Geomerics - Advancing Technology Through Innovation

Geomerics' philosophy is to create a unique blend of technology and research experience, coupled with strong industry focused management. Our main areas of activity are highlighted here.

Real-time radiosity

Geomerics has developed a radical new approach to radiosity, allowing scenes to be lit in real time with fully dynamic light sources. Further details of this technology can be found on the Enlighten pages.

Fast per-pixel specular for PRT Lighting

In 2002 Peter-Pike Sloan et al. popularised a lighting technique based on pre-computed radiance transfer (PRT) known as Spherical Harmonic PRT. The kernel of the technique is pre-computing a visibility function for each point on a surface and storing this in a suitably compressed format. If the lighting environment can be computed at run time in a similar basis to the visibility function, then the full lighting integral can be reduced to a dot product. Peter-Pike Sloan's original suggestion was to use spherical harmonics as the compression basis. These have the advantage that they can easily incorporate a diffuse BRDF. He found that impressively realistic effects could be generated with as little as 16 coefficients.

Geomerics' research into geometric algebra and spherical wavelets has produced a new approach to PRT lighting that is faster and more accurate than existing methods based on spherical harmonics, and supports view-dependent lighting through more general BRDFs. The images below show sample screenshots. (Note that the facetisation in the final image is an artifact of the model, and nothing to do with the use of wavelets.)

A shiny head in a complex lighting environment.	A metallic head in a cathedral lighting environment.	The method also works for more general scenes, provided they are lit by a distant environment.

Physics

Geometric algebra provides an extended set of geometric primitives, all with orientations naturally defined. This is a superb basis for building a collision detection system. The screenshot is taken from Geomerics' demo of GA-based collision detection and resolution. In this case the simulation is of 2000 boulders tumbling down a ravine. It runs at 60 fps on a standard modern CPU.

Geometric algebra also provides new approaches to rigid body mechanics. Three-dimensional geometric algebra naturally includes the quaternions, which are widely known to be better for rotational dynamics than 3x3 matrices. But GA incorporates quaternions into a wider framework of objects known as 'rotors', which can describe both rotations and translations. These have a number of advantages when it comes to simulating rigid body motion, including analysing constraints and resolving collisions.

Animation

Geomerics has developed a wealth of experience in problems relating to animation, and is currently engaged in further joint research with Cambridge University.

Geomerics first developed technology to tackle two problems in motion capture. The first concerns the camera calibration step. We are able to compute the camera geometry from arbitrary images in real time, allowing cameras to be moved as data is captured. The second problem is that of skeleton fitting. Once point correspondences are established, the underlying skeleton configuration of each character must be computed. We can again perform this in real time, even for noisy data.

A natural extension to the ability to generate skeletons from motion capture data in real time is to extend the process to high-end authored animations, feeding directly into the animation tool chain. The idea is to compute a compressed skeleton interactively, and skin it (see below), so that the artist can immediately see how their character will actually appear in game.

Geometric algebra provides a wealth of interpolation schemes, some of which are well suited to the problem of skinning a skeleton. Standard schemes are notorious for their unrealistic crushing effects, but GA based schemes have none of these defects. Rotor interpolation schemes are particularly well suited to skinning problems. They handle interpolation along a bone in a manner that avoids the ugly crushing effects that plague traditional methods.

Electromagnetic modelling

Geomerics has developed a radical new approach to electromagnetic modelling (EMM). This involves a complete solution to the Maxwell equations, so automatically includes self-shadowing, reflections, caustics, diffraction and self-interference. Unlike 'line of sight' solutions our approach is 'infinite bounce'; reflections, hot-spots and caustics can be caused by any number of reflections.

The following images are the output from our advanced EM modelling technology on a variety of reflectors.

A plane-wave incident on a collection of small planes from the left.	A point-source placed at the focus of a parabolic reflector.	A plane-wave inident on a parabolic reflector from the top-left. A caustic is formed in the bowl of the parabola.