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From: KBH on 27 Jul 2010 04:23 > Center of circle: (0.0, 20.0) (long,lat) > Point on circle: (0.0, 30.0) > I want the point on the circle to be 90 deg ccw to the west. > > Seemingly, that should be at (-10,20) in the original xyz. But I get > (19.68,-10.63). > Okay, I can do this best with UTM coordinates. Point A is a lat,lon of 20,0 . Point B is a lat,lon of 25,0 . I want to set a point 90 degrees off this line from Point A. Convert lat,lon 20,0 to UTM N,E coordinates of 2214294.0 , 813926.3 and that's in Zone 30. Then convert lat,lon of 25,0 to UTM N,E coordinates of 2768300.2 , 802818.7 . Next inverse the direction from Point A to Point B as InvTan((802818.7 - 813926.3) / (2768300.2 - 2214294.0)) or N01.1486W . The direction is North since the difference in North coordinates was positive and the direction is West since the difference in East coordinates was negative. Then inverse the distance from Point A to Point B as Square Root of ((802818.7 - 813926.3)^2 + (2768300.2 - 2214294.0)^2) or 554117.5 . Now 90 degrees to the left off this line is a direction of N01.1486W + 90 degrees or S88.8514W . So I will forward a point from Point A using a direction of S88.8514W and a distance of 554117.5 . That's 2214294.0 - (Cos(88.8514) * 554117.5) for a Point C North coordinate of 2203186.4 and minus was used since the direction was South. Then 813926.3 - (Sin(88.8514) * 554117.5) is the Point C East coordinate of 259920.1 and minus was used since the direction was West. Finally, convert the Point C UTM N,E coordinates of 2203186.4 , 259920.1 to lat,lon of 19.91025 , -5.29333 . Now I don't post my transverse mercator code. But also note state plane tm would be more accurate than UTM.
From: KBH on 27 Jul 2010 04:52 On Jul 27, 4:23 am, KBH <emptyp...(a)hotmail.com> wrote: > > Center of circle: (0.0, 20.0) (long,lat) > > Point on circle: (0.0, 30.0) > > I want the point on the circle to be 90 deg ccw to the west. > > > Seemingly, that should be at (-10,20) in the original xyz. But I get > > (19.68,-10.63). > > Okay, I can do this best with UTM coordinates. > > Point A is a lat,lon of 20,0 . Point B is a lat,lon of 25,0 . I want > to set a point 90 degrees off this line from Point A. > > Convert lat,lon 20,0 to UTM N,E coordinates of 2214294.0 , 813926.3 > and that's in Zone 30. Then convert lat,lon of 25,0 to UTM N,E > coordinates of 2768300.2 , 802818.7 . > > Next inverse the direction from Point A to Point B as InvTan((802818.7 > - 813926.3) / (2768300.2 - 2214294.0)) or N01.1486W . The direction is > North since the difference in North coordinates was positive and the > direction is West since the difference in East coordinates was > negative. > > Then inverse the distance from Point A to Point B as Square Root of > ((802818.7 - 813926.3)^2 + (2768300.2 - 2214294.0)^2) or 554117.5 . > > Now 90 degrees to the left off this line is a direction of N01.1486W + > 90 degrees or S88.8514W . > > So I will forward a point from Point A using a direction of S88.8514W > and a distance of 554117.5 . That's 2214294.0 - (Cos(88.8514) * > 554117.5) for a Point C North coordinate of 2203186.4 and minus was > used since the direction was South. Then 813926.3 - (Sin(88.8514) * > 554117.5) is the Point C East coordinate of 259920.1 and minus was > used since the direction was West. > > Finally, convert the Point C UTM N,E coordinates of 2203186.4 , > 259920.1 to lat,lon of 19.91025 , -5.29333 . > > Now I don't post my transverse mercator code. But also note state > plane tm would be more accurate than UTM. The geodetic direction from Point A to Point C is 269.877 degrees. The UTM grid direction from Point A to Point C is 268.851 degrees. So the method that was used is closer to a geodtic direction of 270 degrees since a grid forward of N90W would have made a geodetic direction of about 271.026 degrees. Of course the distance here is over 300 miles.
From: W. eWatson on 27 Jul 2010 10:02 Possibly I need to insert the purpose here. I'm working on a problem that involves two earth stations that scan the skies. I'm writing a simulation program (no physics involved) that simply finds the (sky) azimuth/altitude (horizon based. az is measured cw from north, alt from horizon towards north pole) of an event observed simultaneously by each station. UTM is not needed here. No geodesics required at this time. I'm just trying to find a coord system or method that allows me to position my view at each station to determine alt/az from the two stations of two points on the path of an event, start and end. An event occurs that has a path in the sky whose start is given by a lat/long and vertical height above the surface of the (spherical) earth. The user specifies a direction of the path from that surface point ccw from north. The arc length of the path in degrees is specified to the last point. One needs to then compute the lat/long below the end point, and the height of the object at that point, assuming it's diving at some given angle. The idea of the circle described above is just to get a start on this problem by picking a start point on the earth's surface, center of the circle in my example, and moving in a direction (angle ccw from north) to a point on the circumference of the circle (end of ground track of the event). I didn't really need the circle idea, but it just seemed convenient for illustrating the simplistic part of what I was actually doing. It gave me, I thought, a way to see if the rotation around the "center" worked.
From: spudnik on 27 Jul 2010 14:15 I may recommend tripolars, to set-up the problem. > UTM is not needed here. No geodesics required at this time. > > I'm just trying to find a coord system or method that allows me to > position my view at each station to determine alt/az from the two > stations of two points on the path of an event, start and end. > The idea of the circle described above is just to get a start on this > problem by picking a start point on the earth's surface, center of the > circle in my example, and moving in a direction (angle ccw from north) > to a point on the circumference of the circle (end of ground track of > the event). I didn't really need the circle idea, but it just seemed > convenient for illustrating the simplistic part of what I was actually > doing. It gave me, I thought, a way to see if the rotation around the > "center" worked. thus: although one is primary, is it ever considered to be a proper divisor? > A number is prime if and only if it have two divisors. --les ducs d'oil! http://tarpley.net/online-books/george-bush-the-unauthorized-biography/chapter-8-the-permian-basin-gang/ --Light, A History! http://wlym.com/~animations/fermat/index.html
From: KBH on 27 Jul 2010 18:12
On Jul 27, 10:02 am, "W. eWatson" <wolftra...(a)invalid.com> wrote: > Possibly I need to insert the purpose here. I'm working on a problem > that involves two earth stations that scan the skies. I'm writing a > simulation program (no physics involved) that simply finds the (sky) > azimuth/altitude (horizon based. az is measured cw from north, alt from > horizