Re: Rectangle and Circle
- To: mathgroup at smc.vnet.net
- Subject: [mg105550] Re: Rectangle and Circle
- From: dh <dh at metrohm.com>
- Date: Tue, 8 Dec 2009 06:44:49 -0500 (EST)
- References: <hfi936$cj4$1@smc.vnet.net>
Hi,
Assuming that you have a rectangle and a circle, and all vertices of the
rectangle have a greater distance from the center of the circle than the
radius. Then your question boils down to whether some point on an edge
has a distance smaller that the radius from the center.
Assume for simplicity that the center is at the origin (subtract the
origine).
Given the 4 vertices: p1={x1,y1},p2,p3,p4. The edge direction: e1=p2-p1,..
Any point on the edge p2...p1 can be written:line1= p1+z1 (p2-p1) with a
parameter z1.
The direction perpendicular to e1 is: r1={{0,1},{-1,0}}.e1
For the distance of the edge from the origin and the intersection of the
corresponding line with line1 we have the equation:
eq= r1 + z1(p2-p1) == z2 r1/Norm[r1]
we may solve for the parameter z1 and distance z2:
{param,dist}={z1,z2}/. Solve[eq,{z1,z2}][[1]]
Now, if 0<param<1 and dist> radius, the the circle cuts the edge.
Daniel
zowtar wrote:
> I don't know if here is the right place to ask it, but I don't know
> where to go... so...
>
> I have...
> a circle: center point and radius size.
> a rectangle: 4 corner points.
>
> I already know if the circle is inside of the rectangle, or if the
> rectangle is inside the circle, or if the case 1 of my image
> happens... I want to know if the circle has an intersection with the
> rectangle like the case 2 of my image... Any ideia?
>
> http://img199.imageshack.us/img199/9347/cases.gif
>
