computational geometry - OpenGenus IQ: Computing Expertise & Legacy

Inside Outside Test [2 algorithms: Even-Odd and Winding Number]

In Computer Graphics, Inside Outside is performed to test whether a given point lies inside of a closed polygon or not. Mainly, there are two methods to determine a point is interior/exterior to polygon: Even-Odd / Odd-Even Rule or Odd Parity Rule and Winding Number Method.

Algorithms

Number of rectangles from a given set of points

We have discussed how to find the number of rectangles (parallel to the axes) possible from a given set of coordinate points.

Algorithms

Xiaolin Wu's Line Drawing Algorithm

Xiaolin Wu's Line Drawing Algorithm is a recognized Line Drawing Algorithm in Computer Graphics which is used to produce Anti-aliased lines. In this article, we have explored this in depth.

Algorithms

Cohen Sutherland Line Clipping Algorithm

Cohen Sutherland Algorithm is a linear time complexity line clipping algorithm that cuts lines to portions which are within a rectangular area. It eliminates the lines from a given set of lines which belongs outside the area of interest and clip those lines which are partially inside

convex hull

Kirkpatrick-Seidel Algorithm (Ultimate Planar Convex Hull Algorithm)

Algorithm Complexity Applications Reading time: 15 minutes | Coding time: 9 minutes The Kirkpatrick–Seidel algorithm, called by its authors "the ultimate planar convex hull algorithm", is an algorithm for computing the

convex hull

Chan's Algorithm to find Convex Hull

In computational geometry, Chan's algorithm, named after Timothy M. Chan, is an optimal output-sensitive algorithm to compute the convex hull of a set P of n points, in 2- or 3-dimensional space. The algorithm takes O(n log h) time, where h is the number of vertices of the output (the convex hull).

convex hull

Graham Scan Algorithm to find Convex Hull

Graham's Scan Algorithm is an efficient algorithm for finding the convex hull of a finite set of points in the plane with time complexity O(N log N). The algorithm finds all vertices of the convex hull ordered along its boundary. It uses a stack to detect and remove concavities in the boundary.

convex hull

Gift Wrap Algorithm (Jarvis March Algorithm) to find Convex Hull

Gift Wrap Algorithm ( Jarvis March Algorithm ) to find the convex hull of any given set of points. We start from the leftmost point (or point with minimum x coordinate value) and we keep wrapping points in a counterclockwise direction. Find pseudocode, implementations, complexity and questions

convex hull

Divide and Conquer algorithm to find Convex Hull

Divide and Conquer algorithm to find Convex Hull. The key idea is that is we have two convex hull then, they can be merged in linear time to get a convex hull of a larger set of points. It requires to find upper and lower tangent to the right and left convex hulls C1 and C2

convex hull

Quick Hull Algorithm to find Convex Hull

Quickhull is a method of computing the convex hull of a finite set of points in the plane. It uses a divide and conquer approach. It was published by C. Barber and D. Dobkin in 1995. average case complexity is considered to be Θ(n * log(n))