Post by thread:[PICLIST] [PIC]Find center point of circle?

----- Original Message ----- From: "James Williams" <.....jlw.creditviewKILLspam@spam@VERIZON.NET> To: <PICLISTKILLspamMITVMA.MIT.EDU> Sent: Thursday, January 10, 2002 1:48 PM Subject: [PIC]Find center point of circle? > Hello, > > Can someone tell me how to find the center point of a circle when given the > radius and two points which lie on the circle. You can draw a circle of the same radius around each point. These circles have one or two points of intersection. (1 if the points are on a diameter, else 2). Then you have to decide which of the two points is the true center, because your problem is not well constrained -- you need one more point on the circle to be sure. /\/\/\/*=Martin -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email .....listservKILLspam.....mitvma.mit.edu with SET PICList DIGEST in the body

Let's try this: 1. Draw a line through the 2 points 2. Where the line intersects the circle, draw a circle around each point 3. Draw a line through the intersection of these circles 4. Where this line intersects the 1st circle, draw a circle around each point 5. Draw a line between the intersections of these circles 6. Where the line in (5) and (3) intersect, is that not the center? Regards Chris A -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email EraseMElistservspam_OUTTakeThisOuTmitvma.mit.edu with SET PICList DIGEST in the body

> -----Original Message----- > From: Jafta [jaftaspam_OUTADEPT.CO.ZA] > > Let's try this: > 1. Draw a line through the 2 points > 2. Where the line intersects the circle, draw a circle > around each point > 3. Draw a line through the intersection of these circles > 4. Where this line intersects the 1st circle, draw a > circle around each > point > 5. Draw a line between the intersections of these circles > 6. Where the line in (5) and (3) intersect, is that not the center? > > Regards > > Chris A I think you're close, but the intersection of the two lines is just inside the real circle, not the center. Here's one way you might solve the problem: 1. Draw a circle of the same radius as your circle around each of your points. 2. If the circles have one intersection, you're lucky and that is your center and you're done. 3. Draw a line between your two original points. 4. The point of intersection between the two circles you drew that is closest to your line is the center of your circle. -Mike -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email @spam@listservKILLspammitvma.mit.edu with SET PICList DIGEST in the body

----- Original Message ----- From: "Jafta" <KILLspamjaftaKILLspamADEPT.CO.ZA> To: <RemoveMEPICLISTTakeThisOuTMITVMA.MIT.EDU> Sent: Thursday, January 10, 2002 2:58 PM Subject: Re: [PIC]Find center point of circle? > Let's try this: > 1. Draw a line through the 2 points > 2. Where the line intersects the circle, draw a circle around each point > 3. Draw a line through the intersection of these circles > 4. Where this line intersects the 1st circle, draw a circle around each > point Which was the first circle? The one we don't know? > 5. Draw a line between the intersections of these circles > 6. Where the line in (5) and (3) intersect, is that not the center? For a given radius there are always two possible circles that go through two arbitrary points unless the points are exactly two radii apart. There is just not enough information available to resolve the matter no matter how many circles and lines you draw. /\/\/\/*=Martin -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email spamBeGonelistservspamBeGonemitvma.mit.edu with SET PICList DIGEST in the body

> > Let's try this: > > 1. Draw a line through the 2 points > > 2. Where the line intersects the circle, draw a circle around each > point > > 3. Draw a line through the intersection of these circles > > 4. Where this line intersects the 1st circle, draw a circle around each > > point > > Which was the first circle? The one we don't know? Well, no one said that we don't know the circle ... We don't know it's center .... > > > 5. Draw a line between the intersections of these circles > > 6. Where the line in (5) and (3) intersect, is that not the center? > > For a given radius there are always two possible circles that go through two {Quote hidden}> arbitrary points unless the points are exactly two radii apart. There is > just not enough information available to resolve the matter no matter how > many circles and lines you draw. > /\/\/\/*=Martin > > -- > http://www.piclist.com#nomail Going offline? Don't AutoReply us! > email TakeThisOuTlistservEraseMEspam_OUTmitvma.mit.edu with SET PICList DIGEST in the body > > > > -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email RemoveMElistservTakeThisOuTmitvma.mit.edu with SET PICList DIGEST in the body

