New Approximation Methods for Planar Offset and Convolution Curves

We present new methods to approximate the offset and convolution of planar curves. These methods can be used as fundamental tools in various geometric applications such as NC machining and collision detection of planar curved objects. Using quadratic curve approximation and tangent field matching, the offset and convolution curves can be approximated by polynomial or rational curves within the tolerance of approximation error > 0. We suggest three methods of offset approximation, all of which allow simple error analysis and at the same time provide high-precision approximation. Two methods of convolution approximation are also suggested that approximate convolution curves with polynomial or rational curves.