Fast Navigation through an FRep Sculpture Garden

The function representation (FRep) allows for construction of quite complex shapes such as isosurfaces of real-valued functions composed using the functionally defined primitives and operations. Calculating such functions in the complex cases can be very time-consuming. Extraction and visualization of isosurfaces for them can hardly be imagined interactive. In this paper we present a method of an interactive navigation through a "sculpture garden" containing non-intersecting FRep objects defined in the terms of specialized high-level language HyperFun. Before the actual isosurface extraction and visualization occurs, the objects are voxelized on a regular 3D grid with a possibility of a further adaptive voxelization. Polygonization employs a hierarchical representation of the voxelized data and a view-dependent isosurface reconstruction at the different levels of detail. To speedup the extraction process, an isosurface is constructed only in the visible part of the dataset with its updates performed incrementally as observer moves. Due to low preprocessing costs required for isosurface mesh construction, it is possible to visualize timedependent objects, if hardware is capable to calculate updates in real time.