Function-based representation of complex geometry and appearance

Abstract

In this paper, we introduce a function-based extension of Virtual Reality Modeling Language. In this extension, analytical functions are used for defining geometry and appearance of 3D shapes, as well as transformations of them. By analytical functions we understand definitions with parametric, implicit and explicit formulas. In our hybrid function-based web visualization model, these very different analytical representations can be used concurrently for defining geometry and appearance of the shapes. We also illustrate how the proposed extension can be further enriched with any proprietary function-based models. The presented VRML plug-in is very useful for building both static and interactive virtual environments on the Web. This is illustrated with the implementation of the Virtual Collaborative Shape Modeling Laboratory.

Tubular triangular mesh parameterization and applications

“…Also, the compact representation benefits the data transmission over the Internet and makes it suitable for various web-based virtual reality applications. 18 Therefore there is a need to convert triangular meshes into spline surface. The conversion can be achieved by surface fitting.…”

Partial Differential Equations for Function Based Geometry Modelling within Visual Cyberworlds

“…The FVRML/FX3D was originally introduced in [14] and subsequent work on this theme have been discussed in [16,17,15]. This framework enables modelling of function based shapes and their metamorphosis in visual cyberworlds in an efficient and neat way.…”

Function-based time-dependent shape modeling on the Web

“…The extension of VRML with function-based shape modeling was proposed by the authors in [12] following the preliminary works [ 13 , 14 ]. The proposed hybrid function-based nodes (FShape, FGeometry, FMaterial, FTexture3D, FAppearance, FTransform) allow for extending VRML97 with practically any type of object's geometry and sophisticated graphics appearances by defining the object's geometry, appearance (color and 3D texture) and transformations with analytical formulas which are implicit, explicit and parametric representations used concurrently.…”

“…Based on the idea of employing analytical functions for defining time-dependent geometry, texture and color, the nodes proposed in [12] must be extended accordingly to constitute the new Function-based Extension of VRML (FVRML).…”