Point Inside Convex Polygon

Star-shaped polygon: The entire polygon is visible from some point inside the polygon. How could you as a teacher create an activity or project that involves your topic? A great activity to try with students would be to look at regular and irregular polygons and the triangles "inside" of them. identify the set of inflex points, i. It is used in computer graphics (especially 2D graphics) to reduce the complexity of a scene being displayed by eliminating parts of a polygon that do not. a Convex Polygon In Competitive Location Joy Bhadury, College of Business and Economics, California State University, Hayward, CA Craig Tovey, School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA. For a point to be inside a convex polygon, it must be to the "right" of all the lines with clockwise orientation. For the planar problem, you can classify a point as within the offset region by testing whether it is inside the polygon itself, inside any of the 36 rectangles, or within a distance r of a vertex. Does point fall within polygon? VBA Function. But i need a better approach for solving a certain problem. The longest stick problem in a simple polygon was first solved in subquadratic time (O(n1. Definions of properes of polygons (simple/non-simple, concave/convex) 4. •Testing if two polygons intersect is (log𝑛). Concave Heptagon: A Concave Heptagon is a polygon with one or more interior angles greater than 180 degrees and some diagonals will lie outside the polygon. In general, a convex polygon is one whose vertex list P satisfles the following condition: the angle inside P formed by (pi¡1 mod n;pi;pi+1 mod n) is strictly less than 180 degrees, 8i 2 [0;n ¡ 1]. Fastgraph includes functions for drawing filled and unfilled polygons, as well as a function for determining if a given point is inside a convex polygon. Apologies if this is a repost. Now, test your test point against every line. Point in Polygon Description. check if a polygon is simple. You cannot choose one point inside and one point outside the figure The following figure is convex:. Problem 1 (100 points). A polygon P is convex if and only if for any pair of points x, y in P the line segment between x and y lies entirely in P. Does a point lie inside a polygon. convex_hull. Points in convex polygons A convex polygon is just one without any indentations. If the sum is 360 the point is inside the polygon, if the angle is 0 the. In the case of a convex polygon, it is easy enough to see, however, how triangulating the polygon will lead to a formula for its centroid. Actually I only really need the area occupied by the intersection - so a floating point number for the resulting area would be fine. convex regions of a polygon with holes from any point inside the polygon or from any of its vertices, where each query runs in O(f’h’ + log n) for a polygon with n vertices, f’ visible convex partitions, andh’ visible holes, with a preprocessing stage that runs in O(n log* n) with O(n) space. A Convex Hull polygon is defined as the smallest convex polygon bounding all of the members of a point set. show under this assumption that the largest axis-aligned inscribed rectangle inside a convex polygon can be computed in logarithmic time [2]. All the polygon functions observe the clipping limits. To get the points inside the polygon as row-column coordinates, you need to get their indices. It is known as the Point in polygon test. These points make up a concave polygon. Non-convex regular polyhedrons. In a non-convex (or concave) polygon, at least one interior angle is a reflex angle. Please see the example image:. Unlike a convex polygon, the sides do not connect the vertices in sequence. Point in Polygon Description. • Smallest (area) convex polygon enclosing the. Convex Hull Andre Kessler December 18, 2009 1 Convex Hull Given a collection of points in the plane, we want to nd the convex polygon with smallest area such that each point is contained within (or on the boundary of) the polygon. With a concave thing, I really don't know what to do. Points where two successive edges meet are called vertices. Regular polygons that are not convex form various types of star shape, depending on the total number of vertices. • Shortest (perimeter) fence surrounding the points. the angles together. Now the turtle can draw a square of any size, but what about other shapes. Since there are no points lying on the edge of the polygon area, all 80 points identified by xq(in), yq(in) are strictly inside the polygon area. A polygon is convex if any two points inside the polygon can be connected by a line segment that does not intersect any side. nd a point inside R opt. In ArcMap, click the Geoprocessing tab or open. identify the set of inflex points, i. This model leads to a broad class of new art gallery type problems, which we call “sculpture. Regular Polygons. Concave Polygon, Convex Polygon. This implies that every vertex of the convex hull is a point in P. There may be intersections between polygons. It surely works but I do not know how to prove it. using$the$implicit$line$equation$of$the$triangle$edges:$ let$$$$$be$the$normalized$normal$of$$$$$,$. ppt from AMS 345 at Stony Brook University. The red dot is a point which needs to be tested, to determine if it lies inside the polygon. For arbitrarily shaped convex polygons, when the arbitrary reference point is located anywhere inside the polygon, an algorithm to obtain the distance distributions was proposed in. UPDATE: