RangeFinder: Accelerating ball-interference queries against steady lattices
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Advances in additive manufacturing techniques are enabling the fabrication of new microstructures and materials. These may often be defined in terms of a set of balls and of beams that each connects two balls. To support application needs, we must support lattices with billions of such elements. To address this problem, we focus on architected and periodic structures in which the connectivity pattern repeats in three directions, and in which the positions and radii of the balls evolve through the structure in a prescribed and steady way that is defined by three similarity transforms. We propose here an algorithm that accelerates the Ball-Interference Query (BIQ), which establishes which elements of the lattice interfere with a query ball Q. Our RangeFinder (RF) solution reduces the asymptotic complexity of BIQs, which, in our tests, reduced the query time by a factor of between 45 and 5500. RF does not use any spatial occupancy data structure and can be trivially parallelized. We demonstrate the effectiveness of RangeFinder through the generation of multi-level lattices that we call Lattice-in-Lattice (LiL).