The integument of the Drosophila adult abdomen bears oriented hairs and bristles that indicate the planar polarity of the epidermal cells. We study four polarity genes, frizzled (fz), prickle (pk), Van gogh/strabismus (Vang/stbm) and starry night/flamingo (stan/fmi), and note what happens when these genes are either removed or overexpressed in clones of cells. The edges of the clones are interfaces between cells that carry different amounts of gene products, interfaces that can cause reversals of planar polarity in the clone and wild-type cells outside them. To explain, we present a model that builds on our earlier picture of a gradient of X, the vector of which specifies planar polarity and depends on two cadherin proteins, Dachsous and Fat. We conjecture that the X gradient is read out, cell by cell, as a scalar value of Fz activity, and that Pk acts in this process, possibly to determine the sign of the Fz activity gradient. We discuss evidence that cells can compare their scalar readout of the level of X with that of their neighbours and can set their own readout towards an average of those. This averaging, when it occurs near the edges of clones, changes the scalar response of cells inside and outside the clones, leading to new vectors that change polarity. The results argue that Stan must be present in both cells being compared and acts as a conduit between them for the transfer of information. And also that Vang assists in the receipt of this information. The comparison between neighbours is crucial, because it gives the vector that orients hairs--these point towards the neighbour cell that has the lowest level of Fz activity. Recently, it has been shown that, for a limited period shortly before hair outgrowth in the wing, the four proteins we study, as well as others, become asymmetrically localised in the cell membrane, and this process is thought to be instrumental in the acquisition of cell polarity. However, some results do not fit with this view--we suggest that these localisations may be more a consequence than a cause of planar polarity.