Abstract
This work presents an algorithm to polygonize the surface of triangulated 3D digital objects by unifying the edge-adjacent face triangles having similar norms. If the cosine of the dihedral angle between two faces is above a predefined threshold, then the faces are considered to be similar with respect to their norms. By applying the Least Square Method on the boundary vertices of the set of the merged face triangles, a new norm is computed, optimizing the norms of the individual face triangles constituting the merged set. The coordinates of the boundary vertices are recomputed based on this new norm. Final coordinates are the mean value of all the instances of each vertex. As a consequence, many of the vertices of the original input object are removed. In effect, the object can be described by a number of polygons, which is significantly less than the number of original face triangles. Hence, a substantial amount of compression is achieved. Also, the shape and structure of the object can be discerned from the polygons representing it. This process may further be utilised in improved shape analysis. Distortion is computed to illustrate that a trade-off may be made between distortion and compression.
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A preliminary version of this work appeared in Saha and Biswas (2020).
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Saha, S., Biswas, A. Surface polygonization of 3D objects using norm similarity. J Comb Optim 44, 2729–2747 (2022). https://doi.org/10.1007/s10878-021-00786-2
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DOI: https://doi.org/10.1007/s10878-021-00786-2