Minimum constraint removal problem for line segments is NP-hard

In the minimum constraint removal ([Formula: see text]), there is no feasible path to move from a starting point towards the goal, and the minimum constraints should be removed in order to find a collision-free path. It has been proved that [Formula: see text] problem is NP-hard when constraints have arbitrary shapes or even they are in shape of convex polygons. However, it has a simple linear solution when constraints are lines and the problem is open for other cases yet. In this paper, using a reduction from Subset Sum problem, in three steps, we show that the problem is NP-hard for both weighted and unweighted line segments.

ANALISIS KONSEP MATEMATIKA SEKOLAH DALAM PEMULASARAAN JENAZAH

This research aim to identify the elementary and junior high school mathematic concepts which included the funeral procession. The process of funeral procession that was researched included measuring and cutting the shroud, bathing the corpse, shrouding the corpse, praying the corpse, and burying the corpse. The method of this research is a qualitative, and the form of this research is a literature study. Then the data were collected using documents in the form of books, articles, and notes on the results of the funeral procession by the fardhu kifayah team of Ummu Al-Athiyyah Al-Anshoriyyah. Based on the Miles and Huberman analysis method, elementary and junior high school mathematical concepts are found in the funeral procession, namely rectangles, mixed arithmetic operations, addition, subtraction, multiplication, division, number sequences, sets, linear inequalities of one variable, line segments, vertical lines, horizontal lines, parallel lines, perpendicular lines, point outside the line, 180 degree angel, and cuboids.

The Perceptual Organisation of Visual Elements: Lines

The aim of this study is to verify the conditions under which a series of visual stimuli (line segments) will be subjectively perceived as visual lines or surfaces employing four experiments. Two experiments were conducted with the method of subjective evaluation of the line segments, and the other two with the Osgood semantic differential. We analysed five variables (thickness, type, orientation, and colour) potentially responsible for the lines’ categorisation. The four experiments gave similar results: higher importance of the variables thickness and type; general lower significance of the variable colour; and general insignificance of the variable orientation. Interestingly, for the variable type, straight lines are evaluated as surfaces more frequently than curved lines and perceived as geometrical, flat, hard, static, rough, sharp, bound, sour, frigid, masculine, cold and passive. Curved lines are prevalently evaluated as lines, and categorised as organic, rounded, soft, dynamic, fluffy, blunt, free, sweet, sensual, feminine, warm and active. These results highlight the specificity of perceptual characteristics for the considered variables and confirm the relevance of the characteristics of variables such as thickness and type.

Study of Indoor Visual SLAM System for Semi-autonomous Robot Platform

This study propose the use of heterogeneous visual landmarks, points and line segments, to achieve effective cooperation in indoor SLAM environments. In order to achieve un-delayed initialization required by the bearing-only observations, the well-known inverse-depth parameterization is adopted to estimate 3D points. Similarly, to estimate 3D line segments, we present a novel parameterization based on anchored Plücker coordinates, to which extensible endpoints are added

Method for Orthogonal Edge Routing of Directed Layered Graphs with Edge Crossings Reduction

This paper presents a method for automated orthogonal edge routing of directed layered graphs using the described edge crossings reduction heuristic algorithm. The method assumes the nodes are pre-arranged on a rectangular grid composed of layers across the flow direction and lanes along the flow direction. Both layers and lanes are separated by rectangular areas defined as pipes. Each pipe has associated segment tracks. The edges are represented as orthogonal polylines consisting of line segments and routed along the shortest paths. Each segment is assigned to a pipe and to a segment track in it. The edge crossings reduction uses an iterative algorithm to resolve crossings between segments. Conflicting segments are reassigned to adjacent segment tracks, either by swapping with adjacent segments, or by inserting new tracks and calculating the shortest paths of edges. The algorithm proved to be efficient and was implemented in an interactive graph design tool.

MENGHITUNG PERKALIAN JARI TANGAN DI MI 02 KEMBANG KERANG

The ability to count is one of the important abilities in everyday life, it can be said that all activities of human life require this ability. this is a separate problem for teachers considering that learning at the primary and secondary education levels has differences where teachers in primary schools must master various materials from all subjects. The training method used is lecture, discussion, practice, and question and answer methods. Based on data, about 83.3% of teachers are enthusiastic about participating in the training and 16.7% of teachers who are not very enthusiastic about participating in the training. This shows that PKM activities with multiplication training using fingers are responded well and are in demand by teachers. There are several obstacles related to counting using finger media, namely errors in calculating line segments, distinguishing multiplier numbers and multiplied numbers. Therefore, we hope that teachers will often repeat or practice themselves by looking at the guidelines that have been given so that there are no mistakes in teaching students.

A Robust Fast Bridging Algorithm for Laser Cutting

Bridging the different parts together is considered a simple but effective strategy to reduce the number of piercing operations during laser cutting. However, fast bridging is never an easy task. In this paper, we present a near-linear bridging algorithm for the input parts with the shortest total bridge length. At first, the input part contours are discretized into a point cloud, then the point cloud is triangulated with the Delaunay standard. The shortest line segments between any two adjacent parts are found in the triangles connecting the two parts. These segments are finally extended into bridges. To solve the problem of the damages to the contour characteristics caused by the bridges, some restrictions are set on the screening of the discrete point cloud and the Delaunay triangles. This algorithm not only ensures the minimum total distance of all bridges, but also avoids the problem of generating bridge loops. Computational experiments show that the proposed bridging algorithm is much faster than that in existing commercial software. The feasibility and superiority of the algorithm are verified by actual lasering cutting experiments.