# Learner's guide

## Welcome to Pixar in a Box!

The goal of

*Pixar in a Box*is to show you how the concepts that you learn in school are the same concepts that we use to tackle creative challenges at Pixar.We’ve taken Pixar’s filmmaking process -- our

**“production pipeline”**-- and broken it down into a series of topics, such as**Animation**,**Character Modeling**,**Patterns**, and**Effects**. These topics represent the fundamental steps we use to make our movies, and you can explore them in any order you want! Each topic in*Pixar in a Box*contains two lessons. The**first lesson**contains videos and fun interactives that will get you solving problems and creating things with tools, while showing you some of the connections to math, science, arts, and humanities.The

**second lesson**gives you a deeper dive into the concepts in the first lesson, and also contains interactives and exercises. Our lessons touch on concepts ranging from grade four through high school and beyond -- but we think they’re a ton of fun for people of all ages!## Topics

**Explore how smooth surfaces are created for Pixar’s characters using the mathematics of subdivision and weighted averages.**

Once a character’s design has been determined through a series of drawings (and, for main characters, clay sculptures), the computer models that actually appear in the film are created in a process called

**character modeling**. This is done by placing and moving digital points in a computer, then using a mathematical principle called**subdivision**to smooth the models out into the organic shapes you’re used to seeing in Pixar movies.**Explore how realistic blades of grass are modeled using parabolic arcs.**

Everything you see in a computer-animated film needs to be created digitally: the characters, the sets and props, and the virtual worlds in which they exist. Pixar creates these worlds in a stage of the pipeline called

**environment modeling**. To produce a believable amount of variety in natural shapes, the technical artists at Pixar closely observe the repetition that they see in nature and then use computer programming to create that same kind of repetition, at magnificent scales.In this lesson, you’ll learn how Pixar uses

**parabolic arcs**to generate grass and other natural phenomena in virtual natural landscapes.**Explore how characters are brought to life with geometric transformations.**

**Rigging**is the process that Pixar artists use to give their character models (and some props) the ability to move. Technical artists called “riggers”

**articulate**the models by adding special controls called

**deformers**, which let them change a model’s shape or pose, frame by frame, to create movement.

In this lesson, you’ll learn how Pixar uses computer programming together with

**geometric transformations**to create these controls.**Explore how organic looking patterns are created using randomness.**

All Pixar models start out as digital 3-dimensional objects, without any surface characteristics. The
process of creating the surface appearance, including colors and textures, is called

**shading**, and in that process they use a variety of patterns to make the objects seem real.In this lesson, you’ll learn how Pixar uses

**randomized variation**to create patterns that make its characters, sets, and props appear real and believable.**Explore how swarms of robots were created for**

*WALL-E*using combinatorics.Modeling a character in the computer point by point takes a lot of time and energy. For crowds of background characters – whether fish, monsters, or robots -- the artists at Pixar design a selection of physical parts that can be recombined in many different ways, so they can quickly create a variety of characters in the necessary quantities.

In this lesson, you’ll learn how Pixar populates its films with crowds of characters using a

**modular**approach and the mathematical principle of**combinatorics**.**Explore how the physics of light and lenses are used to create virtual cameras.**

Just as live-action movies are made using cameras, Pixar uses virtual cameras within the computer environment to “film” their movies. These virtual cameras, with

**optics**that behave like real lenses, are placed in a shot by**cinematographers**who make artistic choices based on what they want each shot to convey.In this lesson, you’ll learn what drives the camera choices made by Pixar’s cinematographers, and how they apply the physics of

**light**and**lenses**to recreate the ways that actual cameras capture real life.**Explore how virtual sets are constructed using geometric transformations.**

Live-action filmmakers make sure that every object in a room or environment is in the right place before they film a scene, and Pixar filmmakers do too, with

**virtual**sets, props, and characters. Pixar’s set-dressing department takes models built earlier in the production pipeline and manipulates the object’s size, orientation, and position in space using**geometric transformations**. Then, the camera and staging departments use virtual cameras to**stage**scenes, making decisions about camera angles and movements just like real cinematographers do.In this lesson, you’ll learn how Pixar uses

**coordinate geometry**and**geometric transformations**to design sets and stage shots, taking into consideration the key elements of**location**,**composition**,**camera movement**, and**character performance**.**Explore how animators bring characters to life with the help of animation curves.**

Animation is acting. It is the process of bringing a character to life by positioning a model in a series of subtly differing poses, and then playing those poses back in a sequence. While traditional animators do this by drawing every frame by hand, computer animators use digital models and the mathematical principles of

**splines**and**animation curves**. The same fundamentals of animation apply to both forms.In this lesson, you will learn how Pixar animators use the mathematics of

**interpolation**to help support the animation process, helping animators create motion and tell stories.**Explore how water, smoke and fire effects are created using millions of tiny particles.**

Explosions, smoke, fire, and water are special effects that require a lot of engineering to create. These effects are too complicated to model and animate using the same methods as characters or sets. So Pixar uses the laws of

**physics**as well as**computer programming**to produce them.In this lesson, you’ll learn just how Pixar uses physics to create many of the special effects seen in their films.

**Explore how pixels are painted by solving systems of linear equations.**

**Rendering**is the process of compiling all of the math, engineering, and artistry of every department on the film into a final image. The rendering group takes each department’s contribution – the textures, camera choices, animation, lighting, etc. – and calculates the color of every pixel in every frame of every shot in the film.

In this lesson, you’ll learn how technical artists at Pixar use

**ray-tracing**and other mathematical algorithms to calculate the color of pixels and to generate the final frames that appear on screen.Looking for more information? Check out our Educator's Guide next, or return to the Pixar in a Box homepage.