Constructive Solid Geometry (CSG) Rendering

As the performance of graphics hardware improves, multi-pass rendering techniques for anti-aliasing, shadowing, specular light, reflection and other effects become increasingly attractive for enhancing the visual realism of real-time interactive graphics. Over time, the graphics hardware feature-set has evolved to include stencil testing and programmability at the vertex and fragment level. This increased flexibility and performance enables the use of sophisticated graphics-hardware based algorithms for interactive applications.
The pervasive availability of z-buffer hardware for hidden surface elimination has encouraged the development of alternative applications of z-buffer graphics hardware. Applications include image compositing, shadow maps, voxelisation, discrete Voronoi diagrams, object reconstruction, symmetry detection and Constructive Solid Geometry (CSG) rendering.
Image-space CSG rendering techniques provide an alternative to object-space evaluation of CSG trees for geometric design or machining simulation. The relative simplicity and robustness of implementation, the interactive flexibility of dynamic CSG trees, and the potential for pixel parallelization make image-space algorithms attractive for some applications.
Existing CSG rendering methods generally require O(n2) time, where n is the number of leaf nodes in the CSG tree. This O(n2) requirement is due to the general strategy of comparing every pair of objects. This can be improved by taking advantage of depth complexity (the number of objects covering each pixel) — resulting in O(kn) execution time, where k is the maximum depth complexity. The Sequenced Convex Subtraction (SCS) algorithm aims to improve CSG performance by reducing the requirement for z-buffer copying — a common bottleneck in contemporary graph-ics hardware.
Figure 1: Z-Buffer Intersection using the z and stencil buffers
This paper introduces a new approach for rendering the intersection of convex objects in linear time, that we call SCS-Intersect. It has been implemented using the z and stencil testing functionality of OpenGL. SCS-Intersect can be used as a stand-alone algorithm for CSG trees of convex objects in the form:...

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