The class now works with sequences of points. We will make the code that determines whether a point is inside or outside a polygon into a function, just like we did for insideTri. Both the algorithms were tested and results are indicated in Fig. That I am able to do, my problem is that I need the point to be counted even if it's slightly outside the polygon(On the edge or something like that). OpenGL and other low-level rendering APIs are limited to rendering convex polygons. calculate the nested convex hull of the inflex point set. If we find at least one wind at the point consider it within the polygon, else we can say that the point is not inside the polygon. The type Polygon_2 can be used to represent polygons. I have resolved the set of points in concave hull. A convex polyhedron is one such that all its inside points lie on one side of each of the planes of its faces. Perimeter of a polygon. " (O'Rourke) Visit. Vertices (plural of vertex) is the point where two or more straight lines meet and create a corner. The best place to put a text label or a tooltip on a polygon is usually located somewhere in its "visual center," a point inside a polygon with as much space as possible around it. Now that you have a polygon, determining whether a point is inside it is very easy. In this post we are looking for algorithms / ideas on how to find the maximum-area-rectangle inside a convex polygon. It is known as the Point in polygon test. How do I test if a circle (x,y,radius) is inside a polygon ([x,y],[x,y],[x,y],[x,y]) without touching the edges? Update I decided to do a point in polygon followed by a circle line collision on each edge, this let me know first if the circle was within the polygon and then told me if it was colliding with any of the edges. For example in 3D. Two polylines cross if they share only points in common, at least one of which is not an endpoint. This quick video answers a question about finding the area of the smallest polygon that covers a set of points. We can also de ne the convex hull as the largest convex polygon whose vertices are all. For planar curves, imagine that each control point is a nail pounded into a board. Find a point that is within the convex hull (find centroid of 3 non-collinear points will do). closed plane figure bounded by straight line segments as sides. Provided, the center point is located inside the polygon, the polygon has no crossing lines. GetIntersectionPoints: Finds intersection point of given line segment and a polygon; IsPointInsidePoly: Checks if a given point is inside a given convex polygon. SVG Polygons - Fix for Convex/CCW : Test an existing svg polygon and arrange its points CCW, and remove any concave points. A convex hull is a polygon in which a line between 2 points inside the hull lies inside the polygon Convex hull can be found using package wrapping, graham’s scan and interior elimination Interior elimination and package wrapping can be extended to any dimensions Graham’s scan has the best worst case performance-NlogN. It surely works but I do not know how to prove it. You cannot choose one point inside and one point outside the figure The following figure is convex:. Points are geometric objects that have only location. All vertices in convex polygons point outward away from the center. In simple terms, if all points on the line AB. We begin with a standard reference frame (typically the x- and y-axes). Almost Convex Polygons. An angle of orientation is chosen for the rectangle (step 1). Suppose the polygon has vertices. In computational geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon. And moreover, if there is a path between points in different sets, then this path must intersect ∂P. x + width of polygon, can be done in O(n) time. A convex polygon can be determined using the following property: A line segment joining any two points inside the figure lies completely inside the figure. As with a convex regular polygon, the vertices are equally spaced around some central point from which they are equidistant. If any internal angle is greater than 180° then the polygon is concave. Also, I believe this method works for higher dimension. They have equal. Determine whether point is inside polygon. UPDATE: There's a newer version of this algorithm that accounts for points that fall on the boundary of a polygon which are included as inside the polygon. Otherwise, the polygon is called Concave. a) Diagonals in convex polygons, such as the pentagon above, will always intersect the polygon at two points (vertices). I have searched the forum and cannot find anything that works in my context. (picture from http://www. convex_hull. show under this assumption that the largest axis-aligned inscribed rectangle inside a convex polygon can be computed in logarithmic time [2]. Convex polygons don’t have any ‘caves’ on their outsides, and none of the interior angles are larger than 180°. Most people find convex polygons look a lot more ‘normal’. The weight-factor w[i] of each point P[i] determines how much that point affects the sum. Two polylines cross if they share only points in common, at least one of which is not an endpoint. But i need a better approach for solving a certain problem. When the number of sides, n, is equal to 3 it is an equilateral triangle and when n = 4 is is a square. A polygon that is not a convex polygon is referred to as a concave polygon. If a convex polygon is defined by a collection of vertices in anticlockwise order, then a point