CODEWITHSUNDEEP
pythonopencvgeometryellipse
ArenMayank
ArenMayank

Reputation: 17

get 16 equidistant points along the circumference of ellipse

I am trying to get the 16 equidistant point on ellipse (equal arc length along the ellipse).

Using some research, I am able to get the angle from which I can get those point by drawing a straight line and getting the intersection point but unable to find the length of line to be drawn from the center. I have also explored https://math.stackexchange.com/questions/172766/calculating-equidistant-points-around-an-ellipse-arc but getting confused in formulaenter image description here

What is the value of φ here?

Can anyone please help me there on getting the points. Thanks

Upvotes: 0

Views: 575

Answers (1)

MBo
MBo

Reputation: 80187

We can define (axis-aligned) ellipse parametrization as

x = a * cos(φ)
y = b * sin(φ)

where parameter φ has range 0..2*Pi.

Resulting point (x,y) is situated at angle θ relative to the ellipse center. Your linked post shows formula for θ/φ transformation.

Note - θ is real angle, φ is not!, it is just parameter.

You perhaps don't need θ here. To solve the problem, you have to find ellipse circumference length L using elliptic integral for φ = 2*Pi (numerically).

Then find φ values corresponding to arc length L/16, 2*L/16...15*L/16 - numerically again, and calculate corresponding point coordinates from the parametrization equations.

Upvotes: 1

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