pipe.

with royal icing??

AYes

The picture you posted is a buttercream cake, in which case buttercream would work just as well.

I have done this on fondant and made a template out of card stock and traced it onto the the cake.  You need to figure out the spacing, so it works out evenly. The template made it so much easier.

Hope that helps.

I would be wanting to put the stitches on a fondant covered cake. What kind of template did you use?
 

Ron Ben Israel had a tutorial on a cake he did with all different kinds of embroidery stitches on it. It was fondant on fondant. For something like this, he used tiny strings and then snipped them at even intervals with a pair of VERY sharp little scissors.

ANo, fondant on fondant.