MAKOVNÍK MarcelConchoids and subdivisionWe discuss the refinement of a planar polyline using conchoids. For each segment of the polyline, we construct a conchoid, which interpolates its endpoints. This is achieved by choosing a feasible coordinate system, scaled by the input global parameter. Then, we choose new points from the interpolating conchoid, symmetrically to the horizontal axis. Afterwards, we transform the new pair of points to the original coordinate system. The refined polyline is obtained in the "corner-cutting" fashion, i. e. by joining the subsequent pairs of new points. The process of refinement may be applied repeatedly to achieve the desired level of detail. The proposed refinement scheme is approximating and non-linear. We provide several examples that demonstrate the behaviour of the refinement. Also, we inspect on the influence of the value of the global parameter. For the specific value, we obtain the well-known Chaikin´ s algorithm. |