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How to split a polygon by the target area?
Since the target area is A p o l y N, and the interpolated point will be A + A p o l y N ∗ A A G B ( G − A) If the minimum cut lies in the trapezoid, then the two points of the split line (shown in red) can be found via linear interpolation based on the target area, similar to the approach we took for the triangle case above.
How to divide a polygon into smaller polygons?
We use the divide and conquer methodology: 1 Calculate the area of the polygon, say A p o l y. 2 Split the polygon into two sub-polygons – smaller one with area of A p o l y N, and bigger one with area of ( N − 1) N A 3 Continue using the same approach on the bigger polygon till the bigger polygon reduces into polygon with desired area.
Which is the best algorithm for dividing polygons?
This approach may not always lead to the correct solution, but the results will be fast. The algorithm has cubic time complexity for convex polygons. Checking every edge pair requires quadratic complexity, and for a given edge pair, the algorithm involves calculating area, and doing linear interpolation for finding split lines.
How to calculate the area of a polygon?
Get an extent of a polygon. Construct a polyline using the vertices of the polygon’s extent with a tiny shift of coordinates. Cut the polygon into two halves using this line. Find what is the area of the smallest polygon. If the area is smaller than the 200 sq. m. (that is, fifth part of the polygon), the shift the line again and re-run steps 2-4.
How are polygons sliced to minimize the amount of computation?
One of them works a little like your description, but instead of slicing the polygons at “random” locations you can do it purposefully in a way designed to minimize the amount of computation. Here is the basic algorithm.
How are the boundaries of a polygon represented?
The outer boundary (shell) and inner boundaries (holes) of the polygon are represented by {@link LinearRing}s. The boundary rings of the polygon may have any orientation.
Can you split a polygon by an overlapping feature?
You can split a polygon representing a forest by an overlapping river line feature. If you have an ArcGIS for Desktop Standard or ArcGIS for Desktop Advanced license, you can use the Split Polygons command to split polygons by overlapping features. Split Polygons allows you to split many polygons simultaneously.
What to do when splitting a polygon in ArcGIS?
If there is no domain assigned to a field, the attribute values are copied from the original feature to the new feature. When you are splitting polygons, make sure your sketch cuts completely through the selected polygon. Edge snapping often helps ensure that the cut operation is completed successfully.
The formula for the area of a regular polygon is, A = l 2 n 4 t a n π n, is the side length and n is the number of sides. We can use the apothem area formula of a polygon to calculate the length of the apothem. A = 1 2 × a × P,where, A is the polygon area, a is the apothem, and P is the perimeter.
How do you check every edge pair of a polygon?
Checking every edge pair requires quadratic complexity, and for a given edge pair, the algorithm involves calculating area, and doing linear interpolation for finding split lines. For concave polygons, another verification step, that involves ensuring split lines don’t intersect with other remaining edges, is needed.
How to determine the angle of a polygon?
Determine the angle bisector of the edge pair. This is dotted line, labelled as m in the figure below. Determine the projected points of the four vertices on their corresponding opposing edge, at the angle perpendicular to the angle-bisector m. Ignore the projected points that don’t lie on the opposing line segment.