Geometric Algorithms – An Overview and its Implementation

Geometric algorithms are a class of algorithms that are used to solve problems related to geometry, such as finding the intersection of two lines or determining the convex hull of a set of points. Geometric algorithms are used in a variety of fields, including computer graphics, computer vision, and robotics.

One of the most basic geometric algorithms is the point-in-polygon algorithm. This algorithm is used to determine whether a point is inside or outside a polygon. The algorithm works by drawing a line from the point to a point outside the polygon, and then counting the number of times the line intersects the edges of the polygon. If the number of intersections is odd, the point is inside the polygon; if the number of intersections is even, the point is outside the polygon.

Another commonly used geometric algorithm is the line intersection algorithm. This algorithm is used to find the intersection point of two lines. The algorithm works by solving a system of linear equations to find the point where the two lines intersect.

The convex hull algorithm is another important geometric algorithm. The convex hull of a set of points is the smallest convex polygon that contains all the points in the set. The convex hull algorithm works by first sorting the points in order of increasing polar angle around a fixed point. The algorithm then proceeds to add each point to the convex hull in turn, checking whether the new point makes a left or right turn with respect to the previous two points on the hull.

The closest pair algorithm is another important geometric algorithm. This algorithm is used to find the two closest points in a set of points. The closest pair algorithm works by first sorting the points in order of increasing x-coordinate. The algorithm then recursively divides the set of points into two halves and finds the closest pair in each half. Finally, the algorithm combines the two solutions to find the closest pair overall.

In conclusion, geometric algorithms are an important class of algorithms that are used to solve problems related to geometry. By understanding how these algorithms work and how they are implemented, we can develop efficient and effective solutions to a wide range of problems in computer graphics, computer vision, and robotics.