Halfspaces are a common concept in computational geometry and machine learning that are used to divide a space into two regions. A halfspace is defined by a hyperplane, which is essentially a flat plane that cuts a space in half. One side of the hyperplane is considered the "positive" side and the other is the "negative" side. In machine learning, halfspaces are often used in binary classification problems, where the goal is to divide a set of data points into two classes. By constructing a hyperplane that separates the two classes, algorithms can make predictions about the class of new data points based on which side of the hyperplane they fall on. In computational geometry, halfspaces are used in a variety of applications, such as convex hull algorithms, intersection testing, and collision detection. By using halfspaces to partition a space, researchers can efficiently perform geometric operations and computations. Overall, halfspaces are a versatile and fundamental concept in both computational geometry and machine learning, playing a key role in a variety of algorithms and applications.