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 …
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 …
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
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.
geometry - Algorithm to find the point in a convex polygon …
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 …
Proof that the number of diagonals of a polygon is $\frac {n (n-3)} …
Feb 3, 2014 · So, e.g. here, where polygon can have arbitrary number of vertices, it is good to use induction. Not enough room for details, but basically: proof by induction is done in two steps, …
Why the sum of interior angles of any concave or convex polygon …
Aug 18, 2021 · I have just read about the sum of interior angles of convex polygons with n sides, which is $$(n-2) × 180°$$ Then I tried to find the sum of interior angles of some concave …
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 …
Explanation/Intuition behind why $C_n$ counts the number of ...
Technically, the triangulated polygons, which we call triagons, are convex, planar, roofed polygons subdivided into triangles by non-crossing diagonals. The roof marks a distinguished …
Recursivley count triangulations of a convex polygon
Dec 5, 2021 · So, instead of a single vertex we choose a single polygon edge, and consider all triangles, which can be drawn using this edge and some vertex ("moving vertex") of the …