Line Segment Rasterization in N-dimensional Space Line Segment Rasterization in N-dimensional Space

The rapid development of scanning and measuring hardware for medical imaging and for scientiic experiments, the introduction of animation techniques into common use have created the need to understand n-dimensional raster geometry, where n > 3. After a brief review of continuous geometry in R n , this paper presents the discrete regular structure called a hyperlattice used for deening n-dimensional raster geometry. The concept of neighbourhood in hyperlattices is studied in detail, introducing a new deenition which extends existing deenitions by taking into account the border of the Voronoi sets associated with neighbouring lattice points. A general deenition of discrete curves based on these new deenitions is then introduced. Finally a general deenition of rasterization onto hyperlattices is given, and algorithms for rasterizing straight lines onto n-dimensional lattices are presented. A detailed analysis of line-drawing algorithms onto hyperlattices is then presented.