* A little Metapost problem.
@ 2001-03-28 16:51 David Arnold
2001-03-28 17:03 ` Marc van Dongen
` (2 more replies)
0 siblings, 3 replies; 5+ messages in thread
From: David Arnold @ 2001-03-28 16:51 UTC (permalink / raw)
Cc: ntg-context
Hans, et al,
Attached is a little doc. At the bottom of the page, I've attempted to draw
to circles tangent to one another. The line PQ is supposed to be a common
tangent line, that is, it is supposed to be tangent to both circles.
I used the formula to compute theta, but the asin routine in Metapost is
not that accurate and the line dips a little too low on the first circle,
and a little high on the second circle.
I'd love to see some Metapost experts demo some cute ways of calculating
the common tangent PQ. Eventually, when I provide answers for my students,
I will need to know that points A and B where the common tangent touches
the two circles, as I will need to draw in radii of the circles
perpendicular to the common tangent to explain how to do the problem.
^ permalink raw reply [flat|nested] 5+ messages in thread
* Re: A little Metapost problem.
2001-03-28 16:51 A little Metapost problem David Arnold
@ 2001-03-28 17:03 ` Marc van Dongen
2001-03-28 18:19 ` Johannes Huesing
2001-03-28 20:38 ` Denis B. Roegel
2 siblings, 0 replies; 5+ messages in thread
From: Marc van Dongen @ 2001-03-28 17:03 UTC (permalink / raw)
Cc: pragma, ntg-context
David Arnold (darnold@northcoast.com) wrote:
: Attached is a little doc. At the bottom of the page, I've attempted to draw
I can't see it.
Regards,
Marc
^ permalink raw reply [flat|nested] 5+ messages in thread
* Re: A little Metapost problem.
2001-03-28 16:51 A little Metapost problem David Arnold
2001-03-28 17:03 ` Marc van Dongen
@ 2001-03-28 18:19 ` Johannes Huesing
2001-03-28 20:38 ` Denis B. Roegel
2 siblings, 0 replies; 5+ messages in thread
From: Johannes Huesing @ 2001-03-28 18:19 UTC (permalink / raw)
On Wed, Mar 28, 2001 at 08:51:10AM -0800, David Arnold wrote:
> Hans, et al,
>
> Attached is a little doc.
Nope, as Marc already observed.
> At the bottom of the page, I've attempted to draw
> to circles tangent to one another. The line PQ is supposed to be a common
> tangent line, that is, it is supposed to be tangent to both circles.
There is a small drawing of an audio tape I did which might be related.
You can get it at http://www.ruhrau.de/hannes/tex/metapost/band.mp
(comments in German, sorry).
Groet
Johannes
--
Domain: Adresse im Internet. Besteht aus einem technischen Teil
(http://www.), einem Namen (erwin_meier) und einer Endung
(zum Beispiel .de fuer Deutschland ...)
Joerg Albrecht, "Die Zeit" 12/2001
^ permalink raw reply [flat|nested] 5+ messages in thread
* Re: A little Metapost problem.
2001-03-28 16:51 A little Metapost problem David Arnold
2001-03-28 17:03 ` Marc van Dongen
2001-03-28 18:19 ` Johannes Huesing
@ 2001-03-28 20:38 ` Denis B. Roegel
2001-03-29 7:22 ` Hans Hagen
2 siblings, 1 reply; 5+ messages in thread
From: Denis B. Roegel @ 2001-03-28 20:38 UTC (permalink / raw)
Cc: pragma, ntg-context
`David Arnold' wrote
>
> Hans, et al,
>
> Attached is a little doc. At the bottom of the page, I've attempted to draw
> to circles tangent to one another. The line PQ is supposed to be a common
> tangent line, that is, it is supposed to be tangent to both circles.
>
> I used the formula to compute theta, but the asin routine in Metapost is
> not that accurate and the line dips a little too low on the first circle,
> and a little high on the second circle.
>
> I'd love to see some Metapost experts demo some cute ways of calculating
> the common tangent PQ. Eventually, when I provide answers for my students,
> I will need to know that points A and B where the common tangent touches
> the two circles, as I will need to draw in radii of the circles
> perpendicular to the common tangent to explain how to do the problem.
Maybe the following is useful?
Denis
beginfig(1);
pair A,B,O,P,Q;
numeric u,r,R;
R=2cm;
r=1cm;
A=origin;
B-A=(5cm,0);
draw fullcircle scaled 2R shifted A;
draw fullcircle scaled 2r shifted B;
O=(1+r/(R-r))[A,B];
P-A=R*(R/arclength(A--O),sqrt(1-(R/arclength(A--O))**2));
Q=(arclength(O--B)/arclength(O--A))[O,P];
draw Q--P--A--B--Q--O--B;
label.rt(btex $O$ etex,O);
label.bot(btex $A$ etex,A);
label.bot(btex $B$ etex,B);
label.top(btex $P$ etex,P);
label.top(btex $Q$ etex,Q);
endfig;
end
^ permalink raw reply [flat|nested] 5+ messages in thread
* Re: A little Metapost problem.
2001-03-28 20:38 ` Denis B. Roegel
@ 2001-03-29 7:22 ` Hans Hagen
0 siblings, 0 replies; 5+ messages in thread
From: Hans Hagen @ 2001-03-29 7:22 UTC (permalink / raw)
Cc: David Arnold, ntg-context
That's a nice one. How about documenting is [i.e. adding a bit of
explanation]. We can then collect them and make a nice example document.
At 10:38 PM 3/28/01 +0200, Denis B. Roegel wrote:
>`David Arnold' wrote
>>
>> Hans, et al,
>>
>> Attached is a little doc. At the bottom of the page, I've attempted to
draw
>> to circles tangent to one another. The line PQ is supposed to be a common
>> tangent line, that is, it is supposed to be tangent to both circles.
>>
>> I used the formula to compute theta, but the asin routine in Metapost is
>> not that accurate and the line dips a little too low on the first circle,
>> and a little high on the second circle.
>>
>> I'd love to see some Metapost experts demo some cute ways of calculating
>> the common tangent PQ. Eventually, when I provide answers for my
students,
>> I will need to know that points A and B where the common tangent touches
>> the two circles, as I will need to draw in radii of the circles
>> perpendicular to the common tangent to explain how to do the problem.
>
>Maybe the following is useful?
>
>Denis
>
>beginfig(1);
>pair A,B,O,P,Q;
>numeric u,r,R;
>R=2cm;
>r=1cm;
>A=origin;
>B-A=(5cm,0);
>draw fullcircle scaled 2R shifted A;
>draw fullcircle scaled 2r shifted B;
>O=(1+r/(R-r))[A,B];
>P-A=R*(R/arclength(A--O),sqrt(1-(R/arclength(A--O))**2));
>Q=(arclength(O--B)/arclength(O--A))[O,P];
>draw Q--P--A--B--Q--O--B;
>label.rt(btex $O$ etex,O);
>label.bot(btex $A$ etex,A);
>label.bot(btex $B$ etex,B);
>label.top(btex $P$ etex,P);
>label.top(btex $Q$ etex,Q);
>endfig;
>end
>
>
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2001-03-28 16:51 A little Metapost problem David Arnold
2001-03-28 17:03 ` Marc van Dongen
2001-03-28 18:19 ` Johannes Huesing
2001-03-28 20:38 ` Denis B. Roegel
2001-03-29 7:22 ` Hans Hagen
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