Christchurch company Applied Research Associates NZ Ltd (ARA) has developed a method to model complex 3D objects that has applications that range from medical imaging to the analysis of weather and financial data.

In association with a team from Canterbury University's Mathematics Department headed by Associate Professor Rick Beatson, ARA's has created an analytical engine that can handle sets of spatial data many times greater than was previously feasible.

Image courtesy of www.aranz.com

ARA research engineer Dr Jonathan Carr says the company's software allows it to describe an object by a single mathematical function. The mathematical algorithm the group has developed makes use of radial basis functions, and is currently known as FastRBFÔ.

"The problem we have solved is to determine an object's shape given a large number of points from its surface generated through a scanner or some other method", Carr says. "This can be difficult when the surface points are unevenly distributed or coverage is incomplete."

"This is non trivial because until now technology has only been able to handle point sets of two or three thousand. With FastRBF we can handle point sets of several million on a desktop PC, not a main frame with terabytes of RAM."

Once FastRBF creates a function that describes an object, ARA's FastSurfÔ technology evaluates a surface for it. To do this it creates a polygon mesh that can be used to create a computer image, plastic prototype or other representation of the object.

Carr explains that the mathematical function compactly represents an object independent of any particular mesh. This is different that other types of modelling, which create a single mesh to describe an object.

ARA's mathematical models can be used to create meshes of different resolution. This is ideal for computer animation that may require a coarse mesh for a distant image of an object but a finer mesh for a close-up shot. It's also an easy matter for FastSurf to generate a mesh with 'constrained optimisation', which is necessary for rapid prototyping.

Several other features of FastRBF and FastSurf make them ideal for use in CAD, 3D visualizations, and computer graphics. These include the abilities to interpolate and extrapolate surfaces from incomplete data sets. This means FastSurf will automatically generate a smooth surface to fill even large, difficult holes in a mesh. It can also make smooth extensions of a surface where there is no data.

Another feature of ARA's 3D modelling technology is the ability to fillet, or smoothly join two different objects together. It also provides new ways to morph objects and to register 3D objects against one another for comparative purposes.

Image courtesy of www.aranz.com

One task ARA has carried out with its modelling software is to reconstruct a 3D model of Eros, an asteroid that could strike the earth. A NASA satellite orbits Eros and it has gathered some data to describe its surface features. The data set varies in accuracy and density but FastSurf interpolated the surface to create a smooth model of the asteroid.

In earlier work at Christchurch Hospital, Beatson, Carr and ARA director Dr Rick Fright used this technique to interpolate the surface of skulls in order to create a CAD model for the manufacture of titanium prostheses to repair skulls damaged in accidents or surgery. The models must be smooth and fit precisely because titanium is difficult to reshape in the surgery theatre.

Currently ARA is developing ways to commercialise it modelling technology. Recently a team from the company attended a major computer graphics and animation conference in the US and now several companies are acting as beta testers, trying out ARA's analytical engine in their software.

Fright says his company is not looking to compete with software producers in their fields. Rather it will look to license its software so producers can incorporate ARA's analytical engine into their software.

"Our modelling technology has potential four dimensional applications in which we can model how three dimensional objects change over time. We will also develop applications in areas such as meteorology. For example we should be able to provide more accurate visual models of changes in temperature or pressure than are currently available.

"The US Atomic Energy Commission has expressed interest in our technology to model the concentration of radiation within their reactors. It also has potential for data mining in such areas as financial markets or insurance," says Fright.

For further information see www.aranz.com.