Point-models for the set of oriented line-elements - a survey

We study point-models for the set L→ of oriented line-elements by reviewing existing ones and by constructing them from different approaches proposed in the literature. We distinguish between point-models resulting from transformations and those implied by representations, where we also pursue the strategy to represent oriented line-elements by oriented line-segments with a constant length. For path planning in robotics (e.g. approximation, interpolation, optimization, ...) it is desirable to have a metric on L→, thus we also study geometric meaningful distance measures. Based on the resulting metric spaces we finally discuss the problem of motion design.