Definition #1: Polygon

A polygon is a closed chain of n line segments (p_i, p_i+1) for 0 <= i <= n-1 and (p_n-1, p₀) , where n >= 3. The polygon P is represented by its vertices P = (p₀, p₁,..., p_n-1).

Definition #2: Simple Polygon

A simple polygon is a polygon P with no two non-consecutive edges intersecting. There is a well-defined bounded interior and an unbounded exterior for a simple polygon, where the interior is surrounded by edges. When referring to P, the convention is to include the interior of P.

Definition #3: Diagonal

A diagonal is a line segment lying entirely inside polygon P and joining two non-consecutive vertices p_i and p_j

Definition #4: Principal Vertex

A vertex p_i is called a principal vertex if the diagonal (p_i-1, p_i+1) intersects the boundary of simple polygon P only at p_i-1 and p_i+1 [5].

Definition #5: Ear

A principal vertex p_i of a simple polygon P is called an ear if the diagonal (p_i-1, p_i+1) that bridges p_i lies entirely in P. We say that two ears p_i and p_j are non-overlapping if the interior of triangle (p_i-1, p_i, p_i+1) does not intersect the interior of triangle (p_j-1, p_j, p_j+1) [4].