Calculus in Graphic Design

Calculus in Graphic Design

Calculus in Pixar

Calculus in Pixar Pt. 2

Originally, in animations only polygons and geometric shapes were used to create the images. However, there was a problem with this. The problem was that when you zoomed up on the image, you could see the edges of the geometric shapes, giving it an unrealistic appearance. Now, animators are using parabolic functions to create the natural curves of the natural world. Mathematicians have worked to develop different methods to quickly generate smoothly curved surfaces. "These surfaces are often called subdivision surfaces because of how they are calculated, by repeatedly splitting and averaging the midpoint of a line."

Hair, clothes, fluids, and things such as clouds, smoke, and fire all require a specific equation to calculate their own physics "Simulating water is easy," says DeRose. "What's hard is, how do you make water more directable?" For Brave, Merida's bright red, highly animated curls required a lot of calculation to build an entirely new physics engine. The animators had to figure out how to make Merida's hair move in such a way that it didn't lose its lifelike qualities. "DeRose and his team of scientists had to engineer a model that makes that animation computationally possible."

The First Time Subdivision was Used in Animation

Now in this, I mention a physics engine. What a physics engine is, is a computer software that provides an approximate simulation of certain physical systems, such as rigid body dynamics (including collision detection), soft body dynamics, and fluid dynamics, of use in the domains of computer graphics, video games and film.

The first time subdivision surfaces were used in computer animation was in the Pixar short "Geri's Game". Tony "DeRose adapted his work on calculating wavelets on multidimensional surfaces to create a new curve-generating algorithm". It was originally used only for very complex situations such as the complex shape of an old man's nose. However, after perfecting it, it is now used for every pixar film there is. "DeRose shows a still from The Incredibles, and gestures to the background. "You might be surprised that the building, its windows, all of the details are generated with subdivision surfaces," he says."

Conclusion

How is Calculus Used in Graphic Design?

(or 3D Animation)

But, How Do They Do This?

Calculus is used even in the most ordinary, every day things. The movies you loved as a child and the video games you play today are all programed with a significant amount of calculus and other math forms in order to achieve the most realistic image and life like movements.

A graphics artist uses calculus to determine how different three-dimensional models will behave when subjected to rapidly changing conditions. This can create a realistic environment for movies or video games.

There are lots of computer software's and programs, such as the physics engine I mentioned before, available to create this animated environments. The software I'm going to focus on today is AutoCAD. AutoCAD is used to create the mesh models of characters and scenes before they are placed into a physics engine and made into more human looking figures. The mesh shape is pretty much a wire outline of the character and when shaded, shows the character you intended. As mentioned before, subdivision is used to create the shape of the character by rapidly generating curved surfaces, which we have done something similar to in our own calculus class. We can find the slope at each point on the curved surface to make sure it is curved to the right degree.

WORKS CITED

https://www.wyzant.com/resources/lessons/math/calculus/introduction/applications_of_calculus

http://www.theverge.com/2013/3/7/4074956/pixar-senior-scientist-derose-explains-how-math-makes-movies-games

Calculus in "Brave"- Merida's Hair

"In the real world, hair keeps its bounciness and volume by constantly colliding with itself," DeRose says. Merida's hair is made of 100,000 individual elements. "If you know any combinatorics, you know that if you have n objects, you have n² possible collisions," he says, or 10 billion. So how do you calculate all of these possible collisions? "You have to create a new spatial data structure that culls extraneous collisions without being too lossy," says DeRose.

Merida's hair is a prime example of the use of calculus and physics within Pixar and most animation studios.

For Example

Like in some of your favorite childhood movies, calculus is used to calculate the shapes and functions needed to create the right response from the variable and make it seem as real as possible.

Tony DeRose

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