Top 5 Ways How Animators Use Math in Their Career

Top 5 Ways How Animators Use Math in Their Career

June 21, 2023


October 09, 2023

Table of Contents

Animation is a visual process that simulates motion; it is all about timing and proportions, which have strong mathematical connections. While the main emphasis in animation production is typically on creativity. Everything uses math, and animation is no exception. Math and art work together to create a masterpiece of animation, much like our brain, which is divided into the practical left and creative right halves. Math plays a big part in calculating how things move and behave in animation movies. Due to their work with moving and changing objects, animators frequently use a number of mathematical techniques, including geometry, linear algebra, and others.

This blog demonstrates how does animation work, how do animators use math in their careers, various math prerequisites for persons in animation, the math animators utilize to construct an animation, and providing an answer to the question “how artists use math?

5 Math Basics in Animation

An animator needs to be knowledgeable in a variety of applied math fields. When working with moving and changing objects, it enables the animator to solve geometrical issues and identify unknowns from a straightforward set of equations.

To create animated movies, animators need a rudimentary understanding of mathematics. The answer to the question “how do video game designers use math” is more complicated, though, when you take into account the sophisticated concepts of geometry, trigonometry, linear algebra, and calculus that are used behind the scenes.

1. Geometry and its role in shaping characters and backgrounds

How do animators use geometry? Geometry examines the connections and characteristics of geometric objects including lines, surfaces, and solids. Examples of this animated geometry can be seen in the various character, weapon, and background sizes. Animators can create balanced and clearly defined drawings and representations by using geometry.

For example, Disney's "The Lion King" used geometric shapes to create the characters and their movements. They use circles, squares, and triangles to create the basic shapes of the characters and then manipulate them to create the final design.
Lion King-Geometrical-Shapes

2. Trigonometry for character movement and rotations

An animated movie’s characters can move in a variety of ways thanks to trigonometry and the understanding of it that animators possess. For example, animators can turn animation characters 180 degrees or 360 degrees by using mathematical concepts. To generate an illusion of motion and give them movement, animators use a combination of geometric and trigonometric computations.

For example, Pixar's "The Incredibles" used trigonometry to create the movement of the characters' hair. They use sine and cosine functions to create the movement of the character's limbs. 

3. Linear algebra for special effects

To create fascinating and entertaining to watch realistic animation and animation special effects, animators need linear algebra and a working grasp of algebraic equations and their solutions.

This technique is used to create special effects. For example, Industrial Light & Magic used linear algebra to create the special effects in "Star Wars: The Force Awakens". They use matrices to create the movement of the camera or the lighting effects in the scene.

4. Calculus for enhancing scenes

Calculus in movies enhances animation production, and animators can gain a considerable edge by being familiar with the calculus concepts behind the software tools they employ to enhance a scene.

Calculus is used to enhance scenes. For example, Pixar used calculus to create the lighting effects in "Finding Nemo". Use mathematical formulas to create the lighting effects and shadows in the scene. 

5. Physics & Anatomy in Animation

Physics and arithmetic are closely related, and physics is frequently employed in real life animation to develop lifelike figures with human-like emotions, gestures, and behavioral patterns. In order to create a realistic animation, an animator has to understand physics topics such as Newton’s laws, gravity, and energy and motion. Thus, physics is essential to an animator in relation to mathematical calculations.

Like physics, anatomy requires a functional understanding of math when it comes to character concept art. To display the movement patterns of their characters, animators must perform simple mathematical computations in addition to adhering to the rules of nature.
For example, DreamWorks Animation used physics and anatomy to create the movement of the dragon in "How to Train Your Dragon".

Math in 2D and Stop-Motion Animation

One of the earliest forms of animation is called cel-animation. In this form, objects are sketched on paper made of celluloid. Every 3D frame in the animation sequence must be drawn by the animator. It operates similarly to a flip book but on a much larger size.