which is inside the polygon will always lie to the left of each side. Take the point and test it against each of the polgyon's edges. Every polygon P has at least one diagonal. calculate the nested convex hull of the inflex point set. Determining If a Given Point Lies inside a Polygon [12/27/2005] I have a finite number of points that constitute a polygon, and a point p(x,y). A link furthest The link distance between two points inside a simple polygon P is defined to be the minimum number of edges required to form a polygonal path inside P that connects the points. The hull is a convex polygon, and any points interior to the polygon have no in uence on the bounding rectangle. To describe their location, we use coordinates. This quick video answers a question about finding the area of the smallest polygon that covers a set of points. To check if a given point is inside a polygon or not is a very useful piece of code. If this sum is 2pi then the point is an interior point, if 0 then the point is an exterior point. And moreover, if there is a path between points in different sets, then this path must intersect ∂P. Here is the code in Python: RIGHT = "RIGHT" LEFT = "LEFT" def inside_convex_polygon (point,. A Convex Hull is the smallest convex polygon that contains every point of the set S. Regularly, a polygon is firmly convex, if each line segment with two nonadjacent vertices of the polygon is strictly internal to the polygon but on its endpoints. Locating a point inside a union of simple polygons. A face plane has an outward normal vector, which directs to outside of the polygon. Here's my code:. The easiest way to do this might be dividing \(N\) into triangles. Convex polygon: The line segment joining any two points of the polygon lies within the polygon. (picture from http://www. A polygon is convex if any two points inside the polygon can be connected by a line segment that does not intersect any side. a point is inside a polygon,. Points in convex polygons A convex polygon is just one without any indentations. The first thing that comes to mind for calculating such a center is the polygon centroid. You cannot choose one point inside and one point outside the figure The following figure is convex:. within(polygon). If we draw a line through any of these convex polygons, the line will cross through only 2 sides of the polygon. Does point fall within polygon? VBA Function. Point Inside Polygon. where a right-turn is made when going around the polygon counter clockwise. This is an example of a convex polygon. convex_hull. A point is on the interior of this polygons if it is always on the same side of all the line segments making up the path. If the polygon is not convex, then the vertex centroid need not lie inside the polygon, consequently the grid points may also seem misaligned. Problem 1 (100 points). Apologies if this is a repost. Ray Casting algorithm: Ray casting algorithm can be used for checking whether a point is inside or outside the polygon. This is because the choice of a reference. All submissions for this problem are available. You can see that if the point is inside the normalized polygon gets closer to a regular polygon and if the point is outside the vertices bunch together, so a way to measure that is to ask whether the centroid of the transformed polygon has moved closer to P or farther away after the midpoint operation. If it crosses the boundary of the triangle once, then the point is inside the triangle. Download: tessellation. A Convex Polygon is a polygon such that any line segment connecting two points inside the polygon is itself entirely in the polygon. Then each point is checked to see if it is strictly inside the convex polygon. efficient algorithm, valid for all convex polygons, open or closed, and topologically connected in n-dimensional space (n ⥠2). Unlike a convex polygon, the sides do not connect the vertices in sequence. , passing round the outside of the frame in one direction, and returning at last to joint 1, then in the polygon the. One way to remember this is to think of con cave polygons being like caves. The red dot is a point which needs to be tested, to determine if it lies inside the polygon. We observe that this result will remain true for any planar lattice, since it just depends on the numbers B and I. Polygons can be used to create amazing patterns. convex components whose union is P. Thus the sum of the interior angles of the network polygon T, is 7g, because T1 has 9 sides. Re: point inside polygon. A convex polygon is defined as a polygon with all its interior angles less than 180°. to determine whether a. The polygons dont overlap and therefore a single point cannot be inside multiple polygons. Find if a point is inside or outside of a triangle to any convex polygon that has n sides to determine if the point p is inside the polygon. a Convex Polygon In Competitive Location Joy Bhadury, College of Business and Economics, California State University, Hayward, CA Craig Tovey, School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA. Note: Points that lie on the boundaries of the polygon or vertices are assumed to be within the polygon. They will also always lie on the inside of a convex polygon. Since there are no points lying on the edge of the polygon area, all 80 points identified by xq(in), yq(in) are strictly inside the polygon area. Antonyms for polygon. •Testing if two polygons intersect is (log𝑛). /// The polygon can be concave or convex. A polygon is called a