A Parameterization Method Based On The Error Minimization Model

The curve and surface modeling technology mainly studies the display, representation,design, and analysis of curve and surface in the computer graphics system. Rational parametric representation is an important one of describing curve and surface in geometric modeling system. Now, the optimal parameterization studies of curve and surface are mostly based on parameter transformation and deducing formula, which is characteristic of differential geometry. Finally the problems of re-parameterization and the optimal parameterization of parametric curve and surface are solved. Research of different parameterization method has an important theoretical significance and practical value for curve and surface modeling.Different parameterized algorithm and its application are analyzed in this paper. On this basis, this paper present a new parameterization method based on error minimization model.The error between polygonal line and curve could reach the minimum approximately, when the parameters of the curve are evenly selected. At first, the standard of measuring the performance of linear approximation algorithm of parametric curve is put forward with the geometry information-- rate and curvature of curve. The sufficient condition of the optimal parameterization is given under this standard. Based on the sufficient condition, optimal rational parameterization formula of the planar quadratic algebra curve and parametric factor of general rational parametric curve to be parameterized once more are determined directly.The experimental results show that the algorithm can greatly reduce the amount of calculation,greatly shorten the time of geometry processing phase, and improve the drawing speed and the working efficiency of the computer in mechanical manufacturing and engineering drawing.The method not only provides a new research idea for solving curve and surface parameterization problem, but also has strong widespread practicability in the practice application.