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From: <HIDDEN>
Newsgroups: comp.soft-sys.matlab
Subject: Re: tangent to circles curve fitting
Date: Thu, 23 Dec 2010 09:26:04 +0000 (UTC)
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Xref: news.mathworks.com comp.soft-sys.matlab:697782

Well,
im having problems when those points are not collinear. Probably ive wrote it wrong.
For example,

%b1 = [p1,q1] r1;
%b2 = [p2,q2] r2;
%b3 = [p3,q3] r3;

p1 = 1;
p2 = 4;
p3 = 10;
q1 = 0;
q2 = 0;
q3 = 0;
r1 = 0.5;
r2 = 2;
r3 = 3;

%Get tangent for consecutive circles
d2 = (p2-p1)^2+(q2-q1)^2;
r = sqrt(d2-(r2-r1)^2);
s = ((q2-q1)*r+(p2-p1)*(r2-r1))/d2;
c = ((p2-p1)*r-(q2-q1)*(r2-r1))/d2;
x1 = p1-r1*s;
y1 = q1+r1*c;
x2 = p2-r2*s;
y2 = q2+r2*c;

d2a = (p3-p2)^2+(q3-q2)^2;
ra = sqrt(d2a-(r3-r2)^2);
sa = ((q3-q2)*ra+(p3-p2)*(r3-r2))/d2a;
ca = ((p3-p2)*ra-(q3-q2)*(r3-r2))/d2a;
x2a = p2-r2*sa;
y2a = q2+r2*ca;
x3 = p3-r3*sa;
y3 = q3+r3*ca;

%Draw the circle
THETA=linspace(0,pi,100);
RHO=ones(1,100)*r1;
[X,Y] = pol2cart(THETA,RHO);
X=X+p1;
Y=Y+q1;
H=plot(X,Y,'r-');
axis square;

hold on

THETA=linspace(0,pi,100);
RHO=ones(1,100)*r2;
[X,Y] = pol2cart(THETA,RHO);
X=X+p2;
Y=Y+q2;
H=plot(X,Y,'g-');
axis square;

hold on

THETA=linspace(0,pi,100);
RHO=ones(1,100)*r3;
[X,Y] = pol2cart(THETA,RHO);
X=X+p3;
Y=Y+q3;
H=plot(X,Y,'g-');
axis square;

hold on

%XT = [x1 x2];
%YT = [y1 y2];
%line(XT,YT);

%Draw the tangent
Y = 0:0.1:10;
Q = [x1 1; x2 1];
E = [y1;y2];
T = Q\E;
Z = T(1)*Y + T(2);

plot(Y,Z);

hold on

Y1 = 0:0.1:10;
Q1 = [x2a 1; x3 1];
E1 = [y2a;y3];
T1 = Q1\E1;
Z1 = T1(1)*Y1 + T1(2);

plot(Y1,Z1);

hold on

%Plot all the curves
axis equal;
axis([0 12 0 5]);
grid on
plot(l1,l2,Z,Z1,'g.-');

"John D'Errico" <woodchips@rochester.rr.com> wrote in message <ieu0k4\$itm\$1@fred.mathworks.com>...
> "Camp Camp" wrote in message <iettmd\$9k4\$1@fred.mathworks.com>...
> > Hi guys,
> > I'm using this question as cue for my own...
> > i have also a series of consecutive circles, defined by someone the center and radius. But this must follow the rule thats is: the second circle has to have radius greater than first, and third has to have radius greater than second. I know that this could be a system with multiple solutions, but is there any possibilities to have a tangent to those 3 circles? Something like a fit linear.
> >
>
> So what stops you from finding the lines that are tangent
> to consecutive circles? Since you tell us that already KNOW
> the radii for these circles, then just check to see if the lines
> are collinear. If you don't know the radii of the circles,
> then the problem is trivial.
>
> What is the problem here?
>
> John
```