MATLAB Central Newsreader - Intersection between line and half-circle

Intersection between line and half-circle

Catherine Szeto — Sun, 08 Nov 2009 05:37:01 -0500

How do I find the intersections between a line and a circle? If I do it by hand, I end up with:

y = mx +b (line equation)
(x-h)^2 + (y- k)^2 = r^2 (circle equation)

do some algebra...

(x-h)^2 + (mx + b - k )^2 = r^2

(x-h)^2 = r^2 - (mx +b -k)^2

How do I make Matlab get x for me?

Re: Intersection between line and half-circle

Rune Allnor — Sun, 08 Nov 2009 08:34:42 -0500

On 8 Nov, 06:37, "Catherine Szeto" <catsz...@gmail.com> wrote:
> How do I find the intersections between a line and a circle? If I do it by hand, I end up with:
>
> y = mx +b (line equation)
> (x-h)^2 + (y- k)^2 = r^2 (circle equation)
>
> do some algebra...
>
> (x-h)^2 + (mx + b - k )^2 = r^2
>
> (x-h)^2 = r^2 - (mx +b -k)^2
>
> How do I make Matlab get x for me?

1) Write out the expression as a 2nd order polynomial in x
2) Write out the standard formula for solving 2nd order
polynomials
3) Find the numbers that go into the formulas
4) Have matlab compute the answers from the formulas and
numbers

Rune

Re: Intersection between line and half-circle

Cat — Mon, 09 Nov 2009 02:58:01 -0500

Rune Allnor <allnor@tele.ntnu.no> wrote in message <0727aeb3-86d2-42f3-b629-4fb12f55a557@d5g2000yqm.googlegroups.com>...
> On 8 Nov, 06:37, "Catherine Szeto" <catsz...@gmail.com> wrote:
> > How do I find the intersections between a line and a circle? If I do it by hand, I end up with:
> >
> > y = mx +b (line equation)
> > (x-h)^2 + (y- k)^2 = r^2 ? (circle equation)
> >
> > do some algebra...
> >
> > (x-h)^2 + (mx + b - k )^2 = r^2
> >
> > (x-h)^2 = r^2 - (mx +b -k)^2
> >
> > How do I make Matlab get x for me?
>
> 1) Write out the expression as a 2nd order polynomial in x
> 2) Write out the standard formula for solving 2nd order
> polynomials
> 3) Find the numbers that go into the formulas
> 4) Have matlab compute the answers from the formulas and
> numbers
>
> Rune

Thanks, I got it working. Turns out I was using a function wrong.