Geometry

The math behind culling and clipping and how it's related to the camera and what it sees. - **Culling** is a process where geometry that’s not visible from the camera is discarded to save processing time. - **Clipping** is a process that removes parts of primitives that are outside the view volume (clipping against the six faces of the view volume).

An affine space is a generalization of the notion of a vector space, but without the requirement of a fixed origin or a notion of "zero".

A vector space is a set whose elements are called "vectors" (denoted as $\v{v}$ or $\mathbf{v}$), which have two operations defined on them: addition of vectors and multiplication of a scalar by a vector. This article covers some examples of vector spaces, bases of vector spaces, and linear maps.

In an affine space, any point can be represented by the sum of an origin point plus a set of scaled vectors. This article covers defining all the points in a triangle within an affine space.

Different algorithms to test geometric properties, such as finding the intersection of two lines.

A **normal vector** to a curve at a particular point is a vector perpendicular to the *tangent* vector of the curve at that point (also called a *gradient*).

In projective geometry, unlike Euclidean geometry, two parallel lines meet at a point. Desargues introduced the concept of a line at infinity where a point at infinity can be defined. This article covers the need for a point at infinity in projective space, the line at infinity, and the projective plane.

Euler angles are a way to describe the orientation of a rigid body with three values. These values represent three angles: - *Yaw* - Rotation around the vertical axis - *Pitch* - Rotation around the side-to-side axis - *Roll* - Rotation around the front-to-back axis

A linear transformation can be represented with a matrix that transforms vectors from one space to another. Transformation matrices allow arbitrary transformations to be displayed in the same format. Also, matrices can be multiplied to enable [composition](../combining-transformations). This article covers how to think and reason about these matrices and the way we can represent them (row vectors vs. column vectors).