An Approach to Describe Parametric Curves Using Hough-Based Arc Spline Approximation

This paper develops the method to approximate a parametric curve by an arc spline with a feature extraction process using Hough transform. This has been done to make the curve compatible with devices and applications which have limitations of parametric inputs. The proposed algorithm uses Hough transform technique to detect linear and circular-arc parts on the curve prioritizing the maximum arc length. Arc spline segments are then generated corresponding to the detected shapes with C¹ continuity. This method is different from other arc spline approximation schemes which subdivide the curve according to time or error data. This work also develops a representation method to describe the shape or pattern of the curve using arc spline information. Experimental results show that similarity of any two curves can be detected and measured by comparing their arc spline data. In application, this method can be used to generate vector graphics and tool paths for numerical control machines with higher compatibility than a parametric description.