----- Original Message ----- From: "Fabio Pereira" <fabioEraseME.....PP.ADV.BR> To: <EraseMEPICLISTMITVMA.MIT.EDU> Sent: Thursday, January 10, 2002 4:40 PM Subject: Re: [PIC]Find center point of circle? {Quote hidden}> > > Let's try this: > > > 1. Draw a line through the 2 points > > > 2. Where the line intersects the circle, draw a circle around each > > point > > > 3. Draw a line through the intersection of these circles > > > 4. Where this line intersects the 1st circle, draw a circle around > each > > > point > > > > Which was the first circle? The one we don't know? > > Well, no one said that we don't know the circle ... We don't know it's > center .... Well the original question was: "Can someone tell me how to find the center point of a circle when given the radius and two points which lie on the circle." I guess I interpreted that too strictly... /\/\/\/*=Martin -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email RemoveMElistservEraseMEEraseMEmitvma.mit.edu with SET PICList DIGEST in the body

{Quote hidden}> -----Original Message----- > From: Martin Peach [RemoveMEmartinrpspam_OUTKILLspamvax2.concordia.ca] > > ----- Original Message ----- > From: "Jafta" <RemoveMEjaftaTakeThisOuTspamADEPT.CO.ZA> > To: <EraseMEPICLISTspamspamBeGoneMITVMA.MIT.EDU> > Sent: Thursday, January 10, 2002 2:58 PM > Subject: Re: [PIC]Find center point of circle? > > > > Let's try this: > > 1. Draw a line through the 2 points > > 2. Where the line intersects the circle, draw a circle > around each > point > > 3. Draw a line through the intersection of these circles > > 4. Where this line intersects the 1st circle, draw a > circle around each > > point > > Which was the first circle? The one we don't know? > > > 5. Draw a line between the intersections of these circles > > 6. Where the line in (5) and (3) intersect, is that not > the center? > > For a given radius there are always two possible circles that > go through two > arbitrary points unless the points are exactly two radii > apart. There is > just not enough information available to resolve the matter > no matter how > many circles and lines you draw. Actually, if you open the problem up to drawing circles of a given radius around two arbitrary points, there are four possibilities: 1. The two points are the same, so both circles intersect at all of their points. 2. The two points are twice the radius apart, so the circles intersect at one point. 3. The two points are unique and less than twice the radius apart, so the circles intersect at two points. 4. The two points are greater twice the radius apart, so the circles don't intersect. The way the original problem was stated, the two points are on a circle of a given radius. That allows for case 1, 2, or 3. If it's case 1, you can't solve the problem. If it's case 2, the center of the original circle is the point of intersection between the two circles. Case 3 is the interesting one. I haven't come up with a formal proof, but I believe that the center of the original circle is the point of intersection closest to the line through your two initial points. -Mike -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email RemoveMElistservKILLspammitvma.mit.edu with SET PICList DIGEST in the body

But ... the two points of intersection are always going to be the same distance from the line joining the two points we were given. Now if we had 3 points there could be no doubt - except in the case you mentioned where all given points are in the same place >>> mdippersSTOPspamspam_OUTHARRIS.COM 01/10/02 04:11PM >>> <snip> 3. The two points are unique and less than twice the radius apart, so the circles intersect at two points. <snip> Case 3 is the interesting one. I haven't come up with a formal proof, but I believe that the center of the original circle is the point of intersection closest to the line through your two initial points. -Mike -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email spamBeGonelistservSTOPspamEraseMEmitvma.mit.edu with SET PICList DIGEST in the body -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email KILLspamlistservspamBeGonemitvma.mit.edu with SET PICList DIGEST in the body

> From: Dipperstein, Michael > > Case 3 is the interesting one. I haven't come up with a > formal proof, but I believe that the center of the original > circle is the point of intersection closest to the line > through your two initial points. > > -Mike Forget that. I just came up with a class of counter examples. -Mike -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email EraseMElistservEraseMEmitvma.mit.edu with SET PICList DIGEST in the body

