ASU Research E-Magazine: Numbers to Wires to Pictures

Computers see an object mathematically—more specifically, they see objects as a bunch of numbers which describe the object’s exact location in space. The technical experts at ASU’s Partnership for Research in Stereo Modeling (PRISM) work to transform those numbers into pictures. In the PRISM laboratory, researchers design visualization software that allows users to view an object just as it appears in real life.

The laser scanner used at PRISM records 10,000 points per every square inch of an object’s surface. Each point is described as a set of x, y, and z coordinates. Those coordinates describe the object’s exact location in space.

The data appears on-screen as a “cloud” of points. To the human eye, this cloud looks a lot like the original object. But to the computer, it is merely a group of unrelated points.

In order to make these disconnected dots into a single object, the scanner software triangulates the data. In other words, it plays connect-the-dots with the data points, creating a “wire frame” image made of triangles.

“It’s kind of like sewing a quilt,” explains PRISM co-director Mark Henderson, an ASU professor of industrial engineering.

Once connected, the dots form a coherent object. The image looks a lot like the original, but it has no real surface, and it has no curves. PRISM’s technical wizards step in at this point. Their computer programs fill in the surfaces and round out the curves.

Gerald Farin is an ASU professor of computer science and special advisor to PRISM. He says that creating curves is one of the trickiest parts of the process, because objects vary in their roundness.

“The extent to which the program computes the curves varies from application to application,” Farin explains. “Mathematically, building a car is different from building a ship or an airplane.”

Cars may need to be curvy so that they look slick. A ship or an airplane needs to be more precise and functional.

The PRISM software uses a mathematical formula to curve the sharp edges of scanned data. However, the exact shape must be determined on a case-by-case basis, depending on the nature of the object being recorded.

Modeling bone surfaces presents a big challenge in this respect, Farin says. “Bone surfaces have a totally irregular boundary. The surface can be very angular in parts and very curved and smooth in others,” he explains.

Unfortunately, the computer has no way of judging which areas to curve and which to leave sharp. As a result, researchers must spend lots of time perfecting the surface.

Once the object has a surface, the computer has a detailed mathematical description that can be used for many applications down the line. For example, objects can be categorized with exceptional precision.

Eventually, scanning objects on an assembly line could assist in quality control, Henderson says. The computer could verify that every component is the proper shape and size. Computer modeling also could be used as a tool to assist with reverse engineering.

“Reverse engineering refers to when we have the object, but not the design,” Henderson explains. A designer can scan the object, make improvements on it, and then output the new model.

All of these applications involve huge amounts of data. But both Henderson and Farin say that most of the work can be done on a high-end personal computer. Behind the scenes, however, PRISM programmers are creating visualization programs using sophisticated Silicon Graphics machines.

“These are the same computers used to create the animated sequences of movies such as Jurassic Park,” Henderson adds.—Diane Boudreau