How to measure asymmetry?
Is there a way to estimate the "centroid of an ideal shape" if I measure a skewed one?
I.e. I produce a measure of the centroid and it's "off", since the object that I measure it from is asymmetric. But can I produce the equivalent "perfect centroid" in order to compare how much offset there is?
How?
The equation to get the centroid of an area is this, it states qualitatively that a certain point times the total area equals the sum of products of moments of pieces of area of the same figure, the result may vary depending on the choise of axis, but the position of such with respect of axis doesnt change. $$\bar{x}A=\Sigma ^i x^ia^i$$ what do you mean with perfect centroid? maybe you are asking about simmetry and how to measure it, then you might be interested to use the product of inertia $$I_{xy}=\Sigma ^i x^iy^ia^i, or \space I_{xy}=\int xy\cdot da$$ fast intuitive approach: if an element of area is in an axis, its product of inertia is zero, also, if there is the same amount area in both sides of an axis, their sum is zero, thus we see that the smaller the product of inertia of the whole area is, the more symmetric it is,(if zero, entirely symmetric to both sides). Any way the axis should be the ones you got from your centroid calculations.