On Thu, 10 Jan 2002, Dipperstein, Michael wrote: > Actually, if you open the problem up to drawing circles of a given radius around > two arbitrary points, there are four possibilities: > > 1. The two points are the same, so both circles intersect at all of their > points. > If it's case 1, you can't solve the problem. Sure you can. Draw a circle with radius r around the point. It will intersect the original circle at two points. Connect these two points with a line l. Now draw a line m perpendicular to line l at its midpoint. That will be a diameter line, simple to find the center from there (thanks, Fr.Tom!!) Dale (so easy to see farther when you can stand on someone's shoulders!) -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email @spam@listserv@spam@spam_OUTmitvma.mit.edu with SET PICList DIGEST in the body

Hi all, As an aside, is there a standard way of doing this in machining? In other words, I have always wondered how machinists find the exact center of a part of circular cross-section, considering that the cross-section may only be approximately circular. I have always done this by measuring across the piece to find the longest line segment that I could across it (a diameter rather than a general chord), and then measure half way across that, or find two diameters and find their intersection, or draw a circle of the same radius on paper with a compass, make a hole where the compass point was, lay the circle on top of the part, and mark through the hole. However, I was never sure if there was a better way to do it. Sean At 04:50 PM 1/10/02 -0500, you wrote: {Quote hidden}> > From: Dipperstein, Michael > > > > Case 3 is the interesting one. I haven't come up with a > > formal proof, but I believe that the center of the original > > circle is the point of intersection closest to the line > > through your two initial points. > > > > -Mike > >Forget that. I just came up with a class of counter examples. > >-Mike > >-- >http://www.piclist.com#nomail Going offline? Don't AutoReply us! >email spamBeGonelistservKILLspammitvma.mit.edu with SET PICList DIGEST in the body ---------------------------------------------------- Sign Up for NetZero Platinum Today Only $9.95 per month! http://my.netzero.net/s/signup?r=platinum&refcd=PT97 -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email .....listservspam_OUTmitvma.mit.edu with SET PICList DIGEST in the body

> As an aside, is there a standard way of doing this in machining? Yes, use a combination square with a center head. www.suncoasttools.com/shop/CombinationSquare-Protractor-CenterGage-Ru le.html The, "V" shaped, center head mounts on the rule so that the edge of the rule runs dead center in the "V". Here's a really nice one with the head installed. http://www.starrett.com/squares.htm Paul ========================================= Paul Hutchinson Chief Engineer Maximum Inc., 30 Samuel Barnet Blvd. New Bedford, MA 02745 TakeThisOuTphutchinson.....TakeThisOuTimtra.com http://www.maximum-inc.com ========================================= -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email TakeThisOuTlistservKILLspamspammitvma.mit.edu with SET PICList DIGEST in the body

In that case a trig solution would go like this: 1. Draw a line between the two known points. 2. From the midpoint of this line, draw a perpendicular line in the known direction of the circle's center point. The endpoint of this line segment will be the center of the circle. Let's call it's unknown length A. 3. A right triangle is now defined by the line segment you just drew (of unknown length A.), half of the line segment drawn in step 1 of known length, let's call B (B is half the distance beween the 2 original points) and finally the hypotenuse is R. 4. For a right triangle, A^2 + B^2 = C^2 or in our case A^2 + B^2 = R^2, solving for R yields: A = sqrt(R^2 - B^2) 5. Now you have the distance to draw the line segment described in step 2 to the center of the circle. You didn't mention what type of coordinate system you were using, but doing this in either a rectangular or polar coordinate system is fairly straightforward. Kirk > {Original Message removed}

> Can someone tell me how to find the center point of a circle > when given the radius and two points which lie on the circle. Recall that two points and a radius are defined by two circles -- mirror images -- on either side of the chord line connecting the two given points. Further data is needed to decide which circle is the desired one. method 1 -------- 1) set a compass (not magnetic, point & pencil type) to the exact given radius of the circle 2) put the compass' pivot on either given point, draw a half circle arc on the side towards the other given point 3) put the compass' pivot on the other given point, draw an arc on the side towards step 2's arc -- two intersections are the centers of the two possible desired circles. method 2 -------- 1) draw a straight line through the two points 2) set a compass (not magnetic, point & pencil type) to a reasonable distance, usually slightly larger than the chord generated in step 1 3) put the pivot on either given point, draw a half circle arc on the side towards the other point 4) put the compass' pivot on the other given point, draw a second half circle arc on side towards step 3's arc 5) the arcs in steps 3 & 4 intersect in two places; use the straight edge to draw a line through these two intersection points -- this line bisects the chord (which may be handy) 6) set the compass for the exact radius of the circle 7) put the compass' pivot on either given point, draw an arc which intersects the chord bisector line -- intersection is the center of the desired circle. Or use both methods together -- skew between the "answers" gives you a measurement of your error in finding the center. Lee Jones -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email RemoveMElistservspamBeGonemitvma.mit.edu with SET PICList DIGEST in the body

