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matrixgraphics3ddeterminants

Is there any use for the determinant of a 4x4 matrix in computer graphics?

In most graphics libraries I've seen, there's some function that returns the determinant from 3x3 and 4x4 matrices, but I have no idea when you'd actually need to use the determinant in 3D computer graphics.

What are some examples of using a determinant in 3D graphics programming?

Solution

  • Off the top of my head...

    If the determinant is 0 then the matrix cannot be inverted, which can be useful to know.

    If the determinant is negative, then objects transformed by the matrix will reversed as if in a mirror (left handedness becomes right handedness and vice-versa)

    For 3x3 matrices, the volume of an object will be multiplied by the determinant when it is transformed by the matrix. Knowing this could be useful for determining, for example, the level of detail / number of polygons to use when rendering an object.