help with geometry. (intersection of 2 circles)

This topic is 2575 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

Recommended Posts

Circle-Circle intersection point article (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 on other sites
(-(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 h 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 on other sites

(-(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 h 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?

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 on other sites
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 doing this in 3D, 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.

1. 1
2. 2
3. 3
4. 4
Rutin
16
5. 5

• 12
• 9
• 12
• 37
• 12
• Forum Statistics

• Total Topics
631419
• Total Posts
2999977
×