> As an aside, is there a standard way of doing this in machining? In other > words, I have always wondered how machinists find the exact center of a > part of circular cross-section, considering that the cross-section may only > be approximately circular. I have always done this by measuring across the I don't know the name of the tool but it's essentially like a "T" square except that the "T" is a "V" shape. The ruler comes out of the inside of the "V". You scribe a line across the end of the piece, move it around roughly 90 degrees and scribe another line. If your stock is round the two lines cross at the center. Tim -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email spamBeGonelistserv@spam@spam_OUTmitvma.mit.edu with SET PICList DIGEST in the body

>Case 3 is the interesting one. I haven't come up with a formal proof, but I >believe that the center of the original circle is the point of intersection >closest to the line through your two initial points. Trouble is there are 2 circles that still correspond to this definition - consider the symbol for a current generator, the line you talk of is between the intersection points of the two circles. Now is it the right hand or left hand (or upper or lower depending on how its drawn) that is the original circle? -- http://www.piclist.com hint: To leave the PICList TakeThisOuTpiclist-unsubscribe-requestspammitvma.mit.edu

>Let's try this: >1. Draw a line through the 2 points >2. Where the line intersects the circle, draw a circle around each >point ^^^ What circle ? >3. Draw a line through the intersection of these circles >4. Where this line intersects the 1st circle, draw a circle around >each >point >5. Draw a line between the intersections of these circles >6. Where the line in (5) and (3) intersect, is that not the center? Graphically you use a compass, set it to the known radius value using a ruler, then apply it on each point and draw a circle. The two circles intersect in two points which are the centers of the two possible circles you are looking for. But I suspect that this is not what he wants... Peter -- http://www.piclist.com hint: To leave the PICList piclist-unsubscribe-requestEraseMEmitvma.mit.edu

There are two circles that satisfy your conditions. The centers of both circles are on a line that cuts the middle of the distance between the tangent points at right angles. To find the centers apply the hypothenuse theorem to the radius (is hyp) and half the distance between the points (a cathete), to find the distance to the center(s). The 'side' on which they are is unedfined (+/-sqrt(0.25*distance^2+r^2)). Then you probably want to adapt this to the actual coordinate system you are using (cartesian, bitmap etc). Peter PS: Are you in an exam ? ;-) -- http://www.piclist.com hint: To leave the PICList RemoveMEpiclist-unsubscribe-requestEraseMEspam_OUTmitvma.mit.edu

> Hi all, > > As an aside, is there a standard way of doing this in machining? In > other > words, I have always wondered how machinists find the exact center of a One way is to use a steel ruler and a scribing needle to find large diameters as you suggest and scribe a line for each such found diameter. After 20 or so scribeds line the center will be pretty easy to see with the bare eye. This is not very accurate. Another way involves a compass with steel needles. It is set to slightly more than half the diameter and used to scribe arcs near the presumed center with a point on the rim (you can use a tight fitting tube around the piece to keep the outer point from slipping off). You scribe 3 arcs about 120 degrees apart, then take 3 positions between the previous 3 120 degree arc's centers and radius the middle of the previously traced triangle. This results in diminishing triangles being traced near the center of the piece. The center is in the middle of the smallest one. Usually you find it to 1% in 9 scribed arcs. This also works with long strings and over long distances by other means (radio df probably). It works because the radius picked in the 'next' try is an improvement vs. the previous estimate. Peter -- http://www.piclist.com hint: To leave the PICList @spam@piclist-unsubscribe-requestRemoveMEEraseMEmitvma.mit.edu