In, for example, a sensor, when you change the sensor angle, the sensor volume cone created is always centered on the containing prim's x-axis. Not so for particle systems using ANGLE_CONE. If you set the OUTER_ANGLE parameter to a vanishingly-small value, the cone becomes a line more-or-less aligned with the containing prim's z-axis. As the OUTER_ANGLE parameter increases in value, the centerline of this cone starts creeping downwards; at one-quarter-PI, it has become aligned halfway between the z- and y-axes.
That's really freaking annoying.
