Swept volumes via spacetime numerical continuation

Autor:	Alec Jacobson, Noam Aigerman, Silvia Sellán
Rok vydání:	2021
Předmět:	Constructive solid geometry Moment (mathematics) Level set Numerical continuation Implicit function Spacetime Lift (data mining) Computer science Trajectory Applied mathematics Computer Graphics and Computer-Aided Design ComputingMethodologies_COMPUTERGRAPHICS
Zdroj:	ACM Transactions on Graphics. 40:1-11
ISSN:	1557-7368 0730-0301
Popis:	Given a solid 3D shape and a trajectory of it over time, we compute its swept volume - the union of all points contained within the shape at some moment in time. We consider the representation of the input and output as implicit functions, and lift the problem to 4D spacetime, where we show the problem gains a continuous structure which avoids expensive global searches. We exploit this structure via a continuation method which marches and reconstructs the zero level set of the swept volume, using the temporal dimension to avoid erroneous solutions. We show that, compared to other methods, our approach is not restricted to a limited class of shapes or trajectories, is extremely robust, and its asymptotic complexity is an order lower than standards used in the industry, enabling its use in applications such as modeling, constructive solid geometry, and path planning.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::738e802930ac778e8371571ef9f366f0 https://doi.org/10.1145/3450626.3459780 Zobrazit plný text záznamu