Adaptive Cubic B-Spline Approximation On Curve And Surface Reconstruction

As one of the important technical ways in both reverse engineering and CAGD fields, curve and surface reconstruction is widely used in the Computer Graphics, medical images, CAD/CAM fields with the help of the fast development of computer techniques these days. In this paper, we research on such problem in Mechanical Engineering field.Firstly, the development history of reverse engineering is introduced. The curve and surface reconstruction, which is the key technique in such field, is given more details. One simple introduction of the paper's contents is presented at the end of this chapter.Chapter Two contains some related knowledge of this paper.In Chapter Three, we use Cubic B-spline to adaptively fit a set of ordered noise data. After analyzing and researching on the algorithm of classical method, we construct 'Tree Chain of Dominant Points' to get the initial control points' number of the spline curve based on the basic knowledge that "The dominant points, which play an important role in convex-preserving fitting, should be differentiate with the key points, which is the key factor of the figure-preserving. Besides, one algorithm for adding or deducting control points is also considered, which is motivated by an insight that the number of control points affect the working efficiency.Five experimental examples demonstrate that it can generate a B-spline curve with higher speed, less deviation, fewer control points.Surface reconstruction is introduced in Chapter Four. Based on the thought of 'Points-Curve-Surface', we use the curve fitting algorithm, which is introduced in Chapter Three, to obtain the contour line of surface after data segmenting. Slant and surface potential is also considered.Some experiments on the sun hat surface and membrane are given at the end of Chapter four. The results of fitting effect and the sketch map of 'Error Needle' show that the algorithm can not only reduce more sample data but also obtain the reconstructed surface with better figure-preserving.