how to calculate tangent between circle and polynomial (from curve fit)
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Hi:
I have a known circle with x0,y0, and r, I also have a polynomial function from curve fitting result, is there any way to find the tangent line between those two? as well as the tangent point on each profile?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1596561/image.jpeg)
the curve fitting polynomia is attached, and the parameter of circle is:
x: 0.9439
y: 0.1063
r: 0.0537
Thank!
Yu
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Matt J
2024년 1월 21일
편집: Matt J
2024년 1월 21일
The equation for the tangent to the polynomial is y=m(x1,y1)*x+b(x1,y1) where m(x1,y1) and b(x1,y1) are a function of the tangent point (x1,y1) and can easily be determined from calculus. Therefore, the tangent point on the circle must satisfy the two equations,
y2=m(x1,y1)*x2+b(x1,y1)
(x2-0.9439)^2+(y2-0.1063)^2=0.0537^2
Also, (x1,y1) must satisfy the polynomial equations
P(x1,y1)=0
And you have a 4th equation to express the fact that the normal vector to the tangent line is perpendicular to the tangent line,
(x2-0.9439)-m(x1,y1)*(y2-0.1063)=0
Four nonlinear equations in four unknowns. I expect there will be two solutions.
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