[FRIAM] Great Circle

Mon Sep 20 20:03:53 EDT 2021

Quaternions avoid much of the ugly trigonometry since quaternion rotation is along a great circle. They’re very useful for smooth rotations in computer graphics and many aerospace applications.

Ed
_______________________

Ed Angel

Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab)
Professor Emeritus of Computer Science, University of New Mexico

1017 Sierra Pinon
Santa Fe, NM 87501
505-984-0136 (home)		 	angel at cs.unm.edu <mailto:angel at cs.unm.edu>
505-453-4944 (cell) 				http://www.cs.unm.edu/~angel <http://www.cs.unm.edu/~angel>

> On Sep 20, 2021, at 9:19 AM, Steve Smith <sasmyth at swcp.com> wrote:
> 
> Answering my own earlier question (with props) it seems that a (smooth) globe and piece of string would be good support for an intuitive approach.    My sister made a "hanging string lampshade" in 3rd grade by wrapping cotton string soaked in glue around a large balloon and letting it dry.    I inherited it when she went into middle school and was "too cool" for it anymore.   I would lay in bed and stare at it, remembering the challenges (I helped wrap the string) of getting the slick string to do *anything* but following near-great-circles.   The shadows it cast on the walls (and furniture) might have been my first awareness of projective geometry...  I abandoned it when I went to college.
> 
> I assume (REC?) that early age-of-exploration navigators were more constrained by trade-winds and convenient resupply/port-of-call than great-circles, though misunderstanding spherical geometry would be very inconvenient.   
> 
> I also believe that Polynesian stick charts would have great-circleness (or more-to-the-point shortest time paths) built into them by their nature, not any arcane understanding of spherical (ellipsoidal) geometry.  I'm sure they have been studied quite thoroughly.
> 
> 
> 
> On 9/19/21 3:36 PM, Stephen Guerin wrote:
>> In the early 90s, my expat friends in Beijing would often debate which were the closer US Cities to Beijing by eyeballing the globe - wish we had this too for easy lookup back then. Of course, we could have used lat/longs and calculated haversine distances but we had pints to drink - and frankly it would have been difficult for me to find the algorithm in the nascent web back then ;-)
>> 
>> Beijing (PEK) Great Circle Distances for 10 US cities <https://www.greatcirclemap.com/globe?routes=%20PEK-SEA%2C%20PEK-LAX%2C%20PEK-DET%2C%20PEK-SAN%2C%20PEK-MSP%2C%20PEK-YYZ%2C%20PEK-EWR%2C%20PEK-ORD%2C%20PEK-ANC%2C%20PEK-BGR%2C%20PEK-HNL>
>> 
>> <image.png>
>> 
>> 
>> _______________________________________________________________________
>> Stephen.Guerin at Simtable.com <mailto:stephen.guerin at simtable.com>
>> CEO, Simtable  http://www.simtable.com <http://www.simtable.com/>
>> 1600 Lena St #D1, Santa Fe, NM 87505
>> office: (505)995-0206 mobile: (505)577-5828
>> twitter: @simtable
>> z <http://zoom.com/j/5055775828>oom.simtable.com <http://oom.simtable.com/>
>> 
>> On Sun, Sep 19, 2021 at 3:22 PM Frank Wimberly <wimberly3 at gmail.com <mailto:wimberly3 at gmail.com>> wrote:
>> That gives a good view, Stephen.  Hawaii is farther south than I thought.  Thanks.
>> 
>> ---
>> Frank C. Wimberly
>> 140 Calle Ojo Feliz, 
>> Santa Fe, NM 87505
>> 
>> 505 670-9918
>> Santa Fe, NM
>> 
>> On Sun, Sep 19, 2021, 3:19 PM Stephen Guerin <stephen.guerin at simtable.com <mailto:stephen.guerin at simtable.com>> wrote:
>> I was going to post this similar site but Ed beat me with his :-) This one also has a globe view...
>> 
>> https://www.greatcirclemap.com/globe?routes=CLT-HNL <https://www.greatcirclemap.com/globe?routes=CLT-HNL>
>> _______________________________________________________________________
>> Stephen.Guerin at Simtable.com <mailto:stephen.guerin at simtable.com>
>> CEO, Simtable  http://www.simtable.com <http://www.simtable.com/>
>> 1600 Lena St #D1, Santa Fe, NM 87505
>> office: (505)995-0206 mobile: (505)577-5828
>> twitter: @simtable
>> z <http://zoom.com/j/5055775828>oom.simtable.com <http://oom.simtable.com/>
>> 
>> On Sun, Sep 19, 2021 at 2:03 PM Frank Wimberly <wimberly3 at gmail.com <mailto:wimberly3 at gmail.com>> wrote:
>> Thanks, Ed.  That's useful.
>> 
>> ---
>> Frank C. Wimberly
>> 140 Calle Ojo Feliz, 
>> Santa Fe, NM 87505
>> 
>> 505 670-9918
>> Santa Fe, NM
>> 
>> On Sun, Sep 19, 2021, 1:54 PM Edward Angel <angel at cs.unm.edu <mailto:angel at cs.unm.edu>> wrote:
>> Close: https://www.airmilescalculator.com/distance/clt-to-hnl/ <https://www.airmilescalculator.com/distance/clt-to-hnl/>
>> _______________________
>> 
>> Ed Angel
>> 
>> Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab)
>> Professor Emeritus of Computer Science, University of New Mexico
>> 
>> 1017 Sierra Pinon
>> Santa Fe, NM 87501
