How do you triangulate a polygon?

How do you triangulate a polygon?

1) For each vertex in the polygon, compute the angle between the two linked edges. 2) Sort vertices by decreasing angle relative to the interior of the polygon. 3) If there is less than 3 vertices in the set, we’re done. 4) Take the last vertex in the set and output the triangle formed by it and its two neighbours.

Can all polygons be triangulated?

Triangulations. Theorem: Any polygon can be decomposed into triangles. Proof: The key idea of the proof goes by the method of mathematical induction. Let n = the number vertices = the number of sides in the polygon.

How many ways can you triangulate a polygon?

42 possible
The 42 possible triangulations for a convex heptagon (7-sided convex polygon).

How do you triangulate a polygon with holes?

Let a polygon P with h holes have n vertices total, counting vertices on the holes as well as on the outer boundary. Then a triangulation of P has t = n + 2h – 2 triangles, and a quadrilateralization has q = n/2 + h — 1 quadrilaterals. ort = n+2h-2. Since q = t/2, q=n/2 + h-l.

Why do we need to triangulate a polygon?

Because of this, it’s often the case that complex shapes are made up of simpler shapes, such as triangles, circles, and rectangles, for which it’s easy to determine whether a point lies in the complex shape or to determine that shape’s bounding box.

How do you triangulate a convex polygon?

A triangulation of a convex polygon is formed by drawing diagonals between non-adjacent vertices (corners), provided you never intersect another diagonal (except at a vertex), until all possible choices of diagonals have been used (see Figure 1).

What is a triangulation of a convex polygon?

What is environmental triangulation?

Environmental Triangulation This type of triangulation involves the use of different locations, settings and other key factors related to the environment in which the study took place, such as time of the day, day of the week or season of the year.