Shape modeling is an area of computer science studying modeling point sets in multi-dimensional geometric spaces. Digital preservation includes capturing, archiving and reproduction of cultural objects using shape modeling. Traditionally, only external surfaces and textures of objects are considered. However, internal structures (revealing logic of construction) of objects, time and other parametric dependencies are also important. In the function representation (FRep), the modeled shape is described by a single procedurally defined real continuous function of point coordinates. This dimension independent description allows for uniform treatment of space-time and higher dimensional shapes and supports modeling of heterogeneous objects in dimensionality and material properties. Original solutions to several selected shape modeling problems have been proposed using FRep for bounded blending, space-time blending and trimming implicit surfaces. The proposed solutions are illustrated by several case studies: Virtual Shikki project on modeling and Web presentation of Japanese lacquerware craft, Dancing Buddhas project and 3D modeling of Escher''s drawings.