pointSize contains the rasterized diameter of both aliased and antialiased points. The initial value is 1. Using a point size other than 1 has different effects, depending on whether point antialiasing is enabled (see pointSmooth) or point sprites are enabled (see pointSprite). Both are initially disabled.

The specified point size is multiplied with a distance attenuation factor and clamped to the specified pointSizeRange, and further clamped to the implementation-dependent point size range to produce the derived point size using

   derivedSize = clamp (size * sqrt (1 / (a + b * d + c * d^2)))

where d is the eye-coordinate distance from the eye to the vertex, and a, b, and c are the distance attenuation coefficients (see pointDistanceAttenuation).

If multisampling is disabled, the computed point size is used as the point's width.

If multisampling is enabled, the point may be faded by modifying the point alpha value (see sampleCoverage) instead of allowing the point width to go below a given pointFadeThresholdSize. In this case, the width is further modified in the following manner:

   width = if derivedSize >= threshold then derivedSize else threshold

The point alpha value is modified by computing:

   alpha = if derivedSize >= threshold then 1 else (derivedSize / threshold)^2

If point antialiasing is disabled, the actual size is determined by rounding the supplied size to the nearest integer. (If the rounding results in the value 0, it is as if the point size were 1.) If the rounded size is odd, then the center point (x, y) of the pixel fragment that represents the point is computed as

   (x, y) = (floor xw + 0.5, floor yw + 0.5)

where xw and yw indicate window coordinates. All pixels that lie within the square grid of the rounded size centered at (x, y) make up the fragment. If the size is even, the center point is

   (x, y) = (floor (xw + 0.5), floor (yw + 0.5))

and the rasterized fragment's centers are the half-integer window coordinates within the square of the rounded size centered at (x, y). All pixel fragments produced in rasterizing a nonantialiased point are assigned the same associated data, that of the vertex corresponding to the point.

If antialiasing is enabled, then point rasterization produces a fragment for each pixel square that intersects the region lying within the circle having diameter equal to the current point size and centered at the point's (xw, yw). The coverage value for each fragment is the window coordinate area of the intersection of the circular region with the corresponding pixel square. This value is saved and used in the final rasterization step. The data associated with each fragment is the data associated with the point being rasterized.

Not all sizes are supported when point antialiasing is enabled. If an unsupported size is requested, the nearest supported size is used. Only size 1 is guaranteed to be supported; others depend on the implementation. To query the range of supported sizes for antialiased points and the size difference between supported sizes within the range, query smoothPointSizeRange and smoothPointSizeGranularity, respectively. For aliased points, query the supported range with aliasedPointSizeRange.

The point size specified when pointSize is set is always returned when it is queried. Clamping and rounding for aliased and antialiased points have no effect on the specified value.

A non-antialiased point size may be clamped to an implementation-dependent maximum. Although this maximum cannot be queried, it must be no less than the maximum value for antialiased points, rounded to the nearest integer value.

An InvalidValue is generated if pointSize is set to a value less than or equal to zero.

An InvalidOperation is generated if pointSize is set during renderPrimitive.

The range to which the derived point size is clamped, see pointSize. Note that the size is further clamped to the implementation-dependent limits, see aliasedPointSizeRange and smoothPointSizeRange. The initial range is (0, 1).

An InvalidValue is generated if the lower or upper bound of the range is set to a value less than zero. If the lower bound is greater than the upper bound, the point size after clamping is undefined, but no error is generated.

The threshold for alpha attenuation of points when multisampling is used, see pointSize. The initial threshold is 1.

An InvalidValue is generated if the threshold is set to a value less than zero.