A straight-line drawing of a plane graph\udis called an open rectangle-of-influence drawing if there is no vertex\udin the proper inside of the axis-parallel rectangle defined by the two ends of every edge.\udIn an inner triangulated plane graph,\udevery inner face is a triangle although the outer face is not always a triangle. In this paper,\udwe first obtain a sufficient condition for an inner triangulated plane graph G\udto have an open rectangle-of-influence drawing;\udthe condition is expressed in terms of a labeling of angles of a subgraph of G.\udWe then present an O(n^{1.5}/log n)-time algorithm to examine whether G satisfies\udthe condition and, if so, construct an open rectangle-of-influence drawing of G on an\ud(n-1) x (n-1) integer grid, where n is the number of vertices in G.\ud
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