Fig. 1. Ambiguity of normal orientation

Fig. 2. Schematic of two-dimensional points. (a) Number of theoretical intersections; (b) phenomena caused by excessive error threshold

Fig. 3. Flow chart of spatial division and algorithm for judging voxel centroid position

Fig. 4. Normal of point cloud inside voxel from different perspectives. (a) Perspective 1: without orientation; (b) perspective 2: without orientation; (c) perspective 1: initial orientation; (d) perspective 2: initial orientation

Fig. 5. Flow chart of normal initial orientation algorithm

Fig. 6. Flow chart of normal quadratic orientation algorithm

Fig. 7. Comparison of frontage effects of three models before and after improvement. (a) Normal estimate by proposed method; (b) Poisson surface reconstruction by proposed method; (c) normal estimation from Ref. [11]; (d) Poisson surface reconstruction from Ref. [11]

Fig. 8. Comparison of backside effects of three models before and after improvement. (a) Normal estimate by proposed method; (b) Poisson surface reconstruction by proposed method; (c) normal estimation from Ref. [11]; (d) Poisson surface reconstruction from Ref. [11]