How do you triangulate a monotone polygon?
A polygon that is monotone with respect to the y-axis is called y-monotone. A monotone polygon with n vertices can be triangulated in O( n ) time. Assuming a given polygon is y-monotone, the greedy algorithm begins by walking on one chain of the polygon from top to bottom while adding diagonals whenever it is possible.
What is triangulation problem?
The triangulation problem is in principle trivial. Since each point in an image corresponds to a line in 3D space, all points on the line in 3D are projected to the point in the image. The problem, then, is to find a 3D point which optimally fits the measured image points.
What is an example of triangulation?
For example, a relationship between two siblings can be triangulated by a parent when the siblings disagree, and a relationship between a couple can be triangulated when one partner relies on a child or parent for support and communication with the other partner.
Can a monotone polygon be triangulated in O ( n ) time?
A monotone polygon with n vertices can be triangulated in O (n) time. Assuming a given polygon is y-monotone, the greedy algorithm begins by walking on one chain of the polygon from top to bottom while adding diagonals whenever it is possible. It is easy to see that the algorithm can be applied to any monotone polygon.
How to triangulate a polygon into a trapezoid?
Overview of the Triangulation Algorithm 1 Decompose the Polygon into Trapezoids. Let S be a set of non-horizontal, non-intersecting line segments of the polygon . 2 Decompose the Trapezoids into Monotone Polygons. A monotone polygon is a polygon whose boundary consists of two y-monotone chains. 3 Triangulate the Monotone Polygons.
How to triangulate a convex polygon in linear time?
This number is given by the 5th Catalan number. It is trivial to triangulate any convex polygon in linear time into a fan triangulation, by adding diagonals from one vertex to all other vertices. The total number of ways to triangulate a convex n -gon by non-intersecting diagonals is the ( n −2)nd Catalan number, which equals
Is there a lower bound for triangulation of polygons?
Seidel’s decomposition algorithm and Chazelle’s triangulation method are discussed in detail in Li & Klette (2011) . The time complexity of triangulation of an n -vertex polygon with holes has an Ω (n log n) lower bound, in algebraic computation tree models of computation.