# OpenGL OpenGL: Camera Transformation

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I have an object orbiting the earth (procedurally generated sphere). The planet is titled on a small angle (15 degrees) on the Z access to represent the tilt of the earth. The earth is slowing rotating around the x axis. The object is rotating around the earth at it's own speed, always staying in front of the equator. The difficulty here was, because the earth is rotated, the equator isn't at y=0 although I finally got this working. Each frame, depending on the location of the object around the earth, I use trig to obtain the x,y and z of where the ship should be (y is constant as it represents the center of the sphere). This x and z would be the final location of the ship had the earth not been titled and rotating however this isn't the case. Then, when drawing the ship, I first rotate Z by 15, Y by the current rotation around the earth and then draw the ship at x, y and z (which places it inline with the equator regardless of the angle of the earth). OpenGL does it's magic and draws the ship in the right place, of course. Now what I'm trying to do is to get a first-person view looking down from the ship at the earth as it orbits (trying to get it working with gluLookAt). I've managed to get the camera in the center of the ship and using matrix multiplication (multiplying the MODELVIEW transformation matrix by the ship location). I used atan to get the angle between the x & z coordinates of the ship / camera position and the earth and then rotate the ship and the camera around y so the face the earth. This works for the ship which is orbiting with it's right wing always pointing toward the equator, however the camera is acting strange. I can't say exactly what's going on but it appears that the camera is rotating around it's own Y axis or something. These are some caps taken from a static view down the Y-axis (this is not the view I'm trying to implement): You can see that the x (red line from ship) and z (blue line) axis are rotating (seemingly independent of the ship although I can't tell for certain) so a call to atan to get the angle between the and the earth probably isn't going to work. I've verified that the rotation of the x & z axis are what's messing the camera. When the angle between the x & z axis is pointing in direction of the earth, the earth is in view. Otherwise it's looking out into space. I'm not exactly sure why these axis are rotating and why the ship always has it's right wing facing the earth but the camera is rotating. Any ideas what could be going wrong?

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Unfortunately I don't have time to go into a full explanation at the moment, but I'd like to make a suggestion that you forget about all this X/Y/Z coordinates business and learn about camera matrix transformations. It is somewhat difficult to learn, but once you understand them you won't have to worry about any trigonometry anymore.

With what you are doing you'll find that it doesn't really scale very well and its not easy to change. You might find some awful combination of trig equations that works for your particular situation, but then you decide you want to tilt the earth's axis a little bit and all of your equations will be shot and you'll have to start over again. Or maybe you want the camera to orbit the moon instead, so theres another set of trig equations you have to work out.

With matrices you can define a matrix for the earth "mE" and a matrix for the camera relative to the object it orbits "mC". Or maybe even a moon matrix "mM". Then if you want to orbit the camera to the moon all you have to do is

glMultMatrixf( inverse(mE * mM * mC) ) //Camera is all set

I made a lengthy post here about a similar topic that might give you some starting ideas, or if you google for opengl camera matrix I'm sure you'll find lots of help there as well.

You can feel free to continue the way you're doing it with trig, but it will help you immensely in the future if you learn the matrix mathematics. Sorry for not answering your specific question, but I hope this helps :)

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Thanks for the reply. I sorta understand where you're coming from although I think it'll take a bit to get my head around.

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Video:

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Take a look at my code:
Sprite Class
(You mostly need to see the Constructor, the Render Method and the Move Method)
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Window Class:
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Brain Class
#include "Brain.h" #include "Sprite.h" #include "Window.h" struct Brain::Implementation { //Just A Flag. bool started; //Window Pointer. Window *window; //Sprite Pointer. Sprite *sprite; }; Brain::Brain(Window *window, Sprite *sprite) { //Create Pointer To Implementation. m_Impl = new Implementation(); //Initialize Implementation. m_Impl->started = true; m_Impl->window = window; m_Impl->sprite = sprite; } Brain::~Brain() { //Delete Pointer To Implementation. delete m_Impl; } void Brain::Start() { } void Brain::Update() { } Window * Brain::GetWindow() { return m_Impl->window; } Sprite * Brain::GetSprite() { return m_Impl->sprite; } bool Brain::GetStart() { return m_Impl->started; } void Brain::SetStart(bool value) { m_Impl->started = value; } Script Class (Its a Brain Subclass!!!)
#include "Script.h" Script::Script(Window *window, Sprite *sprite) : Brain(window, sprite) { } Script::~Script() { } void Script::Start() { std::cout << "Game Started!" << std::endl; } void Script::Update() { Input *input = this->GetWindow()->GetInput(); Sprite *sp = this->GetSprite(); //Move this sprite. this->GetSprite()->Move(200 * this->GetWindow()->GetDeltaTime(), input->GetKeyDown("left"), input->GetKeyDown("right"), input->GetKeyDown("up"), input->GetKeyDown("down")); std::cout << sp->GetTag().c_str() << ".x = " << sp->GetPos()->x << ", " << sp->GetTag().c_str() << ".y = " << sp->GetPos()->y << std::endl; }
Main:
#include "SpaceShooterEngine.h" #include "Script.h" int main() { Window w("title", 600,600); Scene *scene = new Scene(); Sprite *player = new Sprite("Resources/Images/player.png", "Player", 100,100); Sprite *other = new Sprite("Resources/Images/cherno.png", "Other", 400, 100); Sprite *other2 = new Sprite("Resources/Images/cherno.png", "Other", 300, 400); Brain *brain = new Script(&w, player); player->AddBrain(brain); scene->AddSprite(player); scene->AddSprite(other); scene->AddSprite(other2); w.LoadScene(scene); w.MainLoop(); return 0; }

