This paper looks into the effectiveness of B-spline approximation algorithm in approximating the bicubic B-spline surface from the set of scattered data points which are taken from the scanned 3D object in the form of point sets. Using the B-spline approximation algorithm, the unknown B-spline control points are determined, followed by the reconstruction of the bicubic B-spline surface. Using a set of neighbourhood of data points, a B-spline surface patch may be constructed, which can be pieced together to form the final surface. Modification of the B-spline approximation algorithm is carried out before the reconstruction in order to fit the scattered data points closely. Here, the density of the data points is scaled down due to the sparseness of the points that may affect the smoothness. The sample of scattered data points is chosen from a specific region in the point set model by using k-nearest neighbour search method. Furthermore, to fit the sample set of scattered data points accurately, they are reoriented in the normal direction. We also observe the effect of noise in the reconstruction of bicubic B-spline surface. Experimental results demonstrate that the scattered data points are better fitted after the modification of the algorithm and the accuracy of the approximated bicubic B-spline surface is easily influenced by the presence of noise.
Digital Object Identifier (DOI)
Jie Liew, Khang; Ramli, Ahmad; and Abd. Majid, Ahmad
"B-Spline Surface Fitting on Scattered Points,"
Applied Mathematics & Information Sciences: Vol. 10:
1, Article 28.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss1/28