, Volume 82, Issue 1, pp 81-84

On the space of oriented affine lines in \( \mathbb{R}^3 \)

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Abstract.

We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean \( \mathbb{R}^3 \) and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces in \( \mathbb{R}^3 \) , as we illustrate with a number of explicit examples.

Received: 17 December 2002