New Approach to Computation of Offset Curves for Point-Based Geometries

This paper proposes a new method for the computation of offset curve in point-based geometries. Point-based tool path calculations are promising for surface milling, rapid prototyping, and engraving using three-axis milling machines. Different from existing methods, in proposed method, the offsets of curves are implemented using level set-based theory in image domain. Therefore problem resulted from topology changes of curves will be remedied automatically, and the level set-based segmentation approaches may be applied to detect the contours of objects on noisy image and compute their offset curves. In order to guide the offset operation at specific direction, the image with offset curve is transformed into binary level set representation at first. Then an offset filter is introduced to perform offset operation. As a result, an initial offset curve in the image can be obtained by filtering at a specific direction. The offset curve is further refined by using curve evolution approach. The resulting algorithm has been demonstrated by numerical experiment results.