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Coarse piecewise linear approximation of surfaces causes the undesirable polygonal appearance of silhouettes. We present an efficient method for smoothing the silhouettes of coarse triangle meshes using efficient 3D curve reconstruction and simple local remeshing. It does not assume the availability of a fine mesh and generates only a moderate amount of additional data at runtime. Furthermore, polygonal feature edges are also smoothed in a unified framework. Our method is based on a novel interpolation scheme over silhouette triangles, and this ensures that smooth silhouettes are faithfully reconstructed and always change continuously with respect to the continuous movement of the viewpoint or objects. We speed up computation with GPU assistance to achieve real-time rendering of coarse meshes with the smoothed silhouettes. Experiments show that this method outperforms previous methods for silhouette smoothing.