Computer Science > Computational Geometry
[Submitted on 31 Oct 2020 (v1), last revised 21 May 2021 (this version, v3)]
Title:A Secure Two-Party Computation Protocol for Intersection Detection between Two Convex Hulls
View PDFAbstract:Intersection detection between three-dimensional bodies has various applications in computer graphics, video game development, robotics as well as military industries. In some respects, entities do not want to disclose sensitive information about themselves, including their location. In this paper, we present a secure two-party protocol to determine the existence of an intersection between entities. The protocol presented in this paper allows for intersection detection in three-dimensional spaces in geometry. Our approach is to use an intersecting plane between two spaces to determine their separation or intersection. For this purpose, we introduce a computational geometry protocol to determine the existence of an intersecting plane. In this paper, we first use the Minkowski difference to reduce the two-space problem into one-space. Then, the separating set is obtained and the separation of two shapes is determined based on the inclusion of the center point. We then secure the protocol by modifying the separating set computation method as a privacy-preserver and changing the Minkowski difference method to achieve this goal. The proposed protocol applies to any form of convex three-dimensional shape. The experiments successfully found a secure protocol for intersection detection between two convex hulls in geometrical shapes such as the pyramid and cuboid.
Submission history
From: Amirahmad Chapnevis [view email][v1] Sat, 31 Oct 2020 17:21:13 UTC (506 KB)
[v2] Wed, 4 Nov 2020 18:22:02 UTC (504 KB)
[v3] Fri, 21 May 2021 17:08:37 UTC (504 KB)
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