Fast navigation through an FRep sculpture garden

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