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In this paper, we study the problem of finding smooth orthogonal layouts of low \\emph{edge complexity}, that is, with few segments per edge. We say that a graph has \\emph{smooth complexity} k---for short, an SC_k-layout---if it admits a smooth orthogonal drawing of edge complexity at most $k$.\n  Our main result is that every 4-planar graph has an SC_2-layout. 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