OpenGL C++ - Solar System

Question

I've finished building a solar system using OpenGL and C++. One of the features in this system is having camera positions on each planet pointing to the north which moves based on the planet transformation. The camera positions are: One at the top, one a little behind the planet and the last one is far away from the planet. There are some other features but I don't have any issues with them.

So, the issue I am having is that some planets seem to be trembling for some reason while rotating around their centers. If I increase the speed of spinning the planet will stop trembling or the trembling becomes unnoticeable. The entire solar system is fully based on real textures and proportional space calculations and it has multiple camera positions as mentioned earlier.

Here is some code that might help understanding what I am trying to achieve:

//Caculate the earth postion
GLfloat UranusPos[3] = {Uranus_distance*DistanceScaler * cos(-uranus * M_PI / 180), 0, Uranus_distance*DistanceScaler * sin(-uranus * M_PI / 180)};
//Caculate the Camera Position
GLfloat cameraPos[3] = {Uranus_distance*DistanceScaler * cos(-uranus * M_PI / 180), (5*SizeScaler), Uranus_distance*DistanceScaler * sin(-uranus * M_PI / 180)};
//Setup the camear on the top of the moon pointing 
gluLookAt(cameraPos[0], cameraPos[1], cameraPos[2], UranusPos[0], UranusPos[1], UranusPos[2]-(6*SizeScaler), 0, 0, -1);

SetPointLight(GL_LIGHT1,0.0,0.0,0.0,1,1,.9);
//SetMaterial(1,1,1,.2);
//Saturn Object
// Uranus Planet
UranusObject(  UranusSize * SizeScaler,   Uranus_distance*DistanceScaler,   uranusumbrielmoonSize*SizeScaler,   uranusumbrielmoonDistance*DistanceScaler,   uranustitaniamoonSize*SizeScaler,   uranustitaniamoonDistance*DistanceScaler,   uranusoberonmoonSize*SizeScaler,   uranusoberonmoonDistance*DistanceScaler);

The following is the planet function I am calling to draw the object inside the display function:

void UranusObject(float UranusSize, float UranusLocation, float UmbrielSize, float UmbrielLocation, float TitaniaSize, float TitaniaLocation, float OberonSize, float OberonLocation)
{
    glEnable(GL_TEXTURE_2D);
    glPushMatrix();

    glBindTexture( GL_TEXTURE_2D, Uranus_Tex);
    glTexEnvf( GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE );
    glRotatef( uranus, 0.0, 1.0, 0.0 );
    glTranslatef( UranusLocation, 0.0, 0.0 );
    glDisable( GL_LIGHTING );
    glColor3f( 0.58, 0.29, 0.04 );
    DoRasterString( 0., 5., 0., "     Uranus" );
    glEnable( GL_LIGHTING );
    glPushMatrix();
    // Venus Spinning
    glRotatef( uranusSpin, 0., 1.0, 0.0 );
    MjbSphere(UranusSize,50,50);

    glPopMatrix();
    glDisable(GL_TEXTURE_2D);
    glEnable(GL_TEXTURE_2D);
    glPushMatrix();

    glBindTexture( GL_TEXTURE_2D, Umbriel_Tex);
    glTexEnvf( GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE );
    glDisable(GL_LIGHTING);
    if (LinesEnabled)
    {
        glPushMatrix();
        gluLookAt( 0.0000001, 0., 0.,     0., 0., 0.,     0., 0., .000000001 );
        DrawCircle(0.0, 0.0, UmbrielLocation, 1000);
        glPopMatrix();
    }
    glEnable( GL_LIGHTING );
    glColor3f(1.,1.,1.);
    glRotatef( uranusumbrielmoon, 0.0, 1.0, 0.0 );
    glTranslatef( UmbrielLocation, 0.0, 0.0 );
    MjbSphere(UmbrielSize,50,50);

    glPopMatrix();
    glDisable(GL_TEXTURE_2D);
    glEnable(GL_TEXTURE_2D);
    glPushMatrix();

