Technical Report HCIS-2002-02

We present an approach to collaborative Web based modeling using functionally defined shapes specified in the high level language HyperFun. The EmpiricalHyperFun shape modeling system based on Empirical Modeling principles provides users with an unusual degree of mutual interaction through the Web. 2 INTRODUCTION The growing number of applications facilitates the importance of methods and software tools for Web-based shape modeling. These applications include Web authoring, multiuser gaming, distant learning, data visualization, 3D retail environments in e-commerce, collaborative computer-aided design and engineering, and others. Many of these application areas have their own proprietary data representations of shape, making sharing of these shapes for collaborative engagement with a team of users a task for dedicated software with restricted distribution and applicability. There are several well-known protocols for exchanging geometric data such as polygonal file formats (Autodesk DXF, etc.), Alias/Wavefront object files for parametric surfaces, PADL-2 for Constructive Solid Geometry (CSG), and STEP for the boundary representation (B-rep) and CSG. The Virtual Reality Modeling Language (VRML) [VRML97] is an open standard that can be used as a means to distribute a shape to special Internet browsers that can be explored by a distributed set of users. However, the expressive power of VRML is restricted by the polygonal representation of shapes and the set of additional predefined parameterized shape primitives such as a sphere or a cube. This provides only ever an approximation to the real shape model. VRML representations of shapes are typically very large, which is an obstacle to collaboration in the design process through e-mail, bulletin boards or dedicated software. A more high-level and concise format for geometric data transmission would enable truly collaborative and creative shape modeling on the Internet through browsers. This can be achieved by employing shape models of higher level of abstraction than it is provided by polygonal meshes. So-called " implicit surfaces " [B97] and a more general function representation (FRep) are among the best candidates for solving this problem because of their well-known properties such as compact mathematical description of complex shapes, natural blending, covering both free-form organic shapes and mechanical parts with sharp edges, and a rich system of developed operations. The VRML extension proposal [WG97] was the first attempt to introduce a protocol for skeletal implicit surfaces with a limited set of operations (warping, Boolean). However, a more general protocol for the full support of FRep models is needed. This paper presents …