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.

这项工作提出了一种算法，通过统一具有相似范数的边相邻面三角形来多边形化三角化 3D 数字对象的表面。如果两个面之间的二面角的余弦值高于预定义的阈值，则认为这两个面的范数相似。通过对合并的面三角形集合的边界顶点应用最小二乘法，计算新范数，优化构成合并集合的各个面三角形的范数。边界顶点的坐标根据这个新范数重新计算。最终坐标是每个顶点的所有实例的平均值。结果，原始输入对象的许多顶点被移除。实际上，对象可以用许多多边形来描述，这明显少于原始面部三角形的数量。因此，实现了大量的压缩。此外，对象的形状和结构可以从代表它的多边形中辨别出来。该过程可进一步用于改进的形状分析。计算失真以说明可以在失真和压缩之间进行权衡。