# Tangent vectors to a 3-D surface normal: A geometric tool to find orthogonal vectors based on the Householder transformation

@article{Lopes2013TangentVT, title={Tangent vectors to a 3-D surface normal: A geometric tool to find orthogonal vectors based on the Householder transformation}, author={Daniel Sim{\~o}es Lopes and M. T. Silva and J. A. Ambr{\'o}sio}, journal={Comput. Aided Des.}, year={2013}, volume={45}, pages={683-694} }

An important geometric and linear algebraic problem denoted as vector orthogonalization, fundamental to handle contact detection and contact force descriptions in engineering applications, is here considered. The problem is to find a set of linearly independent vectors that span the entire R^3 Euclidean space given only one of the base vectors. This paper contains the explanation on how the Householder transformation, which is extensively used for matrix orthogonalization, provides an elegant…

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