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Ferrada, Héctor; Navarro, Cristóbal A.; Hitschfeld, Nancy

doi:10.1016/j.cam.2019.06.014

Cited by 15 publications

(12 citation statements)

References 20 publications

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“…And the near convex hull is proposed in [32] which is quickly formed by merely determining several special locations and has much lower computational complexity. A new filtering method for the convex hull in two dimensions is proposed for accelerating the computation of the convex hull [33].…”

Section: Convex Hull Methods In Cloud and Green Computingmentioning

confidence: 99%

UB-H: an unbalanced-hierarchical layer binary-wise construction method for high-dimensional data

Ihm

Park

2021

Computing

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Cloud computing, which is distributed, stored and managed, is drawing attention as data generation and storage volumes increase. In addition, research on green computing, which increases energy efficiency, is also widely studied. An index is constructed to retrieve huge dataset efficiently, and the layer-based indexing methods are widely used for efficient query processing. These methods construct a list of layers, so that only one layer is required for information retrieval instead of the entire dataset. The existing layer-based methods construct the layers using a convex hull algorithm. However, the execution time of this method is very high, especially in large, high-dimensional datasets. Furthermore, if the total number of layers increases, the query processing time also increases, resulting in efficient, but slow, query processing. In this paper, we propose an unbalanced-hierarchical layer method, which hierarchically divides the dimensions of input data to increase the total number of layers and reduce the index building time. We demonstrate that the proposed procedure significantly increases the total number of layers and reduces the index building time, compared to existing methods through the various experiments.

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Section: Convex Hull Methods In Cloud and Green Computingmentioning

confidence: 99%

UB-H: an unbalanced-hierarchical layer binary-wise construction method for high-dimensional data

Ihm

Park

2021

Computing

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“…The TORCH algorithm, depends on sorting of the data points on a Cartesian basis at first, which limits it to O(n log n), however a significant improvement in the running time over Quickhull, was claimed for large dataset, due to a use of efficient heuristics steps towards a shape at the goal of the hull. Several recent work are a variant of the approach towards incrementing an initial polygon to the target convex hull on sorted planar dataset [14,15,16].…”

Section: Related Workmentioning

confidence: 99%

“…The incremental approaches [6,14,15,16] apply on a sorted dataset, and ensures the best-case running time of the quickhull algorithm. A largest possible bounding polygon, with vertices from the pointset is used to reject points interior to early in the further computation.…”

Section: Comparison With the State-of-the-art Of The Incremental Appr...mentioning

confidence: 99%

Reduction of Two-Dimensional Data for Speeding Up Convex Hull Computation

Mukherjee¹

2022

Preprint

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An incremental approach for computation of convex hull for data points in two-dimensions is presented. The algorithm is not output-sensitive and costs a time that is linear in the size of data points at input. Graham's scan is applied only on a subset of the data points, represented at the extremal of the dataset. Points are classified for extremal, in proportion with the modular distance, about an imaginary point interior to the region bounded by convex hull of the dataset assumed for origin or center in polar coordinate. A subset of the data is arrived by terminating at until an event of no change in maximal points is observed per bin, for iteratively and exponentially decreasing intervals.Computation of convex hull of planar datasets is well studied in the literature of computational geometry [1,2,3,4,5,6]. A convex hull of a dataset is an ordering defined on the largest subset based on the geometry represented by the set. In two-dimensional dataset, the ordering leads to a closed polygon, where every line segment with any two vertices from the set, is contained entirely in the region bounded by the polygon. Algorithms for construction of convex hull, bears a correspondence with the algorithms for sorting.An algorithm for computation of convex hull is said to be output-sensitive, based on whether the complexity of computation depends on any structural attribute specific to the dataset at input other than its size. A consistent traversal (e.g. a turn in a counter-clockwise (CCW) sense) of the data points in a set, is often considered in computation of convex hull. An earliest output-sensitive algorithm by Jarvis et. al. [1], known as gift wrapping, computes convex hull in O(nh), for dataset of size n, and due to h points on the hull. The algorithm called Jarvis march, starts from a point that is lowest in one coordinate, and then selects the next point on the hull, with a consistent turn, and corresponds to selection sort.

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“…The Graham scan algorithm is a straightforward and efficient convex hull algorithm (Ferrada et al, 2020), the general concept of which is to remove points that are not part of the convex hull. Given a point cloud set S, the point p 0 is obtained from S with the minimum y-coordinate, and the points are then sorted counterclockwise.…”

Section: Modified Graham Scan Algorithmmentioning

confidence: 99%

Intelligent Interpretation of the Geometric Properties of Rock Mass Discontinuities Based on an Unmanned Aerial Vehicle

Chen

Ding

2021

Front. Earth Sci.

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The geometric properties of rock mass discontinuities are essential for the evaluation of the safety of rock masses. Numerous studies have recently been performed on the extraction of discontinuity information. However, most methods are characterized by poor data collection and processing efficiency. This paper presents a UAV-based methodology for the accurate and complete acquisition of rock surface data, as well as the automatic extraction of discontinuity information. Moreover, a program called Random Sample Consensus (RANSAC) Discontinuity Detection (RDD) is developed to extract discontinuity information based on the proposed method. The conclusions of this research are as follows. 1) RANSAC Discontinuity Detection (RDD) can identify the feature point set of discontinuities from a raw point cloud, and can calculate the discontinuity orientation. 2) The boundary of a discontinuity can be precisely depicted using the improved Graham scan algorithm. 3) The orientations of marked discontinuities extracted by RDD are compared with those extracted by the three-point method in CloudCompare. The differences in the orientations extracted by the two methods are found to be less than 3° for flat discontinuities and only about 4.87° for rough discontinuities, which are within a reasonable error range in practical engineering applications. Therefore, the feasibility of the proposed method is verified.

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A filtering technique for fast Convex Hull construction in R2

Cited by 15 publications

References 20 publications

UB-H: an unbalanced-hierarchical layer binary-wise construction method for high-dimensional data

UB-H: an unbalanced-hierarchical layer binary-wise construction method for high-dimensional data

Reduction of Two-Dimensional Data for Speeding Up Convex Hull Computation

Intelligent Interpretation of the Geometric Properties of Rock Mass Discontinuities Based on an Unmanned Aerial Vehicle

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