Spheres, molecules, and hidden surface removal
We devise techniques to manipulate a collection of loosely interpenetrating spheres in three-dimensional space. Our study is motivated by the representation and manipulation of molecular configurations, modeled by a collection of spheres. We analyze the sphere model and point to its favorable properties that make it more easy to manipulate than an arbitrary collection of spheres. For this special sphere model we present efficient algorithms for computing its union boundary and for hidden surface removal. The efficiency and practicality of our approach are demonstrated by experiments on actual protein data.
We present numerical simulations of galaxy formation, one of the most challenging problems in computational astrophysics. The key point in such simulations is the efficient solution of the N-body problem. If the gas of a galaxy is treated by means of smoothed particle hydrodynamics (Sph), the hydrodynamic equations can be reduced to a form similar to that of the N-body problem. A straightforward implementation requires a computational effort ∝ N2, making it prohibitively expensive to simulate systems larger than 105 particles even on the largest available supercomputers.