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In this paper, we propose a complete model handling the physical simulation of deformable 1D objects. We formulate continuous expressions for stretching, bending and twisting energies. These expressions are mechanically rigorous and geometrically exact. Both elastic and plastic deformations are handled to simulate a wide range of materials. We validate the proposed model in several classical test configurations. The use of geometrical exact energies with dynamic splines provides very accurate results as well as interactive simulation times, which shows the suitability of the proposed model for constrained CAD applications. We illustrate the application potential of the proposed model by describing a virtual system for cable positioning, which can be used to test compatibility between planned fixing clip positions, and mechanical cable properties.