>> 505-984-0136 (home)		 	angel at cs.unm.edu <mailto:angel at cs.unm.edu>
>> 505-453-4944 (cell) 				http://www.cs.unm.edu/~angel <http://www.cs.unm.edu/~angel>
>> 
>>> On Sep 19, 2021, at 1:48 PM, Frank Wimberly <wimberly3 at gmail.com <mailto:wimberly3 at gmail.com>> wrote:
>>> 
>>> Not to change the subject but...
>>> 
>>> A large airliner recently, 15 minutes ago, flew over Santa Fe headed west.  My Flight Radar app tells me that it's a Boeing 777 going from Charlotte to Honolulu at an altitude of 38000 feet.  I wouldn't have thought that Santa Fe was on a great Circle route between those two cities.  But maybe it is.
>>> 
>>> ---
>>> Frank C. Wimberly
>>> 140 Calle Ojo Feliz, 
>>> Santa Fe, NM 87505
>>> 
>>> 505 670-9918
>>> Santa Fe, NM
>>> 
>>> .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - .
>>> FRIAM Applied Complexity Group listserv
>>> Zoom Fridays 9:30a-12p Mtn UTC-6  bit.ly/virtualfriam <http://bit.ly/virtualfriam>
>>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com <http://redfish.com/mailman/listinfo/friam_redfish.com>
>>> FRIAM-COMIC http://friam-comic.blogspot.com/ <http://friam-comic.blogspot.com/>
>>> archives:
>>> 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ <https://redfish.com/pipermail/friam_redfish.com/>
>>> 1/2003 thru 6/2021  http://friam.383.s1.nabble.com/ <http://friam.383.s1.nabble.com/>
>> 
>> 
>> .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - .
>> FRIAM Applied Complexity Group listserv
>> Zoom Fridays 9:30a-12p Mtn UTC-6  bit.ly/virtualfriam <http://bit.ly/virtualfriam>
>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com <http://redfish.com/mailman/listinfo/friam_redfish.com>
>> FRIAM-COMIC http://friam-comic.blogspot.com/ <http://friam-comic.blogspot.com/>
>> archives:
>>  5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ <https://redfish.com/pipermail/friam_redfish.com/>
>>  1/2003 thru 6/2021  http://friam.383.s1.nabble.com/ <http://friam.383.s1.nabble.com/>
>> 
>> .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - .
>> FRIAM Applied Complexity Group listserv
>> Zoom Fridays 9:30a-12p Mtn UTC-6  bit.ly/virtualfriam <http://bit.ly/virtualfriam>
>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com <http://redfish.com/mailman/listinfo/friam_redfish.com>
>> FRIAM-COMIC http://friam-comic.blogspot.com/ <http://friam-comic.blogspot.com/>
>> archives:
>>  5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ <https://redfish.com/pipermail/friam_redfish.com/>
>>  1/2003 thru 6/2021  http://friam.383.s1.nabble.com/ <http://friam.383.s1.nabble.com/>
>> 
>> .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - .
>> FRIAM Applied Complexity Group listserv
>> Zoom Fridays 9:30a-12p Mtn UTC-6  bit.ly/virtualfriam <http://bit.ly/virtualfriam>
>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com <http://redfish.com/mailman/listinfo/friam_redfish.com>
>> FRIAM-COMIC http://friam-comic.blogspot.com/ <http://friam-comic.blogspot.com/>
>> archives:
>>  5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ <https://redfish.com/pipermail/friam_redfish.com/>
>>  1/2003 thru 6/2021  http://friam.383.s1.nabble.com/ <http://friam.383.s1.nabble.com/>
>> 
>> .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - .
>> FRIAM Applied Complexity Group listserv
>> Zoom Fridays 9:30a-12p Mtn UTC-6  bit.ly/virtualfriam <http://bit.ly/virtualfriam>
>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com <http://redfish.com/mailman/listinfo/friam_redfish.com>
>> FRIAM-COMIC http://friam-comic.blogspot.com/ <http://friam-comic.blogspot.com/>
>> archives:
>>  5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ <https://redfish.com/pipermail/friam_redfish.com/>
>>  1/2003 thru 6/2021  http://friam.383.s1.nabble.com/ <http://friam.383.s1.nabble.com/>
>> 
>> 
>> .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - .
>> FRIAM Applied Complexity Group listserv
>> Zoom Fridays 9:30a-12p Mtn UTC-6  bit.ly/virtualfriam
>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com <http://redfish.com/mailman/listinfo/friam_redfish.com>
>> FRIAM-COMIC http://friam-comic.blogspot.com/ <http://friam-comic.blogspot.com/>
>> archives:
>>  5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ <https://redfish.com/pipermail/friam_redfish.com/>
>>  1/2003 thru 6/2021  http://friam.383.s1.nabble.com/ <http://friam.383.s1.nabble.com/>
> 
> .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - .
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn UTC-6  bit.ly/virtualfriam
> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> FRIAM-COMIC http://friam-comic.blogspot.com/
> archives:
> 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/
> 1/2003 thru 6/2021  http://friam.383.s1.nabble.com/

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20210920/bfaecafb/attachment.html>