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Interactive simulation of one-dimensional flexible parts
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ACM Transactions on Graphics (TOG)
Animating strings with twisting, tearing and flicking effects
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Contact-friction modeling within elastic beam assemblies: an application to knot tightening
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Exponential integrators for stiff elastodynamic problems
ACM Transactions on Graphics (TOG)
Vector-projection approach to curve framing for extruded surfaces
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Optimizing neighborhood projection with relaxation factor for inextensible cloth simulation
The Visual Computer: International Journal of Computer Graphics
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We present a discrete treatment of adapted framed curves, parallel transport, and holonomy, thus establishing the language for a discrete geometric model of thin flexible rods with arbitrary cross section and undeformed configuration. Our approach differs from existing simulation techniques in the graphics and mechanics literature both in the kinematic description---we represent the material frame by its angular deviation from the natural Bishop frame---as well as in the dynamical treatment---we treat the centerline as dynamic and the material frame as quasistatic. Additionally, we describe a manifold projection method 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, we retain the dynamic bending of the centerline and accurately reproduce the coupling between bending and twisting modes. We validate the discrete rod model via quantitative buckling, stability, and coupled-mode experiments, and via qualitative knot-tying comparisons.