Abstract: Described is a technology by which an application program such as a gadget may communicate with a sidebar program to output content for consumption by an auxiliary display device. The gadget may communicate with the sidebar program via sidebar APIs, and in turn the sidebar program communicates with an auxiliary display device platform via auxiliary display device APIs. Among its capabilities, the sidebar program may install gadgets on a host computer system, and upon detecting that the host computer system is configured to operate with an auxiliary display device, may install the gadget such that the gadget is configured to work with an auxiliary display device. The installation may be accomplished by having the sidebar program write information to a system registry.

Abstract: The convex hull of two polygons having congruent corresponding angles with the same orientation can be determined by analyzing the relationship of each vertex of one of the polygons relative to its adjacent vertices. More particularly a line may be defined between a selected vertex on one of the polygons and its corresponding vertex on the other polygon. If the vertices adjacent to the selected vertex both fall on the same side of the line, then a line connecting the selected vertex with its corresponding vertex lies on the convex hull of the two polygons. If, on the other hand, the vertices adjacent to the selected vertex are located on different sides of the line, then the line connecting the selected vertex with its corresponding vertex does not lie on the convex hull.

Abstract: The convex hull of two polygons having congruent corresponding angles with the same orientation can be determined by analyzing the relationship of each vertex of one of the polygons relative to its adjacent vertices. More particularly a line may be defined between a selected vertex on one of the polygons and its corresponding vertex on the other polygon. If the vertices adjacent to the selected vertex both fall on the same side of the line, then a line connecting the selected vertex with its corresponding vertex lies on the convex hull of the two polygons. If, on the other hand, the vertices adjacent to the selected vertex are located on different sides of the line, then the line connecting the selected vertex with its corresponding vertex does not lie on the convex hull.