20 Approximation of centroid and radius
The centroid and radius of both a circle and a sphere can be approximated from several points (three for a circle, four for a sphere) located on their circumference. The following must be kept in mind:
• For a circle: the three points cannot be co-linear or no solution will be found (because the points are on a straight line, not a circle).
The solution for both circle and sphere equations is found from analytic geometry.
The circle/sphere equation can be found from the following determinant equation (main matrix):
The general equations are given below.
For the circle or sphere centroid (Pt0):
The radius of a circle is given by:
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