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.
What is the maximum no. of acute angles in a n-sided convex polygon ...
0 As @peterwhy noticed in the comments, the sum of external angles of a convex polygon is $360^\circ$ and an external angle corresponding to internal acute angle is greater than $90^\circ$. …
geometry - Polygon Inequality - Mathematics Stack Exchange
The shortest distance between two points is a straight line, and the other sides form a path from one endpoint of the longest side to the other, which must have greater length than the length of that side. …
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 …
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 …
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
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 …
Why sum of interior angles in convex polygon is $ (n-2)\cdot 180$
Feb 26, 2017 · Hint Pick a point in the interior of the polygon. Then, drawing line segments from the point to each vertex divides the polygon into triangles, but you already know that the sum of the …
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 …