Sharpen&Bend: Recovering Curved Edges in Triangle Meshes Produced by Feature-Insensitive Sampling

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Attene, Marco
Falcidieno, B. (Bianca)
Spagnuolo, Michela
Rossignac, Jarek
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Various 3D acquisition, analysis, visualization and compression approaches sample surfaces of 3D shapes in a uniform fashion, without any attempt to align the samples with the sharp edges and corners of the original shape. Consequently, the interpolating triangle meshes chamfer these sharp features and thus exhibit a relatively large error in their vicinity. We introduce here two new filters that restore a large fraction of the straight or curved sharp edges missed by feature-insensitive sampling processes: (1.) EdgeSharpener restores automatically the sharp edges by identifying and splitting the chamfer edges and by forcing the new vertices to lie on intersections of planes extending the smooth surfaces incident upon these chamfers and (2.) Bender subdivides the resulting triangle mesh using a combination of the Butterfly subdivision scheme, for the smooth portion of the mesh, with a four-point subdivision scheme, for the sharp edges, in order to preserve the sharpness of the recovered sharp edges while bending their polyline approximations into smooth curves. This combined post-processing (named Sharpen&Bend) significantly reduces the error produced by feature-insensitive sampling processes. For example, we have observed that the L2 error introduced by the SwingWrapper remeshing-based compressor can often be reduced down to a fifth by executing EdgeSharpener alone after decompression, with no additional information. For meshes produced by retiling shapes with curved edges, this error may be further reduced by two thirds if we follow the EdgeSharpening phase by Bender. Thus the combined Sharpen&Bend process takes a triangle mesh produced by a feature-insensitive sampling of a curved shape with sharp curved features and automatically refines the mesh to produce a more accurate approximation of the initial shape.
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