We show that a complete doubling metric space (X,d,mu ) supports a weak 1-Poincaré inequality if and only if it admits a pencil of curves (PC) joining any pair of points s,t in X. This notion was introduced by S. Semmes in the 90’s, and has been previously known to be a sufficient condition for the weak 1-Poincaré inequality. Our argument passes through the intermediate notion of a generalised pencil of curves (GPC). A GPC joining s and t is a normal 1-current T, in the sense of Ambrosio and Kirchheim, with boundary partial T = delta _{t} - delta _{s}, support contained in a ball of radius sim d(s,t) around {s,t}, and satisfying Vert TVert ll mu , with d‖T‖dμ(y)≲d(s,y)μ(B(s,d(s,y)))+d(t,y)μ(B(t,d(t,y))).\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\frac{d\\Vert T\\Vert }{d\\mu }(y) \\lesssim \\frac{d(s,y)}{\\mu (B(s,d(s,y)))} + \\frac{d(t,y)}{\\mu (B(t,d(t,y)))}. \\end{aligned}$$\\end{document}We show that the 1-Poincaré inequality implies the existence of GPCs joining any pair of points in X. Then, we deduce the existence of PCs from a recent decomposition result for normal 1-currents due to Paolini and Stepanov.