We introduce a new texture representation that combines standard sampling, to be bilinearly interpolated in smoothly varying regions, with customizable discontinuities, to model sharp boundaries between these regions. The structure consists of a standard signal texture, plus a second texture we call pinchmap, which encodes discontinuities along generally curved lines; at rendering time the fragment processor efficiently decodes this structure with a single access to each texture. We also present a fully automatic way to compute a pinchmap and signal texture pair, starting from an original high resolution image. The final result on the screen is a comparable visual quality for a fraction of the texture storage and with a negligible impact on performance. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Comp. Graph.]: Line and Curve Generation