Abstract: A technique for displaying labels on a digital map comprise displaying the digital map via a user interface at a first zoom level, including displaying non-overlapping labels. The method also comprises receiving, via the user interface, a request to zoom out from the digital map to a second zoom level, where the second zoom level corresponds to smaller magnification than the first zoom level, and where the plurality of labels have the same size at the first zoom level and the second zoom level. Still further, the method includes resolving collisions among the plurality of labels at the second zoom level in response to receiving the request and prior to zooming out from the first zoom level, and zooming out from the digital map at the first zoom level to the second zoom level via at least one intermediate zoom level.

Abstract: A technique for displaying labels on a digital map comprise displaying the digital map via a user interface at a first zoom level, including displaying non-overlapping labels. The method also comprises receiving, via the user interface, a request to zoom out from the digital map to a second zoom level, where the second zoom level corresponds to smaller magnification than the first zoom level, and where the plurality of labels have the same size at the first zoom level and the second zoom level. Still further, the method includes resolving collisions among the plurality of labels at the second zoom level in response to receiving the request and prior to zooming out from the first zoom level, and zooming out from the digital map at the first zoom level to the second zoom level via at least one intermediate zoom level.

Abstract: A method of rasterizing a line on a display having pixels with locations defined by a polar coordinate system uses the sign of a discriminant to choose which of two candidate pixels is to be the next pixel on the rasterized line. The discriminant, which is derived from the desired line, is evaluated at a point in the neighborhood of the candidate pixels. The discriminant value depends on the local slope of the line in polar coordinates. The method divides the line into segments having selected ranges of slope and rasterizes the desired line along each segment.

Abstract: In a cylindrical coordinate system, the dominant direction of a line changes in a predictable manner. A rasterizer uses this fact to efficiently render a desired line on a volumetric display. It does do by determining whether first and second points on the desired line are on first and second constituent line-segments of the desired line, the first and second constituent line-segments having different dominant directions. On the basis of the determination, the rasterizer renders a second voxel representative of the second point on the desired line by incrementally proceeding from a first voxel representative of the first point. The location of the second voxel is selected to minimize a distance between that second voxel and the desired line.