The Mathematics Behind 2D and 3D Animation

Have you ever wondered how animations are done? How did the artists make the drawings move? How did they make it look real?

This week, SAM-UP celebrates its 32nd anniversary with the theme “Mathematics in 2D and 3D animation”. In line with SAM-UP’s objective of promoting the relevance of Applied Mathematics to the Philippine Society, the organization wanted to make it more interactive by putting fun into learning and at the same time enlightening young minds by understanding animation through mathematics.

Animation is a series of still images that are connected together as part of a timed sequence. One can make animation by making bunch of drawings on a paper. These drawings should be a little different from each other so as to make the images look like moving. By compiling these drawings and by arranging it in a sequence, one can observe the simple process of animation. But there is more to animation that just the drawing. The dimensions, the lighting and other variables are considered before an animation become as good as what we are watching these days.

According to computer scientist Tony DeRose of Pixar Animation, “There is indeed a lot of mathematics behind the scenes.” All amazing Disney movies such as Finding Nemo, Mr. Incredible, Wall-E, Frozen, and many more were made possible because of the power of mathematical innovation. Each of these animated films were constructed because of trigonometry which helps on rotating and moving the characters, algebra that creates the special effects of making the images shine and sparkle, and integral calculus that helps on lighting the scenes in order to make it brighter and brilliant to watch. Animation in 3D graphics can be done by transforming the 2D coordinate system to another coordinate system.

Moreover, according to Harold Serrano, a Game Engine Developer, “Basically, whenever you move a character on a screen, Linear Algebra concepts are at play. Vectors are constantly being manipulated by Matrices; essentially Transforming, the coordinate system of the vector.”

Mathematics is really a powerful tool in making everything smooth in animation. With the help of these vectors and linear transformation, animations that were boring will now be full of lives.

If we are to imagine the development that has occurred in animation, one can expressively see the progress of animation with the help of computers and mathematics. Everything in it, starting from the detail of every images, smoothness of curves, brightness of scenes, to the cuteness of characters, are made possible because of incorporating mathematics.

Have you ever observed a year without an animation or cartoons that are showing in different cinemas? No. It is because animation has become an important part of people’s lives. And it is one of the only genre that are suited for kids and adults.

SAM-UP'S EXHIBIT WITH MS. SAM-UP, MS. ALECIA CANGA

Society of Applied Mathematics of UPLB showcased its exhibit through the effort of making 2D and 3D characters and displaying Disney characters that are familiar so as to catch people’s attentions. So next time we watch animated films, we will remember that these great stories were made amazing because of mathematics.

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