Subject: Re: 3D camera question
Thanks for your reply. The mathematical notation is a little confusing to
me, but let me see if I understand this correctly.
I should have a 4x4 matrix representing the location and rotation of the
camera. Do I plug the numbers representing the location and rotation
directly into positions in the matrix or should I use the standard
rotate/translate way of altering the matrix?
Once I have that matrix, I then invert it. Once inverted I multiply any
existing world matrixes of each object by the camera matrix and that should
Any code/psuedocode would be really helpful.
Thanks so much for your help.
> Let the camera be defined by a homogeneous matrix 4*4 C, such that the 3
> first vectors represent the x, y and z axes of the camera (with the
> homogeneous w = 0) and the last vector represents the position of the
> camera (point, thus with w = 1).
> Given any point, the matrix C represent a transformation from camera
> space to the world space. Now I must assume column vectors are used, but
> this should not be an issue. Thus:
> Cx = y
> x is a point in camera space
> y is a point in world space
> If the camera axes x,y,z are linearly independent, then C is invertible
> x = (C^-1)y
> The result:
> To transform a point in world space to the camera space you need to
> transform it with the *inverse* of the camera matrix.
> If you are unfamiliar with homogeneous stuff:
> An affine transformation can be given in the form
> f(x) = Ax + b
> A contains the camera axes
> b is the camera position
> The inverse of the transformation, if exists (A nonsingular), is:
> f^-1(x) = (A^-1)(x - b)
> Using the same reasoning as before then:
> x = f^-1(y) = (A^-1)(y - b)
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