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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Description</title>
<style>
body {
background-color: #131236;
color: #fff;
font-family: Arial, sans-serif;
padding: 20px;
margin: 0;
}
.container {
max-width: 800px;
margin: 0 auto;
}
.section {
margin-bottom: 20px;
}
.section h2 {
font-size: 1.5rem;
margin-top: 0;
}
.section p {
line-height: 1.6;
}
</style>
</head>
<body>
<div class="container">
<div class="section">
<h2>Convex Hull Algorithms</h2>
<p>Convex hull algorithms are computational methods used to determine the convex hull of a set of points in a multi-dimensional space. The convex hull of a set of points is the smallest convex polygon or polyhedron that encloses all the points in the set. In simpler terms, it is the smallest convex shape that contains all the given points.</p>
</div>
<div class="section">
<h2>How Convex Hull Algorithms Work</h2>
<p><strong>Input:</strong> The input to a convex hull algorithm is typically a set of points in a multi-dimensional space. These points can be represented as coordinates (x, y) in a 2D plane or as (x, y, z) in a 3D space, and so on for higher dimensions.</p>
<p><strong>Compute Convex Hull:</strong> The algorithm processes the input points to determine the convex hull. There are various algorithms to accomplish this, with some of the popular ones being Graham's scan, Jarvis march (gift wrapping), Quickhull, and Divide and Conquer.</p>
<p><strong>Identify Convex Boundary:</strong> The algorithm identifies the vertices or points that define the convex hull. These vertices are the points that lie on the boundary of the convex shape enclosing the input points.</p>
<p><strong>Construct Convex Polygon/Polyhedron:</strong> Once the vertices of the convex hull are identified, the algorithm constructs the convex polygon (for 2D) or polyhedron (for 3D or higher dimensions) using these vertices. This convex shape will enclose all the points in the input set.</p>
<p><strong>Output:</strong> The output of the convex hull algorithm is typically a list of vertices or points that define the convex hull. This output can then be used for further processing or analysis depending on the application.</p>
</div>
<div class="section">
<h2>Applications</h2>
<p>Convex hull algorithms are widely used in various fields such as computational geometry, computer graphics, geographic information systems (GIS), image processing, and robotics. They are essential in tasks like collision detection, pattern recognition, path planning, and spatial analysis. The choice of algorithm depends on factors such as the dimensionality of the space, the number of input points, and the desired computational efficiency.</p>
</div>
</div>
</body>
</html>