Concave polygon partitioning software

Ive looked online and havent been able to find any sources that give a straight yes or no answer. Pdf convex partitioning of a polygon into smaller number of. Approximate convex decomposition of polygons gmu cs. Concave polygon definition of concave polygon by the free. This paper proposes an algorithm for partitioning a concave polygon into smaller number of convex pieces. Note that a triangle is a degenerated trapezoid with a zerolength edge. A concave polygon is defined as a polygon with one or more interior angles greater than 180. My rectangles can be any length, but they have maximum widths, and the polygon will never have an acute angle. A trapezoid is a quadrilateral with at least two parallel edges. Our algorithm partitions images into regular convex polygons. The answer seems negative, because heuristically if we remove a concave quadrilateral the new polygon is still convex, and after a finite number of steps we arrive at a concave quadrilateral in end, and therefore a contradiction.

My goal is to convert concave polygon to convex by removing this kind of point by identifying and removing those points. Why the polygon interior angle sum theorem does not apply for. Exterior angles of a concave polygon tutorial sophia learning. How to split a concave polygon into convex polygons in arcpy. The key strategy for solving problems on simple polygons is to decompose simple polygons in simpler polygons trapezoidalization. Again, since the list of edges is really a list of references into the list of vertices, that ordering will be simple. Polygon triangulation graphics and gpu programming tutorials. It looks sort of like a vertex has been pushed in towards the inside of the polygon. Visualizing concave and convex partitioning of 2d contours. Fair partitioning of convex polygons 3 results n2 fair convex partitioning of a convex polygon into n2 pieces proof. A concave polygon will always have at least one reflex interior anglethat is, an angle with a measure that is between 180 degrees and 360 degrees exclusive. You can easily build a triangle strip to represent this shape. Convex polygon definition of convex polygon by the free.

A concave polygon has at least one angle greater than 180. In the context of generating random test data using qgis in a shapefile. Thus in 2d, we now have a list of edges that comprise the enclosing polygon, which may be concave depending on the value of alpha to generate that alpha shape. A simple connected singlecyclic graph in r 2, such that each of its edge is perpendicular or inline with another one of its edges. Given a test point, you traverse the quadtree, and when you visit a node, you do a pointinpolygon test for each polygon associated with that node. This chapter describes functions for partitioning planar polygons into two types of subpolygons \ y\monotone polygons and convex polygons. In other words, all of the interior angles of the polygon must have a measure of no more than 180 for this theorem to work.

Monotone polygons definition a polygonal chain c is strictly monotone with respect to l. Polygon partitioning splits your polygon into convex polygons. A simple polygon that is not convex is called concave, nonconvex or reentrant. The term polygon is often modified by simple to distinguish it from polygons that cross themselves, but in this book all polygons are simple, so we will drop the redundant modifier. For a polygon with holes, there is a lower bound of. Pdf convex partitioning of a polygon into smaller number. Nov 22, 2009 a convex polygon will have all vs facing the same direction, whereas a concave polygon will have vs facing both directions. Often when using 3d modeling programs or vectorbased drawing. Maybe what i am trying to do is minimize the amount of boundry of rectangle that is inside of the polygon. The polygon is not a concave polygon because of the followings two situations occur. This is illustrated in my answers to these older questions. Python code for partitioning rectilinear polygon in on time complexity.

Any straight line through it crosses at most two sides. A partition of a polygon is a set of primitive units e. Most algorithms which have been devised to perform this partitioning suffer from a lack of generality. But if you just traverse the boundary of the polygon to form the star, so that you turn sometimes clockwise and sometimes counterclockwise to draw it then, yes, it is concave. I thought about trying to decompose my concave polygon into triangles that produce a set of minimumally overlapping rectangles minimally bounding each triangle. It is possible to trace a path from any polygon to any other polygon without exiting a polygon in the set, e. Polygon partitioning vs triangulation stack overflow. A related problem is partitioning to triangles with a minimal total edge length, also called minimumweight triangulation. Convex polygon definition of convex polygon by merriam. The term polygon decomposition is often used as a general term that includes both covering and partitioning. Im looking for a tool or algorithm to detect concave polygons and split them into convex polygons. Because a concave polygon has an angle larger than 180 degrees, you could create a cave or a pocket by enclosing.

I am trying to cover a simple concave polygon with a minimum rectangles. This chapter describes functions for partitioning planar polygons into two types of subpolygons ymonotone polygons and convex polygons. Concave polygon definition is a polygon with one angle larger than a straight angle. Euclidean tilings by convex regular polygons a problem of partitioning the entire plane to simple polygons such as rectangles. For a holefree polygon with vertices, a triangulation can be calculated in time. Interpolation by voronoi polygons initially consists in determining these polygons, each point of which is closer to a specific site than to any other site.

