| Reverse engineering is a new technique developing with the development of Computer Science and the progress of data measuring technology. Its appearance has in fact changed the design mode of producing material objects in CAD system from drawing. It designs and offers a new way for fast production and rapid prototyping. Curve and surface reconstruction are two important problems in reverse engineering. Reconstructing the geometrical model of the object from the sample points carries on the foundation of analyzing, calculating and drawing of the object. It is also an important way to study the nature of curves and surfaces.This paper first introduces the development history of Computer Aided Design & Computer Aided Manufacture, and then derive the idea of reverse engineering and curve reconstruction from data points. Some existing methods are introduced.In chapter 2, some important definitions and some common ideas about curve fitting are provided. In the area of fitting a curve , the fitting method can trace back to the least-squares method. The curve final formation has developed from polynomialcurve to parametric curve and then to the new hotspot ------subdivision curve. Toparametric curve, the parameterization is a key step. Some common parameterization method has been introduced in the paper. To subdivision curve, many common concepts and methods are provided too.In chapter 3, a new arithmetic of parameterization is provided in allusion to those common methods. The common methods almost has no affine invariability, that is to say, parameterization has to be executed again after affine transformations to get theright transformation result. Then their efficiency is comparatively low. This new method develops and proves the nielson basic function. And then use the new function to parameterization and abtain the good result. But because of its mathematical definition, the method can not deal with the situation when the points are all on a line.Chapter 4 give a new solution for the carry-over question in chapter 2. I t is subdivision curve. This method itself is not the parametric curve reconstruction, so it need not parameterization. A new point is inserted in accordance with the position of known points, then iteration on every layer to get a curve. This method's arithmetic is simple, and it will not be affected by affine transformation. Different to common subdivision method, the idea of half- static and push-back is adopted. What is more reasonable is that push-back is implemented according to the offset and the characteristic of the known points. At the same time, the method can be used in computer design for its half- static.Finally, the problem of curve reconstruction is analyzed, and this paper summarizes the merit and flaw of the method which is provided in it. All the new ideas given in the paper still settle on research of curve, and they can be used on surface reconstruction in the future. |
