Patent ID: 6985639

Claim:
A method for aligning a first linearly extending geometric shape and a second linearly extending geometric shape so that a comparison can be made as to how closely they match, the method comprising: scaling at least one of the linearly extending geometric shapes, if necessary, so that the first linearly extending geometric shape has a length equal to the second linearly extending geometric shape; determining measurement locations along the first linearly extending geometric shape and corresponding measurement locations along the second linearly extending geometric shape, wherein each measurement location on the first linearly extending geometric shape is located at a specific respective distance from a nominal starting point on the first linearly extending geometric shape, wherein each measurement location on the second linearly extending geometric shape is located at a specific respective distance from a nominal starting point on the second linearly extending geometric shape, and wherein the specific respective distance of each measurement location along the first linearly extending geometric shape is equal to the specific respective distance of each corresponding measurement location along the second linearly extending geometric shape; determining tangent vectors along each linearly extending geometric shape at each measurement location; for each measurement location along the first linearly extending geometric shape, determining an angle between the tangent vector determined with respect to the first linearly extending geometric shape at the measurement location and the tangent vector determined with respect to the second linearly extending geometric shape at the corresponding measurement location; computing a mean of the angles; rotating the second linearly extending geometric shape by the mean of the angles; and translating the second linearly extending geometric shape so that one end thereof coincides with a corresponding end of the first linearly extending geometric shape, if necessary, whereby after translating the first linearly extending geometric shape and the second linearly extending geometric shape can be compared.