"Thomas" <tho### [at] gmxnet> wrote:
> Hi,
>
> For my animation (see animations groups, Lego ladder) I need to calculate the
> intersection between two circles. Does anyone have have an example of this they
> would like to share?
>

I already had some code for this laying around :) It uses calculations from this
page: http://2000clicks.com/mathhelp/GeometryConicSectionCircleIntersection.aspx

The circles are assumed to be laying along the X & Y axes and centered at Z=0.

// code //

#declare Pt1 = <-.7,0,0>;
#declare Rad1 = 1.5;

#declare Pt2 = <.75,0,0>;
#declare Rad2 = 1;

#declare D = vlength(Pt2-Pt1);
#declare K = .25*sqrt((pow(Rad1+Rad2,2)-D*D)*(D*D-pow(Rad1-Rad2,2)));

#declare IntersectX = (.5*(Pt2.x+Pt1.x) +
..5*(Pt2.x-Pt1.x)*(Rad1*Rad1-Rad2*Rad2)/(D*D) + 2*(Pt2.y-Pt1.y)*K/(D*D));
#declare IntersectY = (.5*(Pt2.y+Pt1.y) +
..5*(Pt2.y-Pt1.y)*(Rad1*Rad1-Rad2*Rad2)/(D*D) + 2*(Pt2.x-Pt1.x)*K/(D*D));

// display circles
union{
 torus{Rad1, 3/image_width rotate x*90 translate Pt1}
 torus{Rad2, 3/image_width rotate x*90 translate Pt2}
 pigment{rgb x}
}

// display intersection
union{
 cylinder{
  -y*2,y*2,3/image_width
  translate x*IntersectX
 }
 cylinder{
  -x*2,x*2,3/image_width
  translate y*IntersectY
 }
 pigment{rgb x+y}
 finish{ambient 1 diffuse 0}
}

// end code //


Hope this helps!

Sam

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