Computer Animation

Luxo Jr., by Pixar

Computer animation in films continues to make remarkable progress.  I remember seeing Luxo Jr. shortly after it was first released by Pixar in 1986 at an animation film festival that screened at Stanford University.   I was fascinated by the technology, and briefly thought about taking my studies in that direction before having a really difficult time in a computer graphics course.

Brigham Young University is now at the forefront of developing computer animated films, at its Center for Animation, a collaboration between the College of Engineering and Technology, College of Fine Arts and Communications, and College of Physical and Mathematical Sciences.

One of the faculty in the Computer Science Department, Michael Jones, shared a few images with me:

Still from the BYU student film "Kites"

This image shows a new system to generate clouds as a boy flies through them on a kite.  Each cloud is rendered using a particle that has a position, velocity, and lifespan.  Dr. Jones explains:

Each particle was rendered as a puffy cotton ball (essentially) so that when they are rendered as a group, it looks like a cloud.  The clouds streaming from the boy's head and the from the dragon kite are all made of particles.  Their velocity is keyed to the velocity of the boy or the kite.  The magnitude of the velocity decays a little so that the clouds appear to stream away from the boy and kite as they fly.  The decay rate is inversely proportional to the the distance from the boy or cloud.  

One of Dr. Jones' specialties is creating realistic computer-generated images of natural phenomena, such as scenery in Southern Utah. 

Computer-generated weathered sandstone

This is a generated image of weathered sandstone, with both outward-curving edges and inward-curving caverns.  Dr. Jones says:

We discovered that the weathering rate is inversely proportional to the magnitude of the mean surface curvature.  The mean surface curvature is a measure of the degree to which a surface, when measured over an infinitesimally small neighborhood, fails to be a flat plane. Sharp corners have high positive curvature, flat faces have zero curvature and indentations have negative curvature.  The real insights in this work are an iterative algorithm for efficiently estimating mean surface curvature in 3D.  Previously, people did it analytically in 2D but hadn't generalized to 3D which is much harder. The other insight is that one kind of weathering (spheroidal: in which sharp edges become rounded) happens with positive surface curvature and another kind (cavernous:  in which pits become caverns) happens with negative curvature.   This rock model shows both on one piece of geometry. 

An interesting point is that this is another example of computer scientists trying to learn from and be inspired by nature.

Dr. Jones also mentions that this work is being done about 20 years after the art by Musgrave that I showed in the previous post.  His work require significantly more computation than Musgrave's, but in that 20 years computer power has increased approximately 10,000 times, due to Moore's Law.  That increase in power has lead to the ability of computers to generate much more realistic landscapes.

You can see more of Dr. Jones' work at the Computer Generated Natural Phenomena Lab page.