The Point-by-Point Generating Algorithms For Curves And Surfaces

As the foundation of Computer-Aided Geometric Design(CAGD), it is important to improve the way of the generating algorithms for curve and surfaces .We compare the algorithms in the present work with the traditional algorithms, and can come to the conclusion that the former is more efficient .in the work we discuss the point-by-point algorithms of implicit curve and surface systematically, introduce the general and extended algorithms of line-drawing, and have these algoritms improved. An all-integer arithmetic algorithm is also introduced, we improve the algorithm and extend it to surface. On the basis of the algorithm we bring forward a new point-by-point algorithm for surface-drawing,which can draw a great number of surfaces.As far as parametric curves and surfaces are concerned, we discuss the point-by-point generating algorithms for parametric polynomial curves, parametric rational curves and parametric polynomial surfaces.At last, we point out the faults of the algorithms and bring forward what can be done to improve it.