* 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 > > ------------------------------------------------------------------------- Hans Hagen | PRAGMA ADE | pragma@wxs.nl Ridderstraat 27 | 8061 GH Hasselt | The Netherlands tel: +31 (0)38 477 53 69 | fax: +31 (0)38 477 53 74 | www.pragma-ade.com ------------------------------------------------------------------------- ^ permalink raw reply [flat|nested] 5+ messages in thread
end of thread, other threads:[~2001-03-29 7:22 UTC | newest] Thread overview: 5+ messages (download: mbox.gz / follow: Atom feed) -- links below jump to the message on this page -- 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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