Showing papers by "Ivana Kolingerová published in 2020"

Narrow Passage Problem Solution for Motion Planning

Abstract: The paper introduces a new randomized sampling-based method of motion planning suitable for the problem of narrow passages. The proposed method was inspired by the method of exit points for cavities in protein models and is based on the Rapidly Exploring Random Tree (RRT). Unlike other methods, it can also provide locations of the exact positions of narrow passages. This information is extremely important as it helps to solve this part of space in more detail and even to decide whether a path through this bottleneck exists or not. For data with narrow passages, the proposed method finds more paths in a shorter time, for data without narrow passages, the proposed method is slower but still provides correct paths.

Plane Space Representation in Context of Mode-Based Symmetry Plane Detection.

Abstract: This paper describes various representations of the space of planes. The main focus is on the plane space representation in the symmetry plane detection in \(E^3\) where many candidate planes for many pairs of points of the given object are created and then the most often candidate is found as a mode in the candidate space, so-called Mode-based approach. The result depends on the representation used in the mode-seeking process. The most important aspect is how well distances in the space correspond to similarities of the actual planes with respect to the input object. So, we describe various usable distance functions and compare them both theoretically and practically. The results suggest that, when using the Mode-based approach, representing planes by reflection transformations is the best way but other simpler representations are applicable as well. On the other hand, representations using 3D dual spaces are not very appropriate. Furthermore, we introduce a novel way of representing the reflection transformations using dual quaternions.

Kinetic locally minimal triangulation: theoretical evaluation and combinatorial analysis

Abstract: Kinetic data structures represent an extension to ordinary data structures, where the underlying data become time dependent (e.g. moving points). In this paper, we define the kinetic locally minimal triangulation (KLMT) as a kinetic data structure extension to the locally minimal triangulation in the Euclidean plane. We explore the general properties of this data structure in order to show what types of events need to be considered during its life cycle; we also describe the predicates associated with these events. To describe the general kinetic features, we prove that KLMT is responsive, compact, efficient and non-local. In the combinatorial analysis of KLMT, we briefly describe the mathematical apparatus commonly used to investigate computational complexity properties of kinetic data structures and use it to establish the bounds on the number of events processed during the life cycle of this data structure. Finally, the obtained results are compared to the kinetic Delaunay triangulation showing that KLMT may provide some benefits over kinetic Delaunay triangulation, namely simplifying the mathematical equations that need to be computed in order to obtain the times of events.