I literally can't find what is wrong. If you need more code, ask me to post it. I will also attach all the source files.
Brain.cpp
Error.cpp
IndexBuffer.cpp
Input.cpp
Renderer.cpp
Scene.cpp
Sprite.cpp
Texture.cpp
VertexArray.cpp
VertexBuffer.cpp
VertexBufferLayout.cpp
Window.cpp
Brain.h
Error.h
IndexBuffer.h
Input.h
Renderer.h
Scene.h
SpaceShooterEngine.h
Sprite.h
Texture.h
VertexArray.h
VertexBuffer.h
VertexBufferLayout.h
Window.h

• Hello fellow programmers,
For a couple of days now i've decided to build my own planet renderer just to see how floating point precision issues
can be tackled. As you probably imagine, i've quickly faced FPP issues when trying to render absurdly large planets.

I have used the classical quadtree LOD approach;
I've generated my grids with 33 vertices, (x: -1 to 1, y: -1 to 1, z = 0).
Each grid is managed by a TerrainNode class that, depending on the side it represents (top, bottom, left right, front, back),
creates a special rotation-translation matrix that moves and rotates the grid away from the origin so that when i finally
normalize all the vertices on my vertex shader i can get a perfect sphere.
T = glm::translate(glm::dmat4(1.0), glm::dvec3(0.0, 0.0, 1.0)); R = glm::rotate(glm::dmat4(1.0), glm::radians(180.0), glm::dvec3(1.0, 0.0, 0.0)); sides[0] = new TerrainNode(1.0, radius, T * R, glm::dvec2(0.0, 0.0), new TerrainTile(1.0, SIDE_FRONT)); T = glm::translate(glm::dmat4(1.0), glm::dvec3(0.0, 0.0, -1.0)); R = glm::rotate(glm::dmat4(1.0), glm::radians(0.0), glm::dvec3(1.0, 0.0, 0.0)); sides[1] = new TerrainNode(1.0, radius, R * T, glm::dvec2(0.0, 0.0), new TerrainTile(1.0, SIDE_BACK)); // So on and so forth for the rest of the sides As you can see, for the front side grid, i rotate it 180 degrees to make it face the camera and push it towards the eye;
the back side is handled almost the same way only that i don't need to rotate it but simply push it away from the eye.
The same technique is applied for the rest of the faces (obviously, with the proper rotations / translations).
The matrix that result from the multiplication of R and T (in that particular order) is send to my vertex shader as r_Grid'.
// spherify vec3 V = normalize((r_Grid * vec4(r_Vertex, 1.0)).xyz); gl_Position = r_ModelViewProjection * vec4(V, 1.0); The r_ModelViewProjection' matrix is generated on the CPU in this manner.
// No the most efficient way, but it works. glm::dmat4 Camera::getMatrix() { // Create the view matrix // Roll, Yaw and Pitch are all quaternions. glm::dmat4 View = glm::toMat4(Roll) * glm::toMat4(Pitch) * glm::toMat4(Yaw); // The model matrix is generated by translating in the oposite direction of the camera. glm::dmat4 Model = glm::translate(glm::dmat4(1.0), -Position); // Projection = glm::perspective(fovY, aspect, zNear, zFar); // zNear = 0.1, zFar = 1.0995116e12 return Projection * View * Model; } I managed to get rid of z-fighting by using a technique called Logarithmic Depth Buffer described in this article; it works amazingly well, no z-fighting at all, at least not visible.
Each frame i'm rendering each node by sending the generated matrices this way.
// set the r_ModelViewProjection uniform // Sneak in the mRadiusMatrix which is a matrix that contains the radius of my planet. Shader::setUniform(0, Camera::getInstance()->getMatrix() * mRadiusMatrix); // set the r_Grid matrix uniform i created earlier. Shader::setUniform(1, r_Grid); grid->render(); My planet's radius is around 6400000.0 units, absurdly large, but that's what i really want to achieve;
Everything works well, the node's split and merge as you'd expect, however whenever i get close to the surface
of the planet the rounding errors start to kick in giving me that lovely stairs effect.
I've read that if i could render each grid relative to the camera i could get better precision on the surface, effectively
getting rid of those rounding errors.

My question is how can i achieve this relative to camera rendering in my scenario here?
I know that i have to do most of the work on the CPU with double, and that's exactly what i'm doing.
I only use double on the CPU side where i also do most of the matrix multiplications.
As you can see from my vertex shader i only do the usual r_ModelViewProjection * (some vertex coords).