I recently was dying to know how one could find the intersection of two great circles each defined by two points on their circumference. There were only three responses, but they were all good ones. 1. Henry Mumm <[EMAIL PROTECTED]> found the answer in: > GRAPHICS GEMS II > Edited by JAMES ARVO > > IV.2 GETTING AROUND ON A SPHERE > Clifford A. Shaffer > Virginia Tech Blacksburg, Virginia He tried to send it to me in electronic form, but the technologie didn't transfer. Cut and paste from Adobe Reader becomes ASCII hash in email. (But this is the second time in a week I've seen a useful reference to mapping in this series. The other Graphics Gems worth looking at is # IV. These can be had from http://www.Amazon.com for about 50 US clams each. I don't know what they cost in Euro-clams, but I guess we'll all find out soon.) 2. The prize for downright cleverness goes to Bob Edwards <[EMAIL PROTECTED]>. Instead of trying to solve the problem the hard way, he just looked at what the problem really was made of, and found the easy way to do it. Here's how: > First determine the planes defined by the two great circles. > This can be done several ways, depending on how the great > circles themselves are defined. If they are given by three > points on one of the great circles, you can use your high > school math to determine the parameters for the equation of > a plane given three points in space on the plane. In your > case, a third point on each great circle can be calculated > as a mid-point between each pair you were given. > > Then, given the two planes, determine the line of > intersection between them. That line will go through the > center of the great circles' sphere (here's a quick test: > prove that the intersection of two great circles passes > through the center of the defining sphere!). Then find > points one radius distant from the sphere's center along > this line - these two points will be the intersection points > you are looking for. In a follow-up message Bob came up with yet an easier solution. Noting that great circles are straight lines on a Gnomic projection, the trick here is to use the formulae given in Snyder[1] to project the two known points of each great circle and calculate the intersection of the resulting straight lines. 3. I thought I had sifted the net pretty thoroughly in my earlier search, but was fairly amazed to find I had completely missed the "Perfect Page" to answer my question. Thanks go to Richard Herrington <[EMAIL PROTECTED]> for steering me to Ed Williams' "Aviation Formulary" page at http://www.best.com/~williams/avform.htm. This was EXACTLY what I was looking for! Every formula for great circles you could imagine is here, including some I had never considered. Turns out that strictly mapping-oriented web sites were the wrong place to search for great circle information. Sometimes you have to scan sideways when you're on a surfing safari. Williams' page is for aviators. Another group with strong interests in great circles are ham radio operators. Thanks again, folks! - Bill Thoen [1] Snyder, John P., 1987, "Map Projections--A Working Manual" US Geological Service Professional Paper 1395, GPO, Washington, DC. Available from: USGS Information Services (http://www.usgs.gov/esic) Box 25286 Denver Federal Center Denver, CO 80225 Tel: 303-202-4700; Fax: 303-202-4693 reference: P1395 Map projections; a working manual. 1987 $32.00 ---------------------------------------------------------------------- To unsubscribe from this list, send e-mail to [EMAIL PROTECTED] and put "unsubscribe MAPINFO-L" in the message body, or contact [EMAIL PROTECTED]