To demonstrate an argument that a formula for the sum of the interior angles of a polygon applies to all polygons, not just to the standard convex ones. Polygon partitioning is an important class of problems in computational geometry. Thus software which prepares data for electron beam systems must partition polygons into suitable geometric primitives. A new path planning method based on concave polygon convex. Concave polygon definition of concave polygon by the. Image partitioning into convex polygons liuyun duan, florent lafarge inria sophia antipolis, france figure 1. Hence our algorithms will reduce the run time of current vlsi software that uses. Polypartition implements multiple algorithms for both convex partitioning and triangulation. Polygon partitioning for electron beam lithography of. This then lets you do a smaller number of pointinpolygon tests.

Jul 28, 2008 if a star polygon crosses itself then, one turns continually in one direction to draw the polygon, so it is not concave. Calculate the sum of the interior angles of each polygon. Open problem 67 fair partitioning of convex polygons. Is there any algorithm for covering a concave polygon. Rectilinear holefree polygons, partition, complexity, computational geometry. Bounding size of convex partition lemma chazelle let. I have written a program that does both for a class and if you want i can. Single concave polygon can be decomposed into convex polygons by connecting concave points with their visible vertex. In this paper, we address the problem of partitioning images into atomic regions with convex polygons while imposing geometric guarantees on the shape and connection of these regions. From each of the concave vertices from which a chord was not drawn in. I can generate random, continuous adjacent polygons by first creating n random points using ftools and then generating a voronoi diagram from those.

The most wellstudied polygon partition problem is partitioning to a smallest number of triangles, also called triangulation. Some diagonals of a concave polygon lie partly or wholly outside the polygon. Method of labelling the graph we take input as a rectillinear polygon from cursor keys, i. I think the trick has to do with the perimeters of the rectangles. If a polygon does have an angle that points in, it is called concave, and this theorem does not apply. In a concave polygon, at least one diagonal passes outside the figure in addition, at least one angle inside the polygon will have a measure greater than 180 degrees.

In the beginning, the voronoi partitioning into a polygon depends solely on the position of the points and is by no means related. A concave polygon will always have at least one reflex interior anglethat is, an angle with a measure that is between 180 degrees and 360 degrees exclusive some lines containing interior points of a concave polygon intersect its boundary at more than two points. Some lines containing interior points of a concave polygon intersect its boundary at more than two points. But is there any generalization for exterior angles of a convex polygon. Convex polygon definition of convex polygon by merriamwebster. A concave polygon is the opposite of a convex polygon. The red diagonal is completely located outside the polygon. An equilateral polygon is a polygon which has all sides of the same length. If a star polygon crosses itself then, one turns continually in one direction to draw the polygon, so it is not concave. A partition of a polygon \ p\ is a set of polygons such that the interiors of the polygons do not intersect and the union of the polygons is equal to the interior of the original polygon \ p\. A convex polygon is the opposite of a concave polygon. Although partitioning covers the entire polygon, number of convex polygons can be reduced by second approach. However, if you only need to draw the halfmoon type shapes that you use in your example, and not arbitrary concave polygons, this all seems much more complicated than necessary.

Those four points make that polygon a concave polygon thats why i want to remove it. Connect the edges into a polygon, traversing one to the next in order. The black diagonal is partially located outside the polygon. Fair partitioning of convex polygons 2 problem definition a fair partitioning of a polygon.

Is it possible to partition every convex polygon into a finite number concave quadrilaterals. If all the resulting pieces are convex, call it a fair convex partitioning. Why the polygon interior angle sum theorem does not apply. Information and translations of convex and concave polygons in the most comprehensive dictionary definitions resource on the web. Convex polygon definition is a polygon each of whose angles is less than a straight angle. Visualizing concave and convex partitioning of 2d contours article in pattern recognition letters 24. Adding the hawaii multipolygon would fail the contiguity test because one has to exit california for example, enter unbounded planar space, and then reenter the polygon set. Additionally, i know that all the polygons are contiguous and it is possible to build an adjacency matrix. A series of images and videos raises questions about the formula n180360 describing the interior angle sum of a polygon, and then resolves these questions. A concave polygon is a polygon with at least one angle larger than 180 degrees. Monotone polygon triangulation of monotone polygon trapezoidal decomposition decomposition in monotone mountain convex decomposition 3.

In this case there can be overlap between the convex polygons. Im looking for an algorithm to partition any simple closed polygon into convex subpolygonspreferably as few as possible. Move p clockwise keeping the two areas equal q is also moving, but maybe not at the same speed until 2 pieces have equal perimeters. Each resultant convex piece then can be processed using a simple algorithm applicable to. A convex polygon is defined as a polygon with all its interior angles less than 180. Convex partitioning of a polygon into smaller number of pieces with. A convex polygon with n vertices can always be triangulated into n2 triangles in on time by taking any vertex as the origin and adding edges to all vertices except its two adjacent vertices without further calculations.

Using this technique i get n convex polygons within some extent. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. For example, convex polygons are easier to triangulate than concave. There are many different polygon partition problems, depending on the type of polygon being partitioned and on the types of units allowed in the partition. Not a full answer to your question, but if you have a general polygon concave, convex. Like explained in the picture, the blue polygon is split into a and b polygons. Convex polygons partitioned into concave quadrilaterals. Exterior angles of a concave polygon tutorial sophia. Triangulation of concave polygon using triangle library.