Non-linear Refinement of Point-Normal Data Using Conics

We introduce a novel non-linear refinement scheme for planar polygonal lines with normals at vertices. Subsequently, the data is refined by adding a new point and normal between every two consecutive points. A newly generated point is taken from a conic section approximating the neighboring points, the center of these points and the corresponding normal vectors. The method provides result which seems to be \(G^{1}\) based on experiments. It also preserves circles, ellipses, parabolas and hyperbolas. The proposed method is compared with the circle-preserving method.