circle through 3 points equation

Hi, i have an exercise for the university.

Through three points A, B, C ∈ R2 that do not lie on a straight line can be exactly one circle lay. Circle center M and radius r can be calculated using a linear 3 × 3 system of equations u1 := m(1)^2 + m(2)^2 -r^2 ; u2 := 2m(1) and u3 := 2m(2)

u1 − a1u2 − a2u3 = −a1^2 − a2^2

u1 − b1u2 − b2u3 = −b1^2 − b2^2

u1 − c1u2 − c2u3 = −c1^2 − c2^2

m1 = u2/2 ,

m2 = u3/2

r =sqrt( m1^2 + m2^2 − u1)

How can i write the function and what shold i do?

Answer 1

[Image Analyst]

See the FAQ:

https://matlab.fandom.com/wiki/FAQ#How_can_I_fit_a_circle_to_a_set_of_XY_data.3F

Answer 2

[Matt J]

You can use circularFit() from this File Exchange submission

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

fitobj=circularFit([A(:),B(:),C(:)])