Reference Frames for Kirchhoff Rods
Lead Inventors: Eitan Grinspun, Ph.D.Problem or Unmet Need:Kirchhoff rods are computer-simulated unshearable, inextensible elastic rods that can be used in computer models to efficiently simulate rods and rod-like objects (such as hair, threads, etc.) with minimal computation time. These rods can be used in simulations such as physics engines for video games, design software, hair simulation in film and animation, suture simulations in medicine, and viscous threads in mechanics. However, some complex simulations take an exceptionally long computation time. This technology is a method for representing Kirchhoff rods. The model consists of the position of the centerline, (a curve in 3-D space) along with an orthonormal frame at each point along the centerline, representing the orientation of the elastic material of the rod. The orthonormal frame is adapted to the curve, meaning one of its basis vectors lies along the tangent to the centerline. The representation for this model is to use a reference frame at each point along the centerline and keep track of the material frame using only an angle at each point, which is the angle of rotation between the reference frame and the material frame. The reference frame is determined by the condition of zero angular velocity about the tangent (computed via parallel transport along the time dimension). Compared to the Discrete Elastic Rods model (which uses parallel transport in the spatial dimension), the use of this novel reference frame provides superior numerical performance for simulation of general rods.
Efficiency and simplicity of elastic rod and viscous thread simulation Simple update rules for the degrees of freedom v
Simulation software for films and video games Computer aided design Biological simulation Virtual surgery simulation Tactile-feedback simulation Viscous thread (e.g., honey) simulation in mechanics Manufacturing and geophysics
This technology is a method for representing Kirchhoff rods. The model consists of the position of the centerline, (a curve in 3-D space) along with an orthonormal frame at each point along the centerline, representing the orientation of the el...
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