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The β-shape and the β-complex are recently announced geometric constructs which facilitate efficient reasoning about the proximity among spherical particles in three-dimensional space. They have proven to be very useful for the structural analysis of bio-molecules such as proteins. Being non-manifold, however, the topology traversal on the boundary of the β-shape is inconvenient for reasoning about...
Given a set of points P, finding near neighbors among the points is an important problem in many applications in CAD/CAM, computer graphics, computational geometry, etc. In this paper, we propose an efficient algorithm for constructing the elliptic Gabriel graph (EGG), which is a generalization of the well-known Gabriel graph and parameterized by a non-negative value α. Our algorithm is based on the...
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