A new precision vectorization method has been developed for building centerlines of plain shapes. First a dense skeleton is computed. Centerlines are obtained as a subset of branches of the dense skeleton. The dense skeleton can also be used for obtaining medial axes of shapes. To obtain high precision, the distance transformation 12-17-38 was developed, which gives a good approximation of the Euclidean metrics. The expression the Voronoi L-diagram was coined. Key words: Vectorization, distance transformation, dense skeleton, medial axis, centerline, L-veinerization.