    glBindTexture( GL_TEXTURE_2D, Titania_Tex);
    glTexEnvf( GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE );
    glDisable(GL_LIGHTING);
    if (LinesEnabled)
    {
        glPushMatrix();
        gluLookAt( 0.0000001, 0., 0.,     0., 0., 0.,     0., 0., .000000001 );
        DrawCircle(0.0, 0.0, TitaniaLocation, 1000);
        glPopMatrix();
    }
    glEnable( GL_LIGHTING );
    glColor3f(1.,1.,1.);
    glRotatef( uranustitaniamoon, 0.0, 1.0, 0.0 );
    glTranslatef( TitaniaLocation, 0.0, 0.0 );
    MjbSphere(TitaniaSize,50,50);

    glPopMatrix();
    glDisable(GL_TEXTURE_2D);
    glEnable(GL_TEXTURE_2D);
    glPushMatrix();

    glBindTexture( GL_TEXTURE_2D, Oberon_Tex);
    glTexEnvf( GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE );
    glDisable(GL_LIGHTING);
    if (LinesEnabled)
    {
        glPushMatrix();
        gluLookAt( 0.0000001, 0., 0.,     0., 0., 0.,     0., 0., .000000001 );
        DrawCircle(0.0, 0.0, OberonLocation, 1000);
        glPopMatrix();
    }
    glEnable( GL_LIGHTING );
    glColor3f(1.,1.,1.);
    glRotatef( uranusoberonmoon, 0.0, 1.0, 0.0 );
    glTranslatef( OberonLocation, 0.0, 0.0 );
    MjbSphere(OberonSize,50,50);

    glPopMatrix();
    glDisable(GL_TEXTURE_2D);
    glPopMatrix();
    glDisable(GL_TEXTURE_2D);
}

Finally, the following code is for the transformation calculations used for solar animation:

uranus += 0.0119 * TimeControl;

if( uranus > 360.0 )
    uranus -= 360.0;

// Clockwise Rotation
uranusSpin -= 2.39 * TimeControl;
if( uranusSpin <= -360.0 )
    uranusSpin = 0.0;

Note: the problem happens only with 4 planets only.

I really appreciate any idea that could solve the problem.

Answer 1

First of all take a look at:

• Is it possible to make realistic n-body solar system simulation in matter of size and mass?

Now to your problem. I am too lazy to go through your code but you most likely hit the floating point accuracy barrier and or have accumulating errors during rotating. My bet is that the error is bigger further away from the sun (outer planets and more in the ecliptic plane). If that is so then it is obvious. So how to remedy that?

1. floating point accuracy

   while rendering you are transforming vertexes by transform matrix. For reasonable ranges is this OK but if you Vertex is very far from (0,0,0) then the matrix multiplication is not that precise. This means when you convert back to camera space the Vertex coordinate is jumping around. To avoid this you need to translate your vertexes to camera origin before feeding it to OpenGL.

   So just subtract camera position from each Vertex (before loading them to OpenGL!!!) you have and then render them with camera with position (0,0,0). This way you get rid of the jumping and even wrong interpolation of primitives. see

   • ray and ellipsoid intersection accuracy improvement

   If your object is still too big (this is not the case for Solar system) then you can stack up more frustums together and render each with separate camera shifted by some step so you get in range.

   Use 64 bit floats where you can, but be aware GPU implementations does not support 64-bit interpolators so fragment shader is feed by 32-bit floats instead.

2. accumulating errors in transform matrix

   If you have some "static" matrix and apply countless operations on it like rotation, translation Then it will lose its precision after while. This is recognizable by changing scale (axises are not unit size anymore) and adding skew (axises are not perpendicular to each other anymore) with time it gets worse and worse.

   To remedy that You can keep counter of operations per matrix and if hit some treshold perform matrix normalization. This is simple just extraxt all the axises vectors, make them perpendicular again, set them back to their original size and write them back to your matrix. With basic vector math knowledge is this easy just exploit cross product (which gives you perpendicular vector). I use Z axis as view direction so I keep Z axis direction as is and correct the X,Y axises directions. The size is easy just divide each vector by its size and you are unit again (or very close to it). for more info see:

   • Understanding 4x4 homogenous transform matrices

[Edit1] What is going on

Have a look at your code for single planet without the rendering stuff:

