Quadratic curve and surface fitting via squared distance minimization

Quadratic curve and surface fitting to a set of data points are fundamental problems in reverse engineering and many other application areas. We develop the fitting methods for quadratic curves and surfaces based on the squared distance minimization technology. The basic idea of squared distance minimization for curve and surface fitting is first presented. Then we devise the corresponding squared distance term for each quadratic curve and surface, and minimize it to obtain its parameters. We repeat the squared distance minimization and update the parameters of the quadratic curve and surface by iterations until convergency. Consequently, the final fitting result is achieved. Experimental results demonstrate the effectiveness of the fitting method.

Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (167 K)Download as PowerPoint slideHighlights► Squared distance minimization is used for quadratic curve and surface fitting. ► Squared distance function is devised for typical quadratic curves. ► Squared distance function is designed for typical quadratic surfaces. ► A variety of experimental results demonstrate that SDM-based method is effective and efficient for quadratic curve and surface fitting.