# Discrete Elastic Rods

Technology #m08-101

Realistic Computer Modeling and Visualization of Elastic Rods
Realistic computer modeling and visualization of natural objects is a complex and memory intensive task. The reason behind such complexity is the interplay of different physical forces such as friction, gravity, viscosity which ultimately results in a motion, e.g. bending of tree in response to wind. There are existing software packages which can calculate these forces on an arbitrary object and then use constraints or boundary conditions to come up with the resulting shape of the object. However such an approach is very cost intensive and therefore slower.

Presently, a major use of these computer models is in geometric shape prediction purposes, such as simulating an object in a video game, or finding various shapes a protein can fold. Such applications do not require an in depth mechanical analysis, hence they can be catered by simplistic algorithms which focus mainly on shape prediction using boundary constraints and simplified dynamical analysis of the system. Moreover such an approach can be more simplified by beginning with a basic set of objects which can be modified or joined together to make numerous complex natural forms. One such basic object shape is of an elastic rod.

Realistic Discrete Elastic Rod Simulation
An elastic rod is defined as curve-like elastic body with one dimension (length) much larger than the others (cross-section). Many common objects satisfy this definition, for example cables in bridges, ropes tied in knots, surgical sutures, DNA strands, thicker objects like the bones in a model skeleton, and many other objects that are defined by a long, central axis.

Current technology simulates the shapes of these elastic rods under various forces as shown in the accompanying Figure 1.

This approach differs from existing simulation techniques in the graphics and mechanics literature both in the kinematic description – the material frame is represented by its angular deviation from the natural Bishop frame – as well as in the dynamical treatment – centerline is treated dynamically and the material frame as quasistatic. Additionally, a manifold projection method is described for coupling rods to rigid bodies and simultaneously enforcing rod inextensibility. The use of quasistatics and constraints provides an efficient treatment for stiff twisting and stretching modes; at the same time, the method retains the dynamic bending of the centerline and accurately reproduce the coupling between bending and twisting modes. This simplicity of approach enables real time simulation of few rod systems; in case of many simultaneous rods it may need some acceleration. The discrete rod model is validated via quantitative buckling, stability, and coupled-mode experiments, and via qualitative knot-tying comparisons. One such validation is seen in the accompanying Figure 2.

Applications:

• This technology would be well-suited to a range of different simulation and computer graphics tasks such as simulating cables, hair, fabric threads, DNA strands, the tiny interlocking filaments of Velcro, etc. Since the simulation is faster for few rods, it can be done real time. This will help in making the simulations of animated objects look more real.
• Additionally, this technology is valuable for biological simulations. Aside from DNA, it may be useful in studies of cellular filaments such as actin cables or larger structures such as bacterial flagella.
• Biomechanical engineers could benefit from using this technology to design new prosthetics. It could help simulate the bones in the body, the prosthetic limb, and all the interactions between them.
• Video game developers are always looking for ways to create more realistic simulations of common objects. One particular difficulty has been making the hair of video game characters look convincingly real. It is too difficult to simulate thousands of hair strands separately, but modeling too few looks unrealistic. This technology, which presents a more efficient algorithm, may be able to tackle such problems.

• Simple to implement and efficient to execute methodology
• Easy to validate and test for convergence
• Faster algorithm, lower cost
• Simulations can be real time in case of a few rods system.

Opportunities:
• Sponsored research funding in alternate methods for enforcing constraints to predict geometries as well as have a good energy behavior
• Licensing.