A robust and efficient Lagrangian constraint toolkit for the simulation of 1D structures

Abstract

This paper introduces an easy and efficient way to constrain a one-dimensional deformable model with Lagrangian constraints, allowing most needed interaction and combinations of 1D parts for the assembly of complex 3D structures like a bridge, a pearl necklace, cable beams and a bow. These examples illustrate non-trivial interactions, e.g. sliding, that can not be easily addressed by previous methods. All constraint formulations we propose are compatible with linear and displacement-based integration schemes. For an optimal integration numerical process, we discuss efficient reordering of the constraint and motion equations. This provides linear-time and robust simulation of complex structures.