Fig 1.
(a)-(d) Polygons with different geometries.
Fig 2.
Example of line-to-point visibility.
Fig 3.
(a) Occlusion with no intersection, (b) occlusion with intersection, (c) no intersection & no occlusion, and (d) no occlusion with intersection.
Fig 4.
Coordinate axes graph.
Fig 5.
Example of polygon initialization.
(a) Random point distribution and (b) polygon initialization.
Fig 6.
New polygon after one iteration.
(a) Polygon 1 and (b) polygon 2.
Fig 7.
Example of line-to-point visibility.
(a) Visibility example and (b) visibility from different regions.
Fig 8.
(a) Random point distribution, (b) polygon initialization, (c) result of one iteration, (d) result of two iterations, (e) result of three iterations, and (f) final polygon.
Fig 9.
Polygons of different shapes constructed from different number of points.
(a) Generation of the initial polygon, (b) polygon constructed from 4 points, (c) polygon constructed from 5 points.
Fig 10.
Polygons constructed with coordinate axes in different directions.
(a) Horizontal x- axis, (b) x- axis rotated by 45º to the left, and (c) vertical x-axis.
Fig 11.
Plane distribution of random points.
Plane distribution of (a) 20, (b) 50, and (c) 80 random points.
Fig 12.
Experimental results of polygon generation.
Polygons consisting of (a1)-(a2) 20, (b1)-(b2) 50, and (c1)-(c2) 80 points.
Fig 13.
Polygon generation and magnification of partial areas.
(a) Polygon consisting of 80 points, (b) enlarged area corresponding to the blue box, (c) enlarged area corresponding to the green box, and (d) enlarged area corresponding to the black area.
Fig 14.
Polygon generation using the polar coordinate sorting method.
Polygon consisting of (a) 20 (b) 50, and (c) 80 points.
Fig 15.
Polygon generating using the dichotomy sorting method.
Polygon consisting of (a) 20 (b) 50, and (c) 80 points.
Table 1.
Time required to generate a simple polygon.
Fig 16.
Polygon generation using the proposed method.
(a) Random point distribution, (b) polygon initialization, (c) result of one iteration, (d) result of two iterations, (e) result of three iterations, and (f) the final polygon.
Fig 17.
Polygon generation using the convex-hull construction method.
(a) Polygon initialization, (b) result of one iteration, (c) result of two iterations, and (d) result of three iterations.