How a polygon can be split into triangles?
The most remarkable and important property of triangles is that any polygon can be split up into triangles simply by drawing diagonals of the polygon. This fact forms the basis for understanding why the interior angles of polygons add up to 180(n-2) degrees.
What are the properties of convex polygon?
Properties
- Every internal angle is strictly less than 180 degrees.
- Every point on every line segment between two points inside or on the boundary of the polygon remains inside or on the boundary.
- The polygon is entirely contained in a closed half-plane defined by each of its edges.
How is a triangulation of a convex polygon formed?
A triangulation of a convex polygon is formed by drawing diagonals between non-adjacent vertices (corners) such that the diagonals never intersect.
How to calculate minimum cost of polygon triangulation?
Minimum Cost Polygon Triangulation. A triangulation of a convex polygon is formed by drawing diagonals between non-adjacent vertices (corners) such that the diagonals never intersect. The problem is to find the cost of triangulation with the minimum cost. The cost of a triangulation is sum of the weights of its component triangles.
How much does a triangulation of a convex pentagon cost?
Weight of each triangle is its perimeter (sum of lengths of all sides) See following example taken from this source. Two triangulations of the same convex pentagon. The triangulation on the left has a cost of 8 + 2√2 + 2√5 (approximately 15.30), the one on the right has a cost of 4 + 2√2 + 4√5 (approximately 15.77).
What is the cost of the triangulation on the left?
The triangulation on the left has a cost of 8 + 2√2 + 2√5 (approximately 15.30), the one on the right has a cost of 4 + 2√2 + 4√5 (approximately 15.77). Recommended: Please try your approach on {IDE} first, before moving on to the solution. This problem has recursive substructure.