Which polygon is concave open study

React Native. Python Design Patterns. Python Pillow. Python Turtle. Verbal Ability. Interview Questions. Company Questions. Artificial Intelligence. Cloud Computing. Data Science. Angular 7. Machine Learning. Data Structures. Operating System. Computer Network. These estimated convex hulls were used to calculate the optimum area of both convex hulls CH Q. The corner vertices of each optimum area of the convex hull were stored.

This estimated optimum area was stored in a memory stack. This procedure was continued until the optimum area of the concave hull was calculated. Step 5: Finally, the corner vertices V X i , Y i of the concave hull CCH Q were obtained when the optimum harvesting area of the concave polygon or concave hull was determined.

The working path of a robot combine harvester was calculated from the estimated corner vertices x i , y i of an optimum harvesting area of a convex or concave polygon field.

First, each edge was calculated by using Eq. By using these edges, the operator determines the working direction of the robot combine harvester. The operator can choose any direction, but in general, the longest direction is better than the shortest one owing to the number of turns.

In Fig. Second, based on header length d and the turning direction, the next path was estimated by using Eq. Third, the cross-point x c , y c was determined by using Eq.

The algorithms were verified by a field experiment of wheat harvesting in the field of Hokkaido University, Japan. The robot combine harvester computer was configured with RTK-GPS and IMU sensors that measured the positions and heading angles during the cutting of surrounding crops for the convex and concave polygon fields.

This computer was also installed with Microsoft Visual studio for supporting computer languages. The red points in Fig. The values a and b can be changed considering the size of the header mounted on the robot combine harvester. The distances a and b taken in Eq. This estimated header end position P X H , Y H indicates the actual perimeter or exact outline of wheat in the field that must be harvested by the robot combine harvester.

For a concave polygon field, the vertices of concave hull CCH Q were estimated by using the split of convex hull and cross-point method shown in Fig.

The result indicates that the convex and concave hull method reduced the number of point clouds of the crop perimeter and determined the vertices of the convex hull that belong to the crop perimeter position on the boundary or inside the convex and concave polygon fields. Estimated vertices of convex and concave hull from the crop perimeter of convex and concave polygon fields. The optimum harvesting area of the convex polygon field was determined from the convex hull of a convex polygon field.

When the operator judges that the shape of the crop periphery is a rectangular polygon, the rotating caliper method is used to create an optimum harvesting area of the rectangular field. Figure 12 a shows the corner vertices V X i , Y i of an optimum harvesting area of a rectangular polygon field by the rotating caliper method. When the shape of the crop periphery is an arbitrary polygon, the optimum N-polygonal algorithm is used to calculate the corner vertices V X i , Y i of an optimum harvesting area of the convex polygon field by using Eq.

Similarly, the corner vertices V X i , Y i of the concave polygon field are determined by using the split of convex hull and cross-point method, as shown in Fig.

The results revealed that the optimum harvesting area of the convex and concave polygon field considers the curved or meandering parts of the convex and concave polygon field.

As a consequence, the robot combine harvester will completely harvest the wheat or paddy crop without leaving any mowing residual in the field. The optimum harvesting area of a rectangular polygon during a wheat experiment was also calculated by using the optimum N-polygon algorithm, which can be compared with the optimum harvesting area from the rotating caliper method shown in Fig.

The estimated optimum harvesting area green line of the rectangular polygon from the optimum N-polygon algorithm was During harvesting, the area of the wheat field periphery blue line from the conventional AB point method was also calculated as If the operator is an expert and can take the corner points perfectly, then the harvesting map will be accurate, and the robot combine harvester will harvest the wheat of the entire field.

Otherwise, some mowing residual will remain in the field. Comparison of the optimum harvesting area with the conventional harvesting area of convex polygon field. Figure 14 shows the simulated working path of the robot combine harvester based on the optimum harvesting area of the convex and concave polygon field.

This working path was generated from the estimated corner vertices V X i , Y i of the optimum harvesting area of the convex and concave polygon field by using Eqs. The total working distances for the convex and concave polygon field in Fig. Afterward, during the experiment in the rectangular wheat field, the working path was estimated based on the corner vertices V X i , Y i from the optimum area method and conventional AB point method, as shown in Fig.

In both methods, the total number of working paths for the robot combine harvester was In the AB point method shown in Fig. The total working distance from the optimum area method was counted as The results indicated that unlike the optimum area method for a working path, if we provide the working path to the robot combine harvester by using the conventional AB point method, the robot will leave In addition, if we take the corner points based on the conventional AB point method to estimate the working path, the system needs almost 20—25 min to perform calculations.

This time can be increased or decreased based on the size of the crop field. On the other hand, the estimated working path based on our proposed optimum area method needs up to 5 min to calculate. Considering these working times and the system estimated time of the working path, the total time was obtained as Estimated working path of the robot combine harvester during experiment in a rectangular wheat field.

Automatic path planning is an important topic for robotic agricultural vehicles. This paper described an automatic path planning algorithm for a robot combine harvester to harvest wheat or paddy that is not in a row. The exact crop outline measured from the RTK-GPS position and IMU heading provides thousands of points, whose number is reduced by using the incremental convex hull method.

Using an estimated convex hull, the optimum harvesting area of a polygon is determined by the rotating caliper and the developed optimum N-polygon algorithm, which is a better optimization of an area than when using the conventional AB point method. Unlike the conventional AB point method, the developed algorithm calculates an optimum harvesting area of the polygon that covers the entirely of the remaining crop and provides appropriate corner vertices.

These corner vertices are used to calculate a working path for the robot combine harvester, which is more effective than the working path obtained from the conventional AB point method. This problem is completely solved by using the developed algorithm in this research.

In addition, the work path estimated based on the conventional AB point method needs more times to process all of the information, whereas the developed algorithm requires only a few minutes. Finally, we conclude that the developed algorithm reduces the operational processing time and completely removes the crop losses during a harvesting operation performed in the field by the robot combine harvester in real time. Int J Robot Res 21 4 — Article Google Scholar.

Comput Electron Agric — Driscoll TM Complete coverage path planning in an agricultural environment. Dissertations, Iowa State University.

Biosyst Eng — Godfried T Solving geometric problems with the rotating calipers. Robot Auton Syst — In: Proceedings of the 7th European conference on precision agriculture, pp — Kallay M The complexity of incremental convex hull algorithms in R d. Inform Process Lett 19 4 A Bradford book. MIT Press, Cambridge. Google Scholar. Oksanen T, Visala A Path planning algorithms for agricultural machines.

In the adjoining figure of a triangle there are three interior angles i. Concave polygon:. Examples of concave polygons:. In the adjoining figure of a hexagon there are six interior angles i. In the adjoining figure of a septagon there are seven interior angles i.

In the adjoining figure of a quadrilateral there are four interior angles i. Note: In this type of polygon, some portion of the diagonals lies in the exterior of the polygon. In the above quadrilateral the portion of the diagonal AC i. Polygon and its Classification.

Terms Related to Polygons. Interior and Exterior of the Polygon.