Exact algorithms for circles on the sphere

We describe exact representations and algorithms for geometric operations o n general circles and circular arcs on the sphere, using integer homogeneou s coordinates. The algorithms include testing a point against a circle, com puting the intersection of two circles, and ordering three arcs out of the same point. These tools support robust and efficient operations on maps ove rs the sphere, such as point location and map overlay, and provide a reliab le framework for robotics, geographic information systems, and other geomet ric applications.