Two algorithms for solving the piecewise linear least–squares approximation problem of plane curves are presented. The first is for the case when theL2residual (error) norm in any segment is not to exceed a pre–assigned value. The second algorithm is for the case when the number of segments is given and a (balanced)L2residual norm solution is required. The given curve is first digitized and either algorithm is then applied to the discrete points. For each segment, we obtain the upper triangular matrixRin theQRfactorization of the (augmented) coefficient matrix of the resulting system of linear equations. The least–squares solutions are calculated in terms of theR(andQ) matrices. The algorithms then work in an iterative manner by updating the least–squares solutions for the segments via up dating theRmatrices. The calculation requires as little computational effort as possible. Numerical results and comments are given. This, in a way, is a tutorial paper.