Convex polygon if we draw a line between any two different points inside the polygon and the line always remain inside the polygon. This way four polygons can be at different stages of the clipping process simultaneously. If all you really need is a point in convex polygon test, it's probably a little too trivial to be worth dragging in a dependency on anything. Regular Polygon Formulas. ,N} Then generate randomly N convex weights. In convex geometry, a convex combination is a linear combination of points where all coefficients are non-negative and sum up to 1. Point Inside SVG Convex Polygon: Determine if a point is located inside of the polygon. This also works for polygons with holes given the polygon is defined with a path made up of coincident edges into and out of the hole as is common practice in many CAD packages. Regular polygons that are not convex form various types of star shape, depending on the total number of vertices. - Point inside convex polygon (sidedness). Click here repeatedly to generate polygons of increasing complexity, but all lit by a single lamp. Convex Hull Background. Points that fall outside all the polygons will be deleted as they are outside my zones of interest. In computational geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon. Can also return -1 to indicate degenerate polygon. ; Every point on every line segment between two points inside or on the boundary of the polygon remains inside or on the boundary. There is a far easier method to check if a given polygon (assume no three collinear points) is convex without using the direct definition above. We give exact. If a convex polygon is defined by a collection of vertices in anticlockwise order, then a point which is inside the polygon will always lie to the left of each side. I want to generate a polygon hull mesh from a point cloud in 3D, for which I've followed this tutorial. A very large lattice polygon might be expected to cover many more lattice points. It is known as the Point in polygon test. Angle Q is an interior angle of quadrilateral QUAD. It requires an array of integer x coordinates as its first parameter, and an array of integer y coordinates as its second parameter. If the inside angle between two edges of the polygon is less than л, the vertex is convex. I have a set of polygons (convex, concave – non-convex, not self-intersecting) in a plane. Or Create a VERY long line starting in the point. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. The idea is to find out how many of these points lie strictly inside the convex polygon (not on the edge or outside). What algorithm is behind?. (Do not create a 'crossed' polygon, this method does not work on those. Now, test your test point against every line. positive or. grid_points_inside_poly: Test whether points on a specified grid are inside a polygon. Our algorithm computes an ACD of a simple polygon with n vertices and r notches in O(nr) time. For a point to be inside a convex polygon, it must be to the "right" of all the lines with clockwise orientation. • Shortest (perimeter) fence surrounding the points. For a given 3D convex polygon with N vertices, determine if a 3D point (x, y, z) is inside the polygon. They may also intersect the polygon at more than two points. The following C# code snippet can determine whether a point is inside a simple 2-D polygon. the angles together. Ordering points in a clockwise manner is straightforward when it is a convex shape. Random points in layer bounds: Generate pseudo-random points over bounds of a given input layer. Any convex vertex of the monotone chain is the tip of an ear, with the possible exception of the vertices of the base. If all the angles are in the range to (when the polygon is defined counterclockwise) or all in to (in the clockwise case), then the point is inside the convex polygon. It is a special case of point location problems and finds applications in areas that deal with processing geometrical data, such as computer graphics, geographical information systems (GIS), motion planning, and CAD. where a right-turn is made when going around the polygon counter clockwise. vertex ordering is common when handling polygons: In fact, Alt et al. 3) Next verify if any of the other vertices in the polygon is inside the triangle. a polygon whose all interior angles are less than or equal to $180^0$, any point inside the polygon can be a reference point that gives the exact same area i. In general, a convex polygon is one whose vertex list P satisfles the following condition: the angle inside P formed by (pi¡1 mod n;pi;pi+1 mod n) is strictly less than 180 degrees, 8i 2 [0;n ¡ 1]. If we find at least one wind at the point consider it within the polygon, else we can say that the point is not inside the polygon. This proof sketch is the basis for an algorithm for deciding whether a given point is inside a polygon, a low-level task that is encountered every time a user clicks inside some region in a computer game, and in many other applications. Taking the center won't work, because the polygon might not be convex. A convex polygon is any polygon that is not concave. ) Note, however, that complex and concave polygons can be subdivided into more manageable polygons (such as triangles) for the purposes of calculating area or other parameters. be a point robot moving in the plane, whose path is con-strained to have curvature at most 1, and let P be a convex polygon with n vertices. x + width of polygon, can be done in