Visibility in Space

The text concludes with an algorithm for visibility in 3D. This chapter merely pulls together the ingredients, as they have all already been encountered. Discarding invisible sets relies on the use of Boolean algebra on regular sets (Chapters 28 and 29) adapted to spherical geometry (Chapters 8 and 9). By using rational numbers as the number type (Chapter 7) and ensuring that the algebraic degree of intermediate objects and predicates remains low (Chapter 6), it is possible to design and implement a 3D vector visibility system that never fails. The resulting half-edge data structure is constructed using only two Euler operators (Chapter 27).

Using a general and layered solution to this most intriguing and most classical [108] of problems in computer graphics and computer-aided design may be what is missing to spur vector rendering. Raster images are well suited for raster displays, but they are ill-matched to the printed page, which are capable of significantly higher resolutions than can be afforded by raster images. The computation of the spherical visibility map [56] may be a suitable starting point for large areas of computer graphics to be restudied with the objective of producing pure vector shaded synthetic imagery aimed at the printed page. The reader interested in a survey of the vast visibility literature is referred to the work just cited for starting pointers.