OpenGL 4.2 (Compatibility Profile) - April 27, 2012

3.6. POLYGONS 243
3.6.5 Depth Offset
The depth values of all fragments generated by the rasterization of a polygon may
be offset by a single value that is computed for that polygon. The function that
determines this value is specified by calling
void PolygonOffset( float factor, float units );
factor scales the maximum depth slope of the polygon, and units scales an
implementation-dependent constant that relates to the usable resolution of the
depth buffer. The resulting values are summed to produce the polygon offset value.
Both factor and units may be either positive or negative.
The maximum depth slope m of a triangle is
m =
√ ( ) 2 ( ) 2 ∂zw ∂zw
+
(3.11)
∂x w ∂y w
where (x w , y w , z w ) is a point on the triangle. m may be approximated as
{∣ ∣ ∣}
∣∣∣ ∂z w ∣∣∣ m = max ,
∂z w ∣∣∣
∂x w
∣ . (3.12)
∂y w
If the polygon has more than three vertices, one or more values of m may be used
during rasterization. Each may take any value in the range [min,max], where min
and max are the smallest and largest values obtained by evaluating equation 3.11
or equation 3.12 for the triangles formed by all three-vertex combinations.
The minimum resolvable difference r is an implementation-dependent parameter
that depends on the depth buffer representation. It is the smallest difference in
window coordinate z values that is guaranteed to remain distinct throughout polygon
rasterization and in the depth buffer. All pairs of fragments generated by the
rasterization of two polygons with otherwise identical vertices, but z w values that
differ by r, will have distinct depth values.
For fixed-point depth buffer representations, r is constant throughout the range
of the entire depth buffer. For floating-point depth buffers, there is no single minimum
resolvable difference. In this case, the minimum resolvable difference for a
given polygon is dependent on the maximum exponent, e, in the range of z values
spanned by the primitive. If n is the number of bits in the floating-point mantissa,
the minimum resolvable difference, r, for the given primitive is defined as
r = 2 e−n .
If no depth buffer is present, r is undefined.
OpenGL 4.2 (Compatibility Profile) - April 27, 2012