O(n) time. Applications. With a concave thing, I really don't know what to do. Now, test your test point against every line. So, if "m" and "n" are the numbers of sides in our polygons, then the problem gives you two equations n - m = 4 (1) - = 30 (2) Step 1. I have searched the forum and cannot find anything that works in my context. Almost Convex Polygons. This function creates a rounded buffer around a point, line, or polygon, or inside a polygon. One way for this to work is simply draw a line segment from each vertex to the point and compare it to the number of intersections with other lines. Here is my implementation in JavaScript of an algorithm counting the number of times a ray crosses the perimeter of the polygon, and subsequently checking the parity. Unlike a convex polygon, the sides do not connect the vertices in sequence. How can i test if a given point is inside? All implementations i found on the web fail for some trivial coun. This is a method to judge if a point is inside of a polygon or not. We study the collision-free, optimal path-planning problem for B moving between two configurations inside P (a con-figuration specifies both a location and a direction of travel ). You are given a convex polygon with N vertices. If it is even, the point lies outside the polygon. x + width of polygon, can be done in O(n) time. Or you can just use the classic thing where you extend a line infinitely in one direction from your point (it doesn't matter what direction) and count the number of times that line intersects your polygon. The Production Points To Line Or Polygon tool allows you to generate a linear or polygon feature from a selected set of points depending on the selected template. We can also de ne the convex hull as the largest convex polygon whose vertices are all. Random points inside polygons: Generate pseudo-random points over a polygon layer (variable number of point or fixed number of point). Convex polygons. The convex hull can be calulated with the TRIANGULATE command. If all of the sides of a convex polygon are extended, none of them will contain any points that are inside the polygon. Full Answer. This problem finds applications in areas that deal with processing geometrical data, such as computer graphics, computer vision, geographical information systems (GIS), motion planning, Computer-aided design (CAD), and has been the. The angle calculation can be accomplished as follows: , where is the rotation matrix through. SVG Polygons - Fix for Convex/CCW : Test an existing svg polygon and arrange its points CCW, and remove any concave points. Heptagons that are not convex are concave Heptagons. (picture from http://www. • Smallest (area) convex polygon enclosing the. Instructions for manual positioning mode:. So that it can be clipped into similar polygons. For example in 3D. numerical array of x-coordinates of polygon. The longest stick problem in a simple polygon was first solved in subquadratic time (O(n1. Convex Hull Background. A 3D convex polygon has many faces, a face has a face plane where the face lies in. , it has no self intersections), then both methods give the same result for all points. A polyhedron is called a regular one, if all its faces are equal regular polygons and the same number of faces join in each its vertex. Given$a$point$in$triangle,$how$to$compute$its!γ (or!α, β)?$ 1. The sides of a polygon are segments that intersect exactly two other segments, one at each endpoint. and I want to test a point (110,10) to see if this lies inside, outside, or on the boundary of a polygon. All the polygon functions observe the clipping limits. convex_hull Point-in-Polygon. A non-convex polygon is said to be concave. Point Inside SVG Convex Polygon: Determine if a point is located inside of the polygon. It is known as the Point in polygon test. I don't need the point to be in any specific location inside the polygon, but I prefer to receive a point which isn't very close to an edge, but that is not a deal-breaker. Point in Polygon & Intersect¶. Let q be the query point and P be. The convex hull of a set of points CH(S) is the smallest convex set that contains all the points in set S. Obviously, the largest square that can be drawn inside P is the red square. 4 Finding the Convex Hull of a 2-D Set of Points Reference: Computational Geometry in C by J. On Sun, 11 Sep 2016, Mateus Bellomo wrote: > I would like to know if there is a way of doing a triangulation of a non > convex polygon. View lecture-triangulation-orourke-Chap2. Both the algorithms were tested and results are indicated in Fig. Draw convex polygon. I need to find any point that is inside of that polygon. A convex hull is a polygon in which a line between 2 points inside the hull lies inside the polygon Convex hull can be found using package wrapping, graham's scan and interior elimination Interior elimination and package wrapping can be extended to any dimensions Graham's scan has the best worst case performance-NlogN. More formally, Lemma 3 ([9]) Let Pbe a convex polygon and R opt. Point Inside SVG Convex Polygon: Determine if a point is located inside of the polygon. The rightmost point of a and leftmost point of b. ; Every point on every line segment between two points inside or on the boundary of the polygon remains inside or on the boundary. Concave Polygons At least one angle measures more than 180°. This function creates a rounded buffer around a point, line, or polygon, or inside a polygon. The Area of a Triangle As the mass is