Given a decorated point set which describes the arrangement of the atoms in a solid, we describe two -algebras, one specified as discrete and the other as continuous. The discrete algebra is adapted to the description of the particles in the solid with the help of tight binding models, the continuous one to the description by differential operators. A key concept is that of the hull of the solid, a compact topological space which also comes in a discrete and in a continuous form. We give a more detailed description in the cases that our point set has finite local complexity or comes from a substitution tiling. We also mention the modification needed if there are external magnetic fields.