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A point sprite is usually used for particle engines. When we draw a
point sprite, we just specify the texture, center, and size. What gets
drawn is a textured square with the specified side-size. It faces the
user ("automatically billboarded"). This reduces the vertex-bandwidth
necessary by a factor of 4, and lets the billboarding
happen automatically on the GPU. We cannot shade a point sprite with a
color AFAIK (unlike a quad, where you can specify per-vertex colors
that get interpolated and multiplied with the texel color by default).
Thanks to Stefan Monov for sending this information.