# How can we convert a concave polygon into a convex polygon?

## How can we convert a concave polygon into a convex polygon?

Single concave polygon can be decomposed into convex polygons by connecting concave points with their visible vertex. Second, decomposition algorithm for multi-connected concave polygon (any map with obstacles) is designed.

## What is the difference between concave polygon and convex polygon?

What is the difference between concave and convex polygon? A convex polygon has all its interior angles less than 180 degrees whereas a concave polygon has at least one interior angle more than 180 degrees.

What is called convex polygon?

In geometry, a convex polygon is a polygon that is the boundary of a convex set. In a convex polygon, all interior angles are less than or equal to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees.

Which of the following algorithms can be used to clip both convex and concave polygons?

Weiler-Atherton polygon clipping algorithm This algorithm helps us to clip a filled area. The filled area may be a convex polygon or concave polygon. This algorithm was introduced to identify the visible surfaces.

### What is a concave polygon in geometry?

A concave polygon is a polygon that is not convex. An example of a non-simple (self-intersecting) polygon is a star polygon. A concave polygon must have at least four sides.

### Which algorithm works well with concave polygon for clipping?

Weiler Atherton Polygon Clipping Algorithm
Weiler Atherton Polygon Clipping Algorithm is an algorithm made to allow clipping of even concave algorithms to be possible. Unlike Sutherland – Hodgman polygon clipping algorithm, this algorithm is able to clip concave polygons without leaving any residue behind.

When a concave polygon is clipped with the Sutherland Hodgman algorithm?

First of all entire polygon is clipped against one edge, then resulting polygon is considered, then the polygon is considered against the second edge, so on for all four edges. If the first vertex is an outside the window, the second vertex is inside the window. Then second vertex is added to the output list.

How can you tell whether a polygon is a convex?

– 3 ≤ n ≤ 1000 – 1 ≤ q ≤ 1000 – 0 ≤ x i, y i, X i, Y i ≤ 1000

#### What is the difference between a concave and a convex?

If something caves-in,that means it falls inward. Concave has the word cave in it.

• Remember,a cave-in goes inward,so that means a concave shape must curve in.
• Convex has ex in it. Ex is the beginning of the word exit. When you exit,what do you do?
• Associate the ex in convex with exiting. This can help you remember that a convex shape curves out.
• #### How to use concave vs. convex correctly?

– f is second differentiable everywhere and f ″ ( x) ≥ 0 ∀ x ∈ R – f is differentiable everywhere and f ′ ( x) is a monotonically increasing function. – f is continuous, piece-wise convex, and either has no extreme points, or one local extreme point which is the global minimizer.

What polygon is always concave?

Polygons can be classified as either convex or concave. In a convex polygon, each interior angle measures less than 180 degrees. A triangle is always convex, and regular polygons are always convex.