Graphical user interfaces are composed of varying elements (text, images, etc.) whose visual arrangement has been relatively well established in the context of rectangular interfaces. The advent of non-rectangular displays questions this knowledge. In this paper we study how traditional content layouts can be adapted to fit different nonrectangular displays. We performed a first qualitative study where graphic designers fitted text and images into different non-rectangular displays. From the analysis of their output we generalize and adapt ten composition principles that have been proposed in the literature for rectangular displays. We evaluate the revised principles through a paired comparison questionnaire where 57 participants compared pairs of layouts. Using the Bradley-Terry-Luce model to analyze our data we show that some results contradict current conventions on visual design for rectangular displays. We then extracted the most interesting cases and conducted a follow up study with additional shapes to investigate how the principles generalize. From these results we propose a set of guidelines for designing visual content for non-rectangular displays.