Tony DeRose, senior scientist at Pixar Animation Studios, spoke to a packed Hamilton College Chapel about the relationship between computer-animated movies and mathematics on April 3. DeRose explained many of the mathematical processes behind computer animation and the role of math in this field, and conveyed his satisfaction at being able to use movies to "deliver [math] in a way that everyone on the planet can enjoy."
DeRose, who holds a doctorate in computer science from the University of California, Berkeley, and won a 2006 Academy Award for his animation work, began his talk discussing the production pipeline of Pixar films. The films begin as a roughly drawn storyboard, which is filmed and mixed with a scratch voice track to generate a complete version of the film before any animation is actually started; this stage lays out the broad story of the film, so that "if the story's working well, you can forget you're looking at little sketches."
Only after this process is complete does the production team move on to character design, first working from sketches and sculpts using traditional artistic methods, recording dialogue and performances of actors as a visual reference, and finally modeling the three-dimensional character. Much of the modeling is done using software packages written in-house, with more than 10 million lines of code. To make their creations easier to animate, animators "rig" the characters, or define the ways in which parts of the body can move relative to each other in a fashion similar to putting strings on a marionette. The process is exhaustive; in the case of the face, Pixar's models typically have 300 points of articulation, whereas a real-life human face can move in only 30 ways. These movements are controlled by equations for curves located in a spreadsheet, so that animators manipulate the curves to move characters as they desire. Although the process is inherently grounded in math, it is highly intuitive; DeRose likened animators to actors who "act through their characters."
In fact, animators at Pixar have specifically rejected putting the constraints of real physics on their work, so that characters may do the impossible (such as changing their volume when they move) to create a better visual effect. DeRose pointed out that in the movies, "physics is really just a starting point" because animators seek a greater sense of "realism" or "visual quality" (ironically, considering physics is a more accurate representation of reality; however, it may not be perceived as such).
The limitations of physics are especially apparent in the case of lighting animated scenes. DeRose demonstrated the advanced differential equations needed to model light sources, since light in reality is expected to scatter off reflective surfaces, greatly complicating calculations. To deal with this problem, DeRose described how computer programs break lines in a model into numerous tiny segments, for each of which a new equation can be created to describe reflection. The result is a system of 10 million equations that is solved using a computer to generate the realistic light effects seen in animated films.
Another mathematical technique employed by Pixar animators is the use of subdivision surfaces. This technique has only recently been developed, the mathematics underlying it being 15-years-old. Subdivision surfaces work similarly to the basic principle that a polygon with enough sides resembles a circle; by subdividing lines on a surface to an increasingly greater degree, animators can create realistic-looking curves that avoid the blocky polygonal look of earlier graphics and videogames. DeRose showed a still from the original Toy Story, in which characters were essentially just collections of shapes with sharp seems; in recent films like The Incredibles, use of subdivision surfaces allows for smoother looking characters generated with less computing power.
A third technique that DeRose described as applying math to animation was the use of special "Barycentric" coordinates to articulate characters. By defining the points on a character model in relation to a polygon, animators are able to greatly simplify their job, since they can move a simple shape with a few hundred points and have a complex shape (such as character models, with 8,000 or more points) follow the simple shapes' movement, similar to a skeletal structure in humans (but on the exterior of the model). This technique is so new that it has not yet been used in a Pixar film, although upcoming productions are expected to employ it to make smoother animations.
DeRose closed by answering audience questions about the specifications of Pixar's animating process. Producing each frame of a Pixar movie typically takes six hours (there are 24 frames in each second of film), yet each frame has a lower resolution than a typical digital camera, since it is the clarity and not the quantity of pixels that matters for a good image. He also clarified the degree to which animation involves "practice and talent"; only by developing a thorough understanding of how changing equations changes digital visuals can animators generate the wonders that they do.
DeRose's talk was part of the James S. Plant Distinguished Scientist Lecture series.
-- by Kye Lippold '10
DeRose, who holds a doctorate in computer science from the University of California, Berkeley, and won a 2006 Academy Award for his animation work, began his talk discussing the production pipeline of Pixar films. The films begin as a roughly drawn storyboard, which is filmed and mixed with a scratch voice track to generate a complete version of the film before any animation is actually started; this stage lays out the broad story of the film, so that "if the story's working well, you can forget you're looking at little sketches."
Only after this process is complete does the production team move on to character design, first working from sketches and sculpts using traditional artistic methods, recording dialogue and performances of actors as a visual reference, and finally modeling the three-dimensional character. Much of the modeling is done using software packages written in-house, with more than 10 million lines of code. To make their creations easier to animate, animators "rig" the characters, or define the ways in which parts of the body can move relative to each other in a fashion similar to putting strings on a marionette. The process is exhaustive; in the case of the face, Pixar's models typically have 300 points of articulation, whereas a real-life human face can move in only 30 ways. These movements are controlled by equations for curves located in a spreadsheet, so that animators manipulate the curves to move characters as they desire. Although the process is inherently grounded in math, it is highly intuitive; DeRose likened animators to actors who "act through their characters."
In fact, animators at Pixar have specifically rejected putting the constraints of real physics on their work, so that characters may do the impossible (such as changing their volume when they move) to create a better visual effect. DeRose pointed out that in the movies, "physics is really just a starting point" because animators seek a greater sense of "realism" or "visual quality" (ironically, considering physics is a more accurate representation of reality; however, it may not be perceived as such).
The limitations of physics are especially apparent in the case of lighting animated scenes. DeRose demonstrated the advanced differential equations needed to model light sources, since light in reality is expected to scatter off reflective surfaces, greatly complicating calculations. To deal with this problem, DeRose described how computer programs break lines in a model into numerous tiny segments, for each of which a new equation can be created to describe reflection. The result is a system of 10 million equations that is solved using a computer to generate the realistic light effects seen in animated films.
Another mathematical technique employed by Pixar animators is the use of subdivision surfaces. This technique has only recently been developed, the mathematics underlying it being 15-years-old. Subdivision surfaces work similarly to the basic principle that a polygon with enough sides resembles a circle; by subdividing lines on a surface to an increasingly greater degree, animators can create realistic-looking curves that avoid the blocky polygonal look of earlier graphics and videogames. DeRose showed a still from the original Toy Story, in which characters were essentially just collections of shapes with sharp seems; in recent films like The Incredibles, use of subdivision surfaces allows for smoother looking characters generated with less computing power.
A third technique that DeRose described as applying math to animation was the use of special "Barycentric" coordinates to articulate characters. By defining the points on a character model in relation to a polygon, animators are able to greatly simplify their job, since they can move a simple shape with a few hundred points and have a complex shape (such as character models, with 8,000 or more points) follow the simple shapes' movement, similar to a skeletal structure in humans (but on the exterior of the model). This technique is so new that it has not yet been used in a Pixar film, although upcoming productions are expected to employ it to make smoother animations.
DeRose closed by answering audience questions about the specifications of Pixar's animating process. Producing each frame of a Pixar movie typically takes six hours (there are 24 frames in each second of film), yet each frame has a lower resolution than a typical digital camera, since it is the clarity and not the quantity of pixels that matters for a good image. He also clarified the degree to which animation involves "practice and talent"; only by developing a thorough understanding of how changing equations changes digital visuals can animators generate the wonders that they do.
DeRose's talk was part of the James S. Plant Distinguished Scientist Lecture series.
-- by Kye Lippold '10
