Geometry

The math behind culling and clipping and how it’s related with the camera and with 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 an scalar by a vector.

This article covers some examples of vector spaces, basis of vectores spaces and linear maps.

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

Different algorithms to test geometric properties like 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 finity where a point at infinity can be defined. This article covers the need of 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 3 values, these values represent 3 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 which 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 . This article covers how to think and reason about these matrices and the way we can represent them (row vectors vs column vectors).