Table of Contents

## What is Qhull package?

Qhull implements the Quickhull algorithm for computing the convex hull. It handles roundoff errors from floating point arithmetic. It computes volumes, surface areas, and approximations to the convex hull.

## What is Delaunay condition?

The Delaunay condition states that a triangle net is a Delaunay triangulation if all the circumcircles of all the triangles in the net are empty. This is the original definition for two-dimensional spaces. It is possible to use it in three-dimensional spaces by using a circumscribed sphere in place of the circumcircle.

**What is Delaunay triangulation method?**

The Delaunay triangulation is a triangulation which is equivalent to the nerve of the cells in a Voronoi diagram, i.e., that triangulation of the convex hull of the points in the diagram in which every circumcircle of a triangle is an empty circle (Okabe et al. 1992, p. 94).

### What is Qhull?

Qhull is a general dimension code for computing convex hulls, Delaunay triangulations, halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay triangulations, and furthest-site Voronoi diagrams. These structures have applications in science, engineering, statistics, and mathematics.

### What Scipy spatial?

scipy. spatial can compute triangulations, Voronoi diagrams, and convex hulls of a set of points, by leveraging the Qhull library. Moreover, it contains KDTree implementations for nearest-neighbor point queries, and utilities for distance computations in various metrics.

**How do you solve a convex hull?**

Example of Convex Hull

- Problem: Find the convex hull for a given set of points using divide and conquer approach.
- Solution:
- Step 1: According to the algorithm, find left most and rightmost points from the set P and label them as A and B.
- Step 2 : FindHull(S1 ,A, B)
- Step 3 : FindHull(X1, A, C)
- Step 4 : FindHull(X2, C, B)

#### How do I install Scipy spatial?

The first step is to go to the official website of python.

- Then we search for the latest release of the version of python.
- Then scroll down to Files and click on Windows x86-64 executable installer for 64-bit or Windows x86 executable installer for 32-bit.
- Then go to downloads and run the installer.
- pip install scipy.