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.

Taking multiple matrices, each encoding a single transformation, and combining them is how we transform vectors between different spaces. This article covers creating a transformation matrix that combines a rotation followed by a translation, a translation followed by a rotation, and creating transformation matrices to transform between different coordinate systems.

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.

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).

The position and orientation of an object in real life can be described with direction and magnitude, e.g., the TV is 3 meters in front of me. While that description is good for me, it might be that for someone else in a room, the TV is 5 meters to the right of that person. Information about objects is given in the context of a reference frame. Usually, in Computer Graphics, objects need to be expressed with respect to the camera frame. This article covers why we need to have multiple reference frames and the math needed to express objects in a different reference frame.