A new linearity measure is developed for open curve segments in 2m>Dm> and 3m>Dm>.

The measure is based on the curve end points and the curve centroid.

The measure is simple to compute.

The measure ranges over the interval an id="mmlsi0022" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S003132031500271X&_mathId=si0022.gif&_user=111111111&_pii=S003132031500271X&_rdoc=1&_issn=00313203&md5=e651d163bd7989135e4c7d7c28143007" title="Click to view the MathML source">(0,1]an>an class="mathContainer hidden">an class="mathCode"><math altimg="si0022.gif" overflow="scroll"><mo>(mo><mn>0mn><mo>,mo><mn>1mn><mo>]mo>math>an>an>an>.

The measure is invariant with respect to translations, rotations and scalings.