distributed over the entire surface of the polygon, it is necessary to compute the area of the triangles resulting from the triangulation. As with a convex regular polygon, the vertices are equally spaced around some central point from which they are equidistant. Concave Polygon, Convex Polygon. In the case of a convex polygon, it is easy enough to see, however, how triangulating the polygon will lead to a formula for its centroid. Can anyone please help me with a tutorial on "How to check whether a point inside a Convex polygon " with complexity O(lg n). This is a Python 3 implementation of the Sloan's improved version (FORTRAN 77 code) of the Nordbeck and Rystedt algorithm, published in the paper:. public bool PolygonIsConvex() { // For each set of three adjacent points A, B, C, // find the cross product AB · BC. from shapely. For each edge type, zero, one, or two vertices are added to the output list of vertices that define the clipped polygon. Use mathematical induction to prove that for all integers n ≥ 3, the angles of any n -sided convex polygon add up to 180( n –2) degrees. Check if point belongs to the convex polygon in $O(\log N)$ Consider the following problem: you are given a convex polygon with integer vertices and a lot of queries. For example say you have a N sided convex polygon with vertices. I have searched the forum and cannot find anything that works in my context. Convex polygon: The line segment joining any two points of the polygon lies within the polygon. I have a point A. In this post we are looking for algorithms / ideas on how to find the maximum-area-rectangle inside a convex polygon. The link distance between two points inside a simple polygon P is defined to be the minimum number of edges required to form a polygonal path inside P that connects the points. More precisely, no internal angle can be more than 180°. But i need a better approach for solving a certain problem. (The terms simple, complex, concave, and convex have the same definitions for polygons as they do for quadrilaterals. Determining If a Given Point Lies inside a Polygon [12/27/2005] I have a finite number of points that constitute a polygon, and a point p(x,y). This technique can be generalized to an arbitrary nonconvex polygon. I need to find any point that is inside of that polygon. The function can be called from other VB code or used as a UDF (user defined function) directly on a worksheet. The existence of such a vertex was established by lemma 1. In this example you can drag the point and the Demonstration determines (and counts) the intersection points. If a convex polygon is defined by a collection of vertices in anticlockwise order, then a point which is inside the polygon will always lie to the left of each side. $\endgroup$ - Andy W Feb 15 '12 at 18:07 $\begingroup$ @AndyW I mean that the NA kill the chull function. And moreover, if there is a path between points in different sets, then this path must intersect ∂P. 4) If you find another point inside the triable skip these three points and get another three points. Any convex vertex of the monotone chain is the tip of an ear, with the possible exception of the vertices of the base. Points in convex polygons A convex polygon is just one without any indentations. Arguments. pixels within the boundary of a polygon belong to the polygon pixels on the left and bottom edges belong to a polygon, but not the pixels on the top and right edges Want a polygon filling routine that handles convex, concave, intersecting polygons and polygons with interior holes. Being inside is defined by the odd-even rule. The input polygon is clipped against one edge and any points that are kept are passed on as input to the next stage of the pipeline. The algorithm is wrapped into a Fortran DLL GeoProc. A good way to describe this is that for any two points inside the polygon, the line between the two points is entirely inside the polygon. Apologies if this is a repost. If all you really need is a point in convex polygon test, it's probably a little too trivial to be worth dragging in a dependency on anything. For example say you have a N sided convex polygon with vertices. The Area of a Triangle As the mass is distributed over the entire surface of the polygon, it is necessary to compute the area of the triangles resulting from the triangulation. public bool PolygonIsConvex() { // For each set of three adjacent points A, B, C, // find the cross product AB · BC. One way to visualize a convex hull is to put a "rubber band" around all the points, and let it wrap as tight as it can. numerical array of y-coordinates of polygon. A convex hull is a polygon in which a line between 2 points inside the hull lies inside the polygon Convex hull can be found using package wrapping, graham’s scan and interior elimination Interior elimination and package wrapping can be extended to any dimensions Graham’s scan has the best worst case performance-NlogN. Winding is important because it allows us to easily determine which points lie within the bounds of a polygon, among other things. Point in Polygon & Intersect¶. Otherwise, the polygon is called Concave. $\endgroup$ - Andy W Feb 15 '12 at 18:07 $\begingroup$ @AndyW I mean that the NA kill the chull function. If that number of times is odd, the point is inside your polygon. It requires an array of integer x coordinates as its first parameter, and an array of integer y coordinates as its second parameter. International Journal of Robotics and Automation, Vol.