Is there a method to calculate the vertices of a polygon given just 1 vertex of the polygon and its center point? I found this post maths - find vertices when 1 vertex and center point is given in polygon on the topic, but it's only for 2 dimensions. Can this be extrapolated to 3 dimensions? Thanks!
Find vertices of a polygon given 1 vertex and the center point in 3D space
2
$\begingroup$
geometry
3d
polygons
1 Answers
4
Given the center of a (regular) polygon and one of the vertices, you can find infinitely many polygons in three-dimensional space.
To get a unique polygon, you'll need (say) another vertex to define the plane the polygon rests in.
-
0That makes sense. If I have a third point, the midpoint of an edge (this edge is connected to the given vertex), how can I calculate the other vertices of the polygon? – 2017-01-03
-
0@namcap I’d build the a polygon in the $x$-$y$ plane centered on the origin (which is almost trivial to do) and then apply a transformation to move it into position. – 2017-01-03