// you are missing glMatrixMode(GL_????) here !!! what if has been changed?
glPushMatrix(); 
// rotate to match dayly rotation axis?
glRotatef( uranus, 0.0, 1.0, 0.0 );
// translate to Uranus avg year rotation radius
glTranslatef( UranusLocation, 0.0, 0.0 );
glPushMatrix();
// rotate Uranus to actual position (year rotation)
glRotatef( uranusSpin, 0., 1.0, 0.0 );
// render sphere
MjbSphere(UranusSize,50,50);
glPopMatrix();

// moons

glPopMatrix();

So what you are doing is this. Let assume you are using ModelView matrix and you are instructing OpenGL to do this operation on it:

ModelView = ModelView * glRotatef(uranus,0.0,1.0,0.0) * glTranslatef(UranusLocation,0.0,0.0) * glRotatef(uranusSpin,0.,1.0, 0.0);

So what is wrong with this? For small scenes nothing but you are using proportional sizes so:

UranusLocation=2870480859811.71 [m]
UranusSize    =     25559000    [m]

So that means the glVertex magnitudes are ~25559000 and after applying transforms ~2870480859811.71+25559000. Now there are few problems with these values.

First any glRotation call applies sin and cos coefficients to the 2870480859811.71 Lets assume we have error of sin,cos around 0.000001 that means the final position after result has position error in it:

error=2870480859811.71*0.000001=2870480.85981171

The OpenGL sin,cos implementation has probably higher precision but not by much. Anyway if you are comparing it to planet radius

2870480.85981171/25559000=0.112308 -> 11%

You get that the jumping error is around 11% of the planet size. That is huge. The implication from this is that the jumping is the bigger the further away from Sun and more Visible for smaller Planets (as our perception is usually relative not absolute).

You can try to boost this by using double precision (glRotated) but that does not mean it would solve the problem (some drivers does not have double precision implementation of sin,cos).

If you want to get rid of these problems you have follow the bullet #1 or do the rotations on your own on at least doubles and feed only the final matrix to OpenGL. So first the #1 approach. Translation of matrix is just +/- operation (also encoded as multiplication) but no un-precise coefficients are present so you are using full precision of used variable. Anyway I would use glTranslated just to be sure. So we need to make sure the rotations does not use big values inside OpenGL. So try this:

// compute planet position
double x,y,z;
x=UranusLocation*cos(uranusSpin*M_PI/180.0);
y=0.0;
z=UranusLocation*sin(uranusSpin*M_PI/180.0);

// rotate to match dayly rotation axis?
glRotated( uranus, 0.0, 1.0, 0.0 );
// translate to Uranus to actual position (year rotation)
glTranslated(x,y,z);
// render sphere
MjbSphere(UranusSize,50,50);

This affects the daily rotation speed as the daily and Year rotations angles are not adding up, but you are not implementing the daily rotation yet anyway. If this does not help then we need to use camera local coordinates to avoid having big values send to OpenGL:

// compute planet position
double x,y,z;
x=UranusLocation*cos(uranusSpin*M_PI/180.0);
y=0.0;
z=UranusLocation*sin(uranusSpin*M_PI/180.0);
// here change/compute camera position to (original_camera_position-(x,y,z))

// rotate to match dayly rotation axis?
glRotated( uranus, 0.0, 1.0, 0.0 );
// render sphere
MjbSphere(UranusSize,50,50);

Hope I matched your coordinate system if not just swap axises or negate them (x,y,z).

It is much better to have own precise matrix math at disposal and compute the glTranslate,glRotate on CPU side with high precision and use only the resultant matrix in OpenGL. see the Understanding 4x4 homogenous transform matrices link above how to do that.

Answer 2

I can not give you an exact answer based on what you have shown. I can not compile and run your current code and test it with numbers and the debugger. What I can do is give you some advise that ought to help you out.

From what I can tell based on the code that you did supply you are creating your Planet objects via a function call. So I can rationalize that you are doing this for every planet. If that is the case then if you take a notice at your full code base you will see that everyone of these functions besides their names, and the numbers that are used are basically copies of themselves or duplicate code. This is where you need a more versatile structure.

Here are some important things to consider in your construct.

