Strictly convex drawings of planar graphs

Every three-connected planar graph with n vertices has a drawing on an O(n(2)) x O(n(2)) grid in which all faces are strictly convex polygons. These drawings are obtained by perturbing (not strictly) convex drawings on O(n) x O(n) grids. Tighter bounds are obtained when the faces have fewer sides. In the proof, we derive an explicit lower bound on the number of primitive vectors in a triangle.