3d

Quaternions are an alternate way to describe orientation or rotations in 3D space using an ordered set of four numbers. They have the ability to uniquely describe any 3D rotation about an arbitrary axis and do not suffer from a problem using Euler angles called gimbal lock.

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).

One matrix transformation in the 3D to 2D transformation pipeline is the viewport transform, where objects are transformed from normalized device coordinates (NDC) to screen coordinates (SC). In short, it's the transformation of numbers in the range [-1, 1] to numbers corresponding to pixels on the screen, which is a linear mapping computed with linear interpolation. In this article, I cover the math behind the generation of the viewport transformation matrix.

In computer graphics, 3D objects created in an abstract 3D world will eventually need to be displayed on a screen. To view these objects on a 2D plane like a screen, objects will need to be projected from the 3D space to the 2D plane with a transformation matrix. In this article, I cover two types of transformations: orthographic projection and perspective projection, and analyze the math behind the transformation matrices.

One matrix transformation in the 3D to 2D transformation pipeline is the view transform, where objects are transformed from world space to view space using a transformation matrix. In this article, I cover the math behind the generation of this transformation matrix.

We build different types of transformation matrices to translate objects along cardinal axes and arbitrary axes in 2D and 3D with matrix multiplication!

Shearing is a transformation that skews the coordinate space. The idea is to add a multiple of one coordinate to another.

The basics of rotation in 2D and 3D for computer graphics, with a focus on 3D rotation about cardinal axes and 3D rotation with quaternions. For quaternions, please also look at [https://eater.net/quaternions](https://eater.net/quaternions) for amazing animations!

We build different types of transformation matrices to scale objects along cardinal axes and arbitrary axes in 2D and 3D with matrix multiplication!

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).