M. Friedrich, C. Roch, S. Feld, C. Hahn, and P. Fayolle
CSG trees are an intuitive, yet powerful technique for the representation of geometry using a combination of Boolean set-operations and geometric primitives. In general, there exists an infinite number of trees all describing the same 3D solid. However, some trees are optimal regarding the number of used operations, their shape or other attributes, like their suitability for intuitive, human-controlled editing. In this paper, we present a systematic comparison of newly developed and existing tree optimization methods and propose a flexible processing pipeline with a focus on tree editability. The pipeline uses a redundancy removal and decomposition stage for complexity reduction and different (meta-)heuristics for remaining tree optimization. We also introduce a new quantitative measure for CSG tree editability and show how it can be used as a constraint in the optimization process.
28th International Conference on Computer Graphics, Visualization and Computer Vision (WSCG)
S. Feld, M. Friedrich, and C. Linnhoff-Popien
The compression of geometry data is an important aspect of bandwidth-efficient data transfer for distributed 3d computer vision applications. We propose a quantum-enabled lossy 3d point cloud compression pipeline based on the constructive solid geometry (CSG) model representation. Key parts of the pipeline are mapped to NP-complete problems for which an efficient Ising formulation suitable for the execution on a Quantum Annealer exists. We describe existing Ising formulations for the maximum clique search problem and the smallest exact cover problem, both of which are important building blocks of the proposed compression pipeline. Additionally, we discuss the properties of the overall pipeline regarding result optimality and described Ising formulations.
IEEE Workshop on Quantum Communications and Information Technology 2018 (IEEE QCIT 2018), 2018, pp. 1-6