How to generate the stair step curve(outline) for any 2d shape(or curve)?

Question

If I have the coordinates of the points on the outline of an arbitrary 2D shape, how can I find the coordinates of points composing the outline of a stair step curve, which

Answer 1

Seems you need any line rasterization algorithm (that gives coordinate of integer grid points approximating line segment).

Consider Bresenham algortihm or DDA one.