Traditional animation is often a 2D image. The best examples of this come from earlier animated films like Aladdin, The Lion King, and others. Many traditional animators still sketch their characters on paper using a pen and refer to geometric shapes. Contrary to 3D animation, 2D animators also utilize squares and circles to characterize a figure in addition to triangles.


To keep characters consistent and make them move on the screen, math animations is used. Animators employ mathematical techniques for stop motion including translation, rotation, and enlargement.

Stop-motion animators hand-create each tiny prop and figure. To operate at the same scale and prevent measurement errors, the animators employ arithmetic to comprehend ratios. An example of illustration of stop-motion using clay models is the animated series, Wallace and Gromit.
Wallace and Gromit

Math in Computer Graphics

Algorithms and data structure are essential for computer graphics to accurately represent physical reality, including light, fluids, and collisions. Then, how do CGI tools are being used? To make objects move convincingly, animators employ math to understand mass, density, and friction. Calculating views, aspect ratios, character movement, artificial lighting, and color balancing all need math in animation.

If you want to understand it, suppose a string puppet with 700 strings, then suppose 700 controllers operating simultaneously to create an animation. This is the challenge faced by mathematical artists while creating animation features.


1. Rendering

Consider a camera that is pointed at a 3D frame and “renders” what it sees into a 2D image. One of the ways lighting artists use math in animation is to calculate all of the light that is coming into the camera lens from the scene.

Isn’t it fascinating?

Animators use statistical methods for the rendering equation since the universe has infinite points and unlimited recursion. Since light is not a scalar number and exhibits polarization, the artist must employ mathematics to determine how to represent light.

Optimizations in engineering and computer science are also needed for the task. All of which demonstrate how CGI artists apply sophisticated mathematics. Although CGI tools handle the bulk of the work, animators still need to use special style tools to customize characters, add realistic effects, and develop complex engineering projects.


2. Simulation

Due to the need for extreme accuracy when depicting an animation frame, major animation studios like Pixar make enormous investments in math. For example, each fabric thread of the clothes acts as a spring in a dampened spring system, which is how the clothing textiles react as the animated actors move. Additionally, the springs in their hair act as a system to collect kinetic energy from head motions and wind-related forces.


3. Scene Representation

Scene Representation frequently use linear algebra. Whether modelers are changing the vertices on a character’s face mesh or a set dresser is rearranging props, transformations are a constant in animation, and linear algebra is essential for the purpose.

Rotations, transformations, and scaling are straightforward, but inverse kinematics difficulties are a part of linear algebra. For instance, animation and numerical solvers for simulation include finding numerical answers to complicated equation systems, spring mechanics, or maintaining volume when characters move.

4. Shading     

Shaders work in tandem with renderers to depict how each patch of geometry in the scene responds to incoming light in order to simulate reality. Some animators employ mathematical tools like machine learning, linear regression, and other parametric models to approximate various surfaces. Depending on how it reflects light, a flat surface can be distinguished from a rough one visibly.

How is math used in graphic design”? Computer graphics make many aspects of math that aren’t seen elsewhere possible. With enough data, machine learning techniques, for example, can do regression on the light field equation and “guess” what the light integral will ultimately be without using route tracing.


5. Signal Processing

From an aesthetic perspective, Signal Processing is essential because compositions with a scale of three-dimensional frequencies are typically more visually appealing. Set designers insert Large blocks into a scene, who then gradually improve the details at higher frequencies. Animators mix various spatial frequencies to create effects like hair and shrubs.


In the world of animation, math holds the key to unlocking new skills and achieving creative breakthroughs. As we have explored, math plays a vital role in various aspects of animation, from management and administrative roles to the artistic execution of projects.

By emphasizing the significance of math in the animation industry, animators can harness its power to take their craft to new heights.

With a solid expertise on math of Ideas Animators to understand proportions, scale, timing, physics, and more. It enables them to create realistic movements, simulate dynamic effects, and design captivating visuals. We have the skills and knowledge to meet your needs. Our animators rely on their expertise in mathematical concepts to create animations that are not only visually stunning but also grounded in reality. Contact us today to guide you toward innovative and awe-inspiring animation experiences. 

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