Homogeneous Coordinates: The 4D Hack for 3D Animations

Did you know all 3D animations actually come from 4D math? In this video, we reveal how animators use homogeneous coordinates to simplify the math behind translations, rotations, and camera movements—using only matrix multiplication. You’ll learn how 4D shear transformations make 3D translations possible, why adding one extra coordinate changes everything, and how this trick makes the animation pipeline much more efficient. Math The World is dedicated to bringing real world math problems into the classroom and answering the age old question “when will I ever use this?” We use unique topics for algebra, trigonometry, calculus, and much more and go beyond context problems and use a technique called mathematical modeling to find solutions to real world questions and real world problems. These videos are great for students who plan to enter technical fields that require real world problem solving, and can be a great resource for teachers looking for ways to bring real world contexts into their classroom. Instagram:   / maththeworld   Twitter/X:   / math_the_world   Facebook:   / maththeworldproject   Email: MathTheWorld@byu.edu Created by Doug Corey Script: Doug Corey and Jennifer Canizales Audio: Doug Corey Animation: Jennifer Canizales Music: Coma Media © 2025 BYU