Based On Quadratic B-spline Curve, Surface Approximation Algorithm

The developments of Computational Geometry, Computer Graphic motivate the developments of modern industry, manufacturing. In turn, the developments of modern industry, manufacturing put forward higher requests to Computational Geometry, Computer Graphic, especially in curve, surface approximation field. But the traditional interpolation, approximation algorithm both have advantages and disadvantages.After research the curve approximation algorithm in reference[1],we use the square B-Spline as the tool and extend the algorithm to surface approximation field.This algorithm avoided their disadvantages and combined their advantages of interpolation,fitting algorithm.The algorithm provided in this text is general and it can be expaned to other field, such as spline approximation, function approximation and the curve fitting.The primary contributions of this paper contain the following points:1) Research the advantages and disadvantages of the traditional methods of spline curve, surface interpolation and approximation algorithm.2) Research the curve approximation algorithm provided in reference[1].Revised some data error. Perfect it's theories proof. Carry on more strict, more general numerical experiment.3) According to the request of suface approximation in modern industry, we setup mathematics model.Put forward the concept of structure vector, structure matrix.4) We expanded the curve approximation algorithm to surface approximation field successfully, and carried on theories proof. Considering it is difficult to express the iteration process in mathematics language, we put forward matrix2vector method.5) Research smooth property of the B-Spline surface. We carried on strict theories poof about smooth properties at the connection field of the surfcae.6) Useing OpenGL, Matlab etc. as painting tools, we carried on approximate effect experiment, numerical experiment.