Geometric multi-covering

•We present a general, unified framework to resolve geometric covering problems.•The geometric covering problem is reduced to a set cover search in parametric space.•Different methods for solving the set-cover query are proposed and compared.•The framework draws from computer graphics and GPGPU techniques.•Two specific applications are addressed: multi-visibility and illuminance satisfaction.

We present a general, unified framework to resolve geometric covering problems. The problem is reduced to a set cover search in parametric space. We propose and implement different methods for solving the set cover problem, allowing for flexible trade-offs between solution quality and computation time. Our framework relies on computer graphics techniques and heavily exploits GPU based computations.Results are demonstrated in two specific applications: firstly, multi-visibility/accessibility analysis of 3D scenes that guarantees coverage, possibly redundant, of the target shape(s) by a minimal number of observers. Secondly, illumination design in 3D environments that ensures the satisfaction of local constraints on illuminance levels using a minimal set of lamps.

Graphical abstractWe propose a framework to closely approximate and solve geometric multi-covering problems in a general way, exploiting computer graphics techniques.Figure optionsDownload full-size imageDownload high-quality image (90 K)Download as PowerPoint slide