s). As I mentoned before, if a node have no child node(s), then this node is a leaf, and it should be rendered (if visible, but for now I do not make any checks on visibility). Each node may be only in two states: a leaf, or a node with 4 children (in that case such node is called a branch). This is the basics of quadtrees.

So, the core problem is to decide what quadtree elements needs to be rendered. This means that  there should be some kind of procedure, that runs via quadtree's nodes, and decides what to render and what to not.

Lets assume we have a quadtree like this. This quadtree have 3 "level of detail" levels (LoD levels, to be more shortly), and a lot of branches and leaves. Green circles are leaves, and brown ones are branches. Despite the visibility factor it's logical, that every leaf should be rendered, so that we could see the final terrain.

No matter how deep is the quadtree, the procedure, that finds all leaves in the quadtree so to render them later should scan all the quadtree's levels, and choose only those nodes, that are leaves. It should start from the very top of the quadtree, see if this node has any children. If it has, then "descent" down by one level until it finds the leaf. After the leaf is found it should "ascend" up to check other branches by going down. It should repeat this steps until all elements of quadtree are examined. It is clear, that if we have a rather big quadtree, it will take a lot of time to scan all its elements. Assuming that in this procedure we do not check for leaf's visibility, then yes, it will take some time to scan all the quadtree. Later on, when visibility check will be performed, the amount of nodes, that needs to be checked will decrease a lot. It can be easily understood if we assume that on the picture above, the third node from the left if no visible - then there's no need to scan its children.

Without visibility checks, the block scheme of such procedure can be the following.

Each node have the levelCheck variable, that is by default equals to 0 and is used to store in quadtree the child node number that has been scanned already. If it is equal to 4, that means that on this level we have scanned all children, so we should go up a level. And the lines "this.levelCheck=0" is used to reset the counter after all children of current node are scanned, so that next time when we will need to scan the quadtree, all nodes have this number reset back to zero.

Texture coordinates

Last two days I was trying to figure out what are texture coordinates. It's name sounds pretty obvious, but in real code it was confusing for me what exactly are texture coordinates and texture buffer, and how they should be properly defined.

I have found a nice picture, that have everything to understand once and for all what they are.

According to OpenGL documentation each texture must have like 2Nx2N for better memory allocation and computation. Each object's vertex should be “bound” to some point on the texture so that when the texture is applied to the object, the graphics card will know how to “wrap” an object with a texture. To do it properly, the corresponding position of each vertex on a 2d texture should be defined. This is called texture coordinates, and they should be defined as [0;1] numbers.

For example, if we have a 3x3 square mesh, that consists from 9 vertices with any dimensions in 3d (lets say 10 by 10), the scheme of defining texture coordinates (and texture buffer lately) should be like this (texture coordinates are always 2d and in range of [0;1] for each vertex):

Black text represent 3d vertex coordinates, and red text - 2d texture coordinates.

Wierd things

Last night at about 1 a.m. I was trying to put some tests to reveal the difference in calculating floats and doubles. The idea was simple - fix a time when the test stars, put in a loop for 1 million times some equations like multiplying and finding a square root of the number, and then fix the end time so do subtract it from the start time.

In first test floats were used. The number like 123456.78 was multiplied, divided, square rooted and etc. for fixed amount of iterations. And then, using doubles (big numbers from previous post) the same type of test was performed.

I was shocked that rather small float numbers had a higher results than doubles!

This is truly the result that let me think more closely to use doubles instead of floats without any doubts regarding performance.

Matter of scale

Yesterday I was thinking more closely about numbers to understand the scales of the star system(s), and ways to deal with them.

I started from understanding how far is the distance from our Sun to the last planet. According to Wikipedia, the Neptune is about 30 AU (astronomical units. 1AU = 149’597’871 kilometers, or 92’960’000 miles). Objects of Kuiper belt, or so called trans-Neptunian objects, may be placed at the distance not far from 55 AU in their average radius, and it consists mostly from small objects, like asteroid belt. The biggest body of Kuiper belt is Eris, which has 97 AU in aphelion and 37 AU in perihelion. Beyond Kuiper belt lies The Oort cloud - a hypothesized spherical cloud of comets which may lie roughly 50’000 AU, or nearly a light-year, from the Sun. Oort cloud consists from asteroids, space dust and comets.

So, for the star like our Sun (G2 star), which has a mass of 1.9+E30kg. the distance from its center to the farthest object could be around 1’000 AU, or about 1.49+E11km. A thousand AU came from the idea that if I want to make project close to reality, I may close my eyes on every and very far object in the star system, but, never the less, make enough space to model some really far objects. My guess is that this number can easily be divided even 10 times, and it will be more than enough, and later I will use the number of 100 AU for the stars like our Sun.

But! According to this nice article, O-class stars may have mass from 15 to 90 times more, than the mass of the Sun. Taking in account the dependency of gravity force from objects mass by Newton’s law, such big stars will have the same about of gravitational force at the distance of square root of mass. So, if the mass is 90 times bigger, then the distance will be a bit more less than 10 times.

With all that in mind, I need to be able to operate with the distances of 1’000 AU for a single star.

