A volumetic approach to interactive CSG modeling and rendering

Volume-based graphics techniques, such as volume rendering and voxelization, have been attracting enormous research attention recently. But they have not yet played a significant role in solid modeling and its CAD/CAM applicatiions. Although there have been many fast rendering algorithms for CSG models[6,9], volume-based techniques have the benefit of explicitly generating the volume representations for the CSG models, wh,ich can be very useful for m.any volume related operations such as volume rendering, integral property computation, finite element analysis and layered manufacturing for rapid prototyping. A volume is a scalar field sampled at a 3D regular grid over a volume space. For a solid object, a binary volume with only 0 and 1 intensity values can be used. The process of converting a geometric model into a volume representation is called uoseli::ation[3]. Conceptually, CSG voxelization is a set membership classification problem agatinst the CSG model for all voxels in a volume space. Early CSG voxelization methods (can date back to the spatial enumeration by point classification[5]. Several more recent works have also been reported[l, 4, 71. Unfortunately, these algorithms are all computationally very expensive, thus do not provide interactive performance. In this .paper, we present a new volumetric solution for the fast volume conversion and rendering of CSG models. It uses existing hardware features in standard 3D graphics systems (e.g. OpenGL), and interactively generates a volume representation for each CSG model in a 3D texture memory, which can then be volume rendered in real time by 3D texture mapping[2, 81, or saved into main memory for post-processing operations and computations.