determinants

This is a discussion on determinants within the Game Programming forums, part of the General Programming Boards category; I know of matricies in OpenGL and in my math class we just went over determinants. Are they of any ...

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    Registered User linuxdude's Avatar
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    determinants

    I know of matricies in OpenGL and in my math class we just went over determinants. Are they of any importance in game programming?

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    Registered User Draco's Avatar
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    determinants have a huge importance in game programming. Doing a vector cross product (which uses determinats) will get you the normal vector to a point/surface, etc. Just one example of this being used is most lighting algorithms. Other parts of graphics such as camera/screen orientation use them extensively as well, which is why it's programmed into OpenGL and DirectX.

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    How does doing a vector cross product use determinants? Maybe there's something in the theory I've missed, but I thought a determinant is basically just a number which you must compute along the process of calculating the inverse of a matrix.

    The determinant of a 3x3 matrix is calculated and returned by this function:

    inline float det3x3(float a1, float a2, float a3,
    float b1, float b2, float b3,
    float c1, float c2, float c3)
    {
    return a1*b2*c3+a2*b3*c1+a3*b1*c2-a3*b2*c1-a1*b3*c2-a2*b1*c3;
    }
    I'm pretty sure that once you have that number, you just divide each element by the determinant, after you've check that the determinant isn't zero (if it's zero, I think that means it's already its own inverse or something like that).
    Last edited by Darkness; 11-18-2004 at 06:28 PM.
    See you in 13

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    "...the results are undefined, and we all know what "undefined" means: it means it works during development, it works during testing, and it blows up in your most important customers' faces." --Scott Meyers

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    That's cool, I guess I never really examined any formal proofs of cross product, which is why I didn't know where the determinant came into play.
    See you in 13

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