A framework for the design of new line parameterizations

Based on four criteria, namely uniqueness, boundedness, uniformness and recursiveness, a framework for the design of new line parameterizations is introduced. It is shown that there does not exist a line parameterization which could satisfy all the above four criteria, and that the line parameterization, formulated as c=ax+(a₀-|a|)y a∈[-a₀,a₀) where a ₀ is an arbitrary positive number, can not only satisfy the uniqueness, boundedness, and recursiveness conditions, but it can also achieve the best goodness to the uniformness one