Sign in to follow this  
16bit_port

help with geometry. (intersection of 2 circles)

Recommended Posts

16bit_port    180
[url="http://paulbourke.net/geometry/2circle/"]Circle-Circle intersection point article[/url] (it's VERY short)

I understood everything up until the very end :

x[sub]3[/sub] = x[sub]2[/sub] +- h ( y[sub]1[/sub] - y[sub]0[/sub] ) / d
y[sub]3[/sub] = y[sub]2[/sub] -+ h ( x[sub]1[/sub] - x[sub]0[/sub] ) / d

why the "y[sub]1[/sub] - y[sub]0[/sub]" and the negative h to get x[sub]3[/sub]?

Share this post


Link to post
Share on other sites
jyk    2094
(-(y1-y0), x1-x0)/d is a unit-length vector perpendicular to the line passing through the centers of the circle. P[sub]3[/sub] is the midpoint (sort of) of the overlap, and [i]h[/i] is half the length of the cord bisecting (sort of) the overlap. Together, these values can be used to compute the intersection points.

Does that help at all?

Share this post


Link to post
Share on other sites
16bit_port    180
[quote name='jyk' timestamp='1307319734' post='4819920']
(-(y1-y0), x1-x0)/d is a unit-length vector perpendicular to the line passing through the centers of the circle. P[sub]3[/sub] is the midpoint (sort of) of the overlap, and [i]h[/i] is half the length of the cord bisecting (sort of) the overlap. Together, these values can be used to compute the intersection points.

Does that help at all?
[/quote]

Actually. Yes it does. I forgot that swapping the coordinates and negating one of them of a vector creates another vector perpendicular to it.

Share this post


Link to post
Share on other sites
16bit_port    180
Also two more things, just out of curiosity if I took the circle formula :

(x - h[sub]1[/sub])[sup]2[/sup] + (y - c[sub]1[/sub])[sup]2[/sup] = r[sub]1[/sub][sup]2[/sup]
(x - h[sub]2[/sub])[sup]2[/sup] + (y - c2)[sup]2[/sup] = r[sub]2[/sub][sup]2[/sup]

and solve this system of equations by solving for x and then substituting it back into either of those and solve for y, would I get the same result? In other words, is that a valid way to find the intersection?

And [url="http://mathforum.org/library/drmath/view/64311.html"]doing this in 3D[/url], I don't understand how he got
r^2 = R1^2 - (a^2+b^2+c^2)*t0^2for the radius of the intersecting circle between two spheres.

Thanks.

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this