Convex-Hull Algorithms: Implementation, Testing, and Experimentation

Abstract

From a broad perspective, we study issues related to implementation, testing, and experimentation in the context of geometric algorithms. Our focus is on the effect of quality of implementation on experimental results. More concisely, we study algorithms that compute convex hulls for a multiset of points in the plane. We introduce several improvements to the implementations of the studied algorithms: plane-sweep, torch, quickhull, and throw-away. With a new set of space-efficient implementations, the experimental results—in the integer-arithmetic setting—are different from those of earlier studies. From this, we conclude that utmost care is needed when doing experiments and when trying to draw solid conclusions upon them.

Detection method of viral pneumonia imaging features based on CT scan images in COVID-19 case study

“…Initially, the approach adopts the convex hull algorithm as in Ref. [43] , which determines the most minor convex shape, enclosing all the points within the lung region. Then, we calculate the difference between the total lung area ( I L ) and the convex hull of the lung area ( I C ).…”

Lane-Level Map Generation and Management Framework Using Connected Car Data

“…ElementFOV is assigned to each map element and comprises the convex hull (series of points) formed by the location, where the extracted element constituting the map element was collected, the maximum angle formed by the extracted element and the vehicle heading, and the range of the element's and coordinates based on the vehicle's coordinate system. The convex hull [45] represents the location range from which the element can be collected based on the statistics of the positions where the extracted element was gathered. The maximum angle between the extracted element and the vehicle's heading at the time of collection allows the determination of whether the element exists within the range perceivable by the sensor and the inference network.…”

The Relationship between “C-Space”, “Heuristic Methods”, and “Sampling Based Planner”

“…In order to have a better understanding of the computational resources required to compute the collision free c-map, let us take into account the same two link planar robot, but with just one polygonal obstacle in the scene (Figure 10). Finding whether the robot collides with a polygonal obstacle is way more expensive as described in book [9,10]. The number of edges of the obstacle covers an important role, but in this chapter every polygonal obstacle is assumed to be defined by no more than 5 edges for sake of simplicity.…”