2D strokes sketched on and around 3D geometry form the input to SecondSkin (a). Layered structures are represented as solid models with volumes bounded by surface patches and curves (b). A majority (91%) of sketch strokes are perceived by viewers as one of four curve-types (c). We automatically classify these strokes based on the relationship between 2D strokes and underlying 3D geometry, producing 3D curves, surface patches, and volumes (d), resulting in layered 3D models suitable for conceptual design (e).