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Z-buffering 250
}
}
display COLOR array.
Mathematics
The range of depth values in camera space (see 3D projection) to be rendered is often defined between a and
value of . After a perspective transformation, the new value of , or , is defined by:
After an orthographic projection, the new value of , or , is defined by:
where is the old value of in camera space, and is sometimes called or .
The resulting values of are normalized between the values of -1 and 1, where the plane is at -1 and the
plane is at 1. Values outside of this range correspond to points which are not in the viewing frustum, and
shouldn't be rendered.
Fixed-point representation
Typically, these values are stored in the z-buffer of the hardware graphics accelerator in fixed point format. First they
are normalized to a more common range which is [0,1] by substituting the appropriate conversion
into the previous formula:
Second, the above formula is multiplied by where d is the depth of the z-buffer (usually 16, 24 or 32
bits) and rounding the result to an integer: [1]
This formula can be inversed and derivated in order to calculate the z-buffer resolution (the 'granularity' mentioned
earlier). The inverse of the above :
where
The z-buffer resolution in terms of camera space would be the incremental value resulted from the smallest change
in the integer stored in the z-buffer, which is +1 or -1. Therefore this resolution can be calculated from the derivative
of as a function of :
Expressing it back in camera space terms, by substituting by the above :