Section 3.3.1.5.3. Representation of surfaces by lines

The commonest means of representing surfaces, especially contour surfaces, is to consider evenly spaced serial sections and to perform two-dimensional contouring on each section. Repeating this on serial sections in two other orientations then provides a good representation of the surface in three dimensions when all such contours are displayed. The density is normally cited on a grid with submultiples of a, b and c as grid vectors, inverse linear interpolation being used between adjacent grid points to locate points on the contour. For vector-graphics applications it is expedient to connect such points with straight lines; some equipment may be capable of connecting them with splines though this is burdensome or impossible if real-time rotation of the scene is required. Precalculation of splines stored as short vectors is always possible if the proliferation of vectors is acceptable. For efficient drawing it is necessary for the line segments of a contour to be end-to-end connected, which means that it is necessary to contour by following contours wherever they go and not by scanning the grid. Algorithms which function in this way have been given by Heap & Pink (1969) and Diamond (1982a). Contouring by grid scanning followed by line connection by the methods of the previous section would be possible but less efficient. Further contouring methods are described by Sutcliffe (1980) and Cockrell (1983).

For raster-graphics devices there is little disadvantage in using curved contours though many raster devices now have vectorizing hardware for loading a line of pixels given only the end points. For these devices well shaped contours may be computed readily, using only linear arithmetic and a grid-scanning approach (Gossling, 1967). Others have colour-coded each pixel according to the density, which provides a contoured visual impression without performing contouring (Hubbard, 1983).