geometry - Algorithm to find the point in a convex polygon closest to ...
Oct 4, 2014 · 2 This is a special case of computing the distance between two convex sets (a point by itself is a convex set). This paper A fast procedure for computing the distance between complex …
Check if point is inside a convex polygon - I need an example for a ...
Jun 25, 2021 · To know if a point (xp,yp) is inside a polygon you must use this formula with all segments of the polygon. If for all of them D has the same sign then the point is inside.
The VC dimension of convex d-gons - Mathematics Stack Exchange
Jun 16, 2018 · I'll assume that you mean the one-sided classifiers which assign $+$ to every point inside the (closed) polygon and $-$ outside. Note that the proof idea you suggest in your question is a little …
Maximum number of acute triangles in a regular convex polygon ...
Jun 22, 2020 · Because the polygon is convex, these "diagonals" are all contained within the polygon. If you start from a pair of consecutive edges, form the first triangle by adding the diagonal between …
Sufficient criteria for proving convexity of a polygon
Jan 21, 2020 · A convex polygon is defined as a polygon that is a convex set (ie. if we define the interior of the polygon to include the boundary, the segment formed by joining any two points in the interior …
Why sum of interior angles in convex polygon is $ (n-2)\cdot 180$
Feb 26, 2017 · The polygon can be "concave," but the theorem does not apply to _all_polygons: if you allow self-intersecting polygons, you can get $180n,$ $180 (n+2),$ or a larger sum.
How do you determine if a point sits inside a polygon?
Jul 21, 2010 · Representing a polygon by its edge path might not be the most useful, especially if you want to ask about inclusion for many points. Consider triangulating the polygon, which is trivial for …
geometry - How can I calculate the centroid of polygon?
What is the way to calculate the centroid of polygon? I have a concave polygon of 16 points, and I want know the centroid of that. thanks
What is the number of intersections of diagonals in a convex ...
Nov 8, 2014 · For example diagonals of a regular convex polygon with $6$ vertexes have only $13$ intersection points but $\frac {6\times 5\times 4\times 3} {24}=15$ because three pairs of diagonals …
Into how many regions do the sides and diagonals of a convex $n
Oct 7, 2019 · 0 If we can tell how many vertices and edges are created by the addition of one vertex to the polygon as a planer graph, we can use Euler's formula to derive the solution by induction.