Planar smooth curves reconstruction from unorganized points

Curves reconstruction from unorganized points is a very important problem in computer vision, computer graphics, industrial and medicinal CT image processing. First a novel algorithm called Matching Adjacent Point Algorithm for reconstruction of planar smooth curves from unorganized points is presented, and the theoretic proof of the algorithm is also given. Based on the Delaunay triangulation of the point set, the algorithm can fast find the adjacent point of a point so that its time complexity can reach O(nlogn). The experimental result shows that the algorithm is efficient. The algorithm is very useful to object reconstruction in computer vision and computer graphics.