• Create a full 3D Motion camera class & a separate Player Class

  • The Camera Class will allow you to look up, down, left & right by (restrained angles) - Via Mouse Controls
  • The Player Class will have the camera object attached to it at camera_eye_level, lookAtDirection that is perpendicular to the upVector. The player class will be able to move freely forward, backward, up, down turn left & turn right via keyboard controls. This gives you flexibility.
  • Note: If You are doing by scale and your planets are considerably far apart, make your player's linear speed rate higher so that you move faster towards the object covering more distance.

• Create a base Geometry class

  • Derived Geometry Classes: Box, Flat Grid, Cylinder, Sphere, Pyramid, Cone
  • These classes will hold a finite container of Vector3s(Vertices), a container of Vector3(Indices), a container of Vector2(Texture Coords), a container of Vector4(Material - Color with Alpha), and a container of Vector3(Normals).
  • The base class will probably only hold an unsigned int (ID value) and or a std::string (Name Identifier) and an Enum Value of Type Geometry that is being created
  • Each Derived class will have a constructor on required parameters, the size of the 3 dimensions (don't need to worry about Texture & Color Information Here that will come later)
• Create a Material Class
• Create a base Light class
  • Derived Types: Directional, Point & Spot
• Create A Texture Class
• Create A Texture Transform Class - This Will Allow you to apply transformations directly on the texture that is attached to your Geometry To give the effect that an object is moving, when only the texture transform is.
  • Example: Geometry Type Box( 2,1,4 ) Texture Applied "conveyor_belt1.png" this way you don't have to change the box's transform and move all the vertices, texcoords, and normals on each render pass, you can just simply make the texture move in place. Less computationally expensive
• Create Node Class - Base class for all nodes that will belong to a Scene Graph
  • Types of Nodes for SceneGraph - ShapeNode(Geometry), LightNode, TransformNode(contains vector & matrix information for Translation, Rotation & Scaling),
  • The combination of the Node Classes and The SceneGraph will create a tree like structure such as this:

// This would be an example of text file that you would read in to parse the data 
// and it will construct the scene graph for you, as well as rending it.
// Amb = Ambient, Dif = Diffuse - The Materials Work With Lighting & Shading and will blend with which ever texture is applied      

// Items needed to construct
// Objects
Grid geoid_1 Name_plane Wid_5 Dep_5 divx_10 divz_10
Sphere geoid_2 name_uranus radius_20 
Sphere geoid_3 name_earth radius_1
Sphere geoid_4 name_earth_moon radius_0.3

// Materials
Material matID_1 Amb_1,1,1,1 Dif_1,1,1,1 // (white fully opaque)

// Textures   
Texture texID_1 fileFromTexture_"assets\textures\Uranus.png"
Texture texID_2 fileFromTexture_"assets\textures\Earth.png"
Texture texID_3 fileFromTexture "assets\textures\EarthMoon.png"

// Lights (Directional, Point, & Spot Types)

Transform Trans_0,0,0 // This is the center of the World Space and has to be a 
+Shape geoID_1 matID_1 // Applies flat grid to root node to create your horizontal plane
+Transform Trans_10,2,10000 // Nest a transform node that is relative to the root; this will allow you to rotate, translate and scale every object that is attached and nested below this node. Any Nodes Higher in the branch will not be affected
++Shape geoID_2 matID_1 texID_1
+Transform Trans_10,1.5,200 // This node has 1 '+' so it is nested under the root and not Uranus
++Shape geoID_3 matID_1 tex1ID_2
+++Transform Trans_10,1.5,201 // This node is nested under the Earth's Transform Node and will belong to the Earth's Moon.
+++Shape geoID_4 matID_1 textID_3

END // End Of File To Parse

With this kind of construct, you would be able to translate, rotate and scale objects independently of each other, or by a hierarchy. For example: And as for the moons of Uranus you can apply the same technique as I showed with the Earth and its moon. Each moon would have its own transform but those transforms would be nested under the planets transforms where the planets transforms would be nested to the root or even the Sun's transform if you added one in. (Sun = Light Source) it would have several light nodes attached. (I've already done this before with the Sun - Earth & Moon and had the objects rotate accordingly.

