CODEWITHSUNDEEP
javageometry
arget888
arget888

Reputation: 69

Determine if a Path describes a circle

I am trying to test if a path or polyline describes a circle in java. How can i do this? I am thinking about testing if the biggest distance between two points is nearly the same for all points on the path (with some mistake in mind). Can this work? What other possibilities did I have to check that?

Upvotes: 3

Views: 634

Answers (2)

Spektre
Spektre

Reputation: 51845

Assuming 2D...

  1. compute bbox

    so find min and max x,y coordinate values from all the sample points x[i],y[i] you got. Lets call them x0,y0,x1,y1 where x0<=x1 and y0<=y1

  2. compute center of circle cx,cy

    simply center of bbox so:

    cx = 0.5*(x1+x0)
cy = 0.5*(y1+y0)

  3. compute radius

    if you got really a circle then bbox should be square so

    fabs((x1-x0)-(y1-y0)) <= zero_threshold

    if not you do not have a circle. If yes radius is

    r = ~0.5*(x1-x0) = ~0.5*(y1-y0)

    so do the average ...

    r = 0.25*(x1-x0 + y1-y0)

  4. check for deviation from circle

    compute max abs difference ...

     d = max ( fabs( (x[i]-cx)^2 + (y[i]-cy)^2 - r^2) )

    if d > max_radius_difference_threshold^2 then you do not have a circle.

Also check this out:

There are also another tell tels like

  • if you know radius and path length then it should match the circle circumference
  • avg point of uniformly sampled closed circular path is also the center
  • angle between line segments of uniformly sampled circular path is constant
  • circle is convex only

Upvotes: 1

bit-shashank
bit-shashank

Reputation: 921

general equation of circle is a^2 + b^2=r^2 with center (0,0); where r is the radius of the circle and a and b the coordinates of point put in a and b and get the values of r if the value of r is same for all the values of a and b then the path is a circle . Note:- for a center at a point (h,k) equation changes to :-

(a-h)^2+(b-k)^2=r^2;

Upvotes: -1

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