International audienceWe extend the notion of canonical orderings to cylindric triangulations. This allows us to extend the incremental straight-line drawing algorithm of de Fraysseix, Pach and Pollack to this setting. Our algorithm yields in linear time a crossing-free straight-line drawing of a cylindric triangulation G with n vertices on a regular grid \mZ/w\mZ\times[0..h], with w≤2n and h≤n(2d+1), where d is the (graph-) distance between the two boundaries. As a by-product, we can also obtain in linear time a crossing-free straight-line drawing of a toroidal triangulation with n vertices on a periodic regular grid \mZ/w\mZ\times\mZ/h\mZ, with w≤2n and h≤1+n(2c+1), where c is the length of a shortest non-contractible cycle. Since c≤2n, the grid area is O(n5/2). Our algorithms apply to any triangulation (whether on the cylinder or on the torus) that have no loops nor multiple edges in the periodic representation