How do I stop the weave distorting over compound curves?

Some distortion is unavoidable over a compound curve, because a woven fabric has to shear to follow a shape that curves in two directions, and that shearing is what skews the pattern. The trick is to control it rather than fight it. Start laying from the centre or the highest point and work the fabric outwards, easing it down so the weave shears gradually and evenly instead of bunching in one spot. A more drapable fabric helps, so a twill or satin weave, a lighter cloth or a spread-tow fabric will conform better than a heavy plain weave. On tighter shapes, splitting the layup into smaller pieces with planned overlaps, ideally where a seam will be hidden, keeps the visible areas neat. For a show-surface part it is worth a dry run first to plan where the pattern lands.