Roundness (object) - Calculation in Two-dimensions

Calculation in Two-dimensions

A single trace covering the full rotation is made and at each equally spaced angle, a measurement, of the radius or distance between the center of rotation and the surface point. A least-squares fit to the data gives the following estimators of the parameters of the circle:

$\hat{R} = \frac{1}{N}\sum\limits_{i=1}^N R_i$

$\hat{a} = \frac{2}{N} \sum\limits_{i=1}^N R_i \cos{\theta_i}$

$\hat{b} = \frac{2}{N} \sum\limits_{i=1}^N R_i \sin{\theta_i}$

The deviation is then measured as:

$\hat{\Delta} = R_i - \hat{R} - \hat{a} \cos{\theta_i} - \hat{b} \sin{\theta_i}$

Read more about this topic: Roundness (object)

Famous quotes containing the word calculation:

““To my thinking” boomed the Professor, begging the question as usual, “the greatest triumph of the human mind was the calculation of Neptune from the observed vagaries of the orbit of Uranus.”
“And yours,” said the P.B.”
—Samuel Beckett (1906–1989)