Function-based shape modelling extension of the Virtual Reality Modelling Language

In this paper we propose a new approach to web visualisation with VRML based on a function-based shape modelling, which unifies different types of mathematical functions in order to enrich the existing web visualisation techniques for modelling. In our method, parametric, implicit and explicit functions can be used concurrently for defining geometry, colour, texture, and other properties of shapes. Geometric shapes and their properties are defined by functions in their respective domains and then merged into function-defined objects. The proposed framework allows for its extending with any function-based model. To illustrate our method and to prove its feasibility, we implemented it for web visualisation as the Function-based Extension of Virtual Reality Modelling Language. In this implementation, parametric implicit and explicit analytical formulae are used for defining geometry and appearance of three-dimensional (3D) shapes. The function-based extension of VRML is used for collaborative shape modelling as well as for building shared virtual worlds.