Modeling Free-form Surface Based On Projection Data, Normal Vectors And Principal Curvatures Of Controlling Points

In the paper, the production and development of CAGD is introduced, as an important geometric modeling techniques, the applications of free-form surface modeling are reviewed in our country and others. As the same time, the free-form surface modeling methods are summed up and compared.Based on the existed surface modeling ideal, free-form surface modeling method is presented, which is from projection data, normal vectors and principal curvatures of controlling points. In addition, differential geometric is used as a math tool to expound on two aspects in different conditions, especially on conversing the two-dimensional coordinates of controlling points, normal vectors and principal curvature into the three-dimensional coordinates. Algorithms and procedure flow charts are also illustrated. And then free-form surface is modeled according to the algorithms of parameter cubic splines. As the same time, graphical examples of the Ferguson curve and bi-cubic surface patches generated by ObjectARX code running on a PC are also included to illustrate the property of a surface.