You have a Model of a Jeep but you have 4 different models to render to make the full object in your game. 1 Body, 2 Front Wheels, 3 Back Wheels & 4 Steering Wheel. With this construct a graph my look like this

Model modID_1 modelFromFile_"Assets/Models/jeep_base.mod"
Model modID_2 modelFromFile_"Assets/Models/jeep_front_wheel.mod"
Model modID_3 modelFromFile_"Assets/Models/jeep_rear_wheel.mod"
Model modID_4 modelFromFile_"Assets/Models/jeep_steering.mod"

Material matID_1 Amb_1_1_1_1 Diff_1_1_1_1
Texture texID_1 textureFromFile_"Assets/Textures/jeep1_.png"    

TextureTransform texTransID_1 name_front
TextureTransform texTransID_2 name_back
TextureTransform texTransID_3 name_steering

+Transform_0,0,0 name_root
++Transform_0,0.1,1 name_jeep
+++Shape modID_1 matID_1 texID_1  texCoord_0,0, size_75,40
+++Transform_0.1,0.101,1 name_jeepFrontWheel
+++Shape modID_2 matID_1 texID_1  texCoord_80,45 size_8,8
+++Transform_-0.1,-0.101,1 name_jeepBackWheel
+++Shape modID_3 matID_1 texID_2  texCoord_80,45 size_8,8
+++Transform_0.07,0.05,-0.02 name_jeepSteering
+++Shape modID_4 matID_1 texID_2  texCoord_80,55 size_10,10

END

Then in your code you can grab the transform nodes that belongs to jeep and when you translate it across the screen all the jeeps parts move together as one object, yet independently all tires can rotate front & back using the texture transforms, and your fronts can turn left and right by is own node transform by a constrained degree, also your steering can turn the same direction as the wheels using the texture transform, but may rotate less or more, depending on the characteristics of this particular vehicle and how it will handle within the scene or game.

With this type of system; the process is a bit harder to construct, but once it is working it allows for a simple automation of generating a scene graph. The down side to this is text file is easy to read at the human level but parsing a text file is much harder than parsing a binary file. The main reason for that is your function that belongs to your Scene class to parse and create all of these different nodes (All Geometry(Shapes), All (Lights), Material Texture and Transform Nodes.

The reason for having the Geometry and Lights having a base class is when you create a ShapeNode or a LightNode that is attached or nested to a TransformNode it can accept any derived type from the base class. This way you don't have to code your scene graph construction and parser to accept every type of geometry and light, you can have it accept any geometry and light, but to tell it what type it is.

Now you can make this a bit easier by creating a parser that works reads in binary files. The plus side is, it is easier to write the parser as long as you know the structure of the file, how much data to read in, and the expected type of data at the current read location. The down side is you can not read or set this up manually as I demonstrated above with a human readable text file. However going with this method would require you to have a decent Hex Editor Program that allows for file template types. such as 010 Editor this way you can add your own template to your file structure and when you read in the binary file with the applied template, you can then see if the values are correct and the fields have the appropriate data type and values.

In truth the best advice I can give you is this: The construct above is still good to follow, but may not be the best, it is a good starting point. But what you are learning right now on OpenGL appears to be OpenGL v1.0 which is basically outdated and deprecated. You should scrap all that you have learned from this relic of an API and begin to learn on modern OpenGL any version that is higher than 3.3. From there you can then learn to build and write shaders in GLSL and it will simplify a lot of things for you once you have your frame work up and working. Then once you get that up and working, instead of rendering everything to the screen from the CPU and rendering it from the GPU instead is much more efficient. Once you have that in place then consider looking into the concept of Batch Rendering. Batch Rendering will allow you to control how many buckets there are and how many vertices each bucket will contain. This batch process prevents the bottle neck between the rate of I/O from the CPU over the BUS to the GPU since GPUs do computation much faster than your CPU. Then with your scene graph you will not have to worry about creating lights, creating materials and applying them for all of these will be done in your fragment shader (GLSL) or what is called pixel shader (DirectX). All of your vertices and index information will be passed into the vertex Shader. Then it is just a matter of linking your shaders to an openGL program.

If you would like to see and learn about everything I have described above then visit the community that I've been a member of since 2007-08 at www.MarekKnows.com and join our community. He has several video tutorial series to learn from.