Roa, EduardoTheoktisto, VíctorFairén, MartaNavazo, IsabelSilva, F. and Gutierrez, D. and Rodríguez, J. and Figueiredo, M.2021-06-182021-06-182021978-3-03868-152-6https://doi.org/10.2312/pt.20111143https://diglib.eg.org:443/handle/10.2312/pt20111143We derive a conformal algebra treatment unifying all types of collisions among points, vectors, areas (defined by bivectors and trivectors) and 3D solid objects (defined by trivectors and quadvectors), based in a reformulation of collision queries from R3 to conformal R4,1 space. The algebraic formulation in this 5D space is then implemented in GPU to allow faster parallel computation queries. Results show expected orders of magnitude improvements computing collisions among known mesh models, allowing interactive rates without using optimizations and bounding volume hierarchies.I.3.1 [Computer Graphics]Hardware ArchitectureGraphics processorsparallel processingI.3.5 [Computer Graphics]Computational Geometry and Object ModelingBoundary representationsCollision detectionI.1.2 [Computer Graphics]AlgorithmsAlgebraic algorithms10.2312/pt.20111143153-156