0
$\begingroup$

I have two Arcs that intersect each other.

One Arc should be translated (Arc B) while the other must stay fixed in place (Arc A).
How can I find the minimum vector that solves the intersection of Arc B in one specific direction?

In my case, for example, I can move Arc B only upwards (+Y).

Is there a mathematical function that works for every possible case (eg. same / opposite orientation, A above / below B, etc...)?

The Problem

Thanks.

PS: Sorry, I am not an expert in mathematics...

PPS: The desired result
The desired result

$\endgroup$
9
  • $\begingroup$ What do you mean by"vector that solves the intersection"? $\endgroup$
    – Qwerty
    Jun 7 '16 at 14:17
  • $\begingroup$ And even experts post questions here, so no need to feel guilty. $\endgroup$
    – Qwerty
    Jun 7 '16 at 14:17
  • $\begingroup$ @Qwerty For example v(0, +15). In this case Arc B should move up by 15 units in Y to not intersect anymore with Arc A. $\endgroup$
    – TesX
    Jun 7 '16 at 14:19
  • $\begingroup$ Well moving up is not the only solution.It could move sideways or any other direction to a certain distance to stop being intersected by Arc A $\endgroup$
    – Qwerty
    Jun 7 '16 at 14:22
  • $\begingroup$ @Qwerty In my case, though, I only need one specific direction (eg. up). $\endgroup$
    – TesX
    Jun 7 '16 at 14:23
0
$\begingroup$

Find the max value of the y coordinates of Arc A. Keep increasing all Y coordinates of Arc B until the minimum Y value of Arc B exceeds The max y value of Arc A.

If your A is above B then put min in place of max and vice versa..

$\endgroup$
2
  • $\begingroup$ That wouldn't work when Arc B is flipped upside down though... i.imgur.com/H94pDOQ.png $\endgroup$
    – TesX
    Jun 7 '16 at 14:58
  • $\begingroup$ @TesX this will work.. Upvote if you like my answer $\endgroup$
    – Qwerty
    Jun 7 '16 at 15:01
0
$\begingroup$

Eliminate x from equations of these two circles.

$$ ( x- H)^2 + ( y- K)^2 = R_A^2; \, ( x- h)^2 + ( y- k)^2 = R_B^2; \, $$

Equate the discrimnant of obtained quadratic equation in $y$ to zero.

You will get $K$ in terms of $ h,k, R_A, H, R_B $

Can you take it up further? If not I could hint further.

$\endgroup$
1
  • $\begingroup$ I'm sorry but how can I eliminate x from those equations? -.- $\endgroup$
    – TesX
    Jun 7 '16 at 15:42

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.