We have proposed and implemented function-based extensions of Extensible 3D (X3D) and its predecessor Virtual Reality Modeling Language (VRML) which allow for defining time-dependent geometric shapes, their appearances and transformations with analytically defined parametric, implicit and explicit functions. The function-defined shapes can be used together with the standard X3D and VRML shapes. In this paper we present the most recent significantly revised and amended definition of the FVRML/FX3D nodes. Besides defining shapes by analytical functions, we have developed interactive function-based shape modeling tools. We have also extended these interactive shape modeling tools to work on the Grid.