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# 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

glLoadIdentity()
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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