According to Wikipedia, almost half of the stars in our galaxy are systems of two stars, or binary star systems, where 2 stars floats around their center of mass. It is written there that some binary systems may have more suitable conditions for planet formation, rather than single stars may have.

But let’s fantasize a bit and assume that even star systems with 3 or 4 stars may have a condition to form planets (stable or not), and to be able to make and fly around such star system I will need, let’s say the double space I have calculated.

So, 2’000 AU will be enough for any condition and any star in my virtual galaxy. And it is equal to 299’195’742’000 km, in every direction from the star system center. That is a HUGE space. By the way, if I move with the speed of light (which is equal to 299’792 km/sec.) I will need about 693 days, or almost 2 years to travel from the center of star system to its boundaries. But why should I worry? I have a hyperspace drive, haven’t I? :)

If I want to have a precision of 1 meter in my project, I will need to be able to operate with the numbers from -2.99+E14 to +2.99+E14, which can perfectly be held by double precision floating points. But dealing with doubles every time with every object may significally decrease the performance.

I came up with idea of so called local space and global space to, probably, solve performance issues I might have, if I use doubles everywhere. The idea is to render/calculate everything using global scale units when player’s cam isn’t near any global object of star system (global units have a precision of, let’s say 10000 km), and switch to local (coordinates), when player’s cam enters some certain region near any global space object, for example planet. If we assume that each space body has its global coordinates, then local space would be bounded and centered to the current position of the body.

Switching back and forth from global to local coordinates should probably spare some CPU power and give me necessary precision.

I should post some more thoughts on this idea later.

Core object scheme and hierarchy

Today I was thinking more closely to the overall object hierarchy of the entire project. As well as the bodies in our solar system “attached” to theirs “parent” bodies (like the moon is a “child” of our Earth, it goes around the Earth, and Earth goes around the Sun), and all the space bodies goes around the Sun, my structure tries to stay closer the same hierarchy.

The scheme of object hierarchy can be seen below. Of course, I believe I will modify it in time due to some new ideas, but the core idea should look that way.



Basically almost every entity on this scheme has a name of “factory”, and it’s pretty self-explanatory. Each this entity handles the generation of the named object in the space, stores it’s parameters and handles some object routines.

For example, PlanetFactory is responsible for generating the planet body with all the stuff, that planet consists of, like surface (that’s been generated by PlanetSurfaceFactory), water (PlanetWaterFactory) or whatever liquid the planet may have, sky (PlanetSkyFactory), and maybe some more later (RiverFactory, CityFactory, etc.). Therefore PlanetFactory is a child to PlanetarySystemFactory – class, that is responsible for processing all the bodies, including the planet itself, that orbits around, let’s say, the center of mass of the planet – Planet itself, planet moons, celestial bodies like Saturn rings, asteroids, debris… If we go higher, there is a SolarSystemFactory, and, as you can guess already, stores and processes all space bodies of the star system, including the star itself, planets, asteroids and asteroid belts, comets and all others.

The scheme looks good and logical for me, and I will definitely try to follow it. Next step will be to define common variables and procedures for each node of the scheme.

Long-awaited update

It’s been a while since I have posted the last message. A lot of thing have changed and a lot of has been redone. It’s a pity that it is now 4th rework on the simple node tree flow, but because I find it essential to the whole project, I think it’s best to find the right solution first, and then continue to make other things.

I have now switched back to Java Monkey Engine due to simplicity of coding from all my platforms that I work on every day. The experience with Ogre3d engine in that area wasn’t very good from the perspective of switching the development platform each day due to the fact that in my work time, I like to put the work away and return to the project, if I have some ideas I want to try. And in that time I work under windows. And at home I have my beautiful iMac with MacOS X in it, of course. Switching back to jME took away the problem of reconfiguring the project settings for each platform each time I put the code written form windows to mac, and vice versa. I know that it’s solvable and my lack of knowledge in that area gives me pain, but for now, it’s better for me to stay with jME to avoid them. Anyway, if you understand the problem completely (and for now, understanding the routines to handle trees for planet surface rendering is the problem), it isn’t very hard to switch to another engine in future.

At the moment I have completely decided what scheme is better for my needs of creating and handling the planet surface, and it’s ROAM. I do not remember whether I posted the link to the ROAM PDF paper or not, but I will do it now anyway. So, here’s the link.

Why ROAM is good? Well, the best way to see it is to define how I want the planet surface to be born and handled. I have found the following scheme the best:

1. Using complex procedural algorithms generate a planetary map (the vision of what the planet will look like with all the coasts, mountains, valleys, etc.) that later can be modified to add crates, rivers, cliffs, and many more.
2. Using the same algorithm make a height map.
3. Make a spherical planet body and apply map to it.
4. Using altitude as the parameter, adjust the height of the planet mesh, and add extra geometry when we approach closer to surface. This means that form space you will see a bump mapped sphere, and as you get closer to surface, the surface will slowly and smoothly change to reveal all the “heights”.

For that scheme I find ROAM is a perfect choice. Later on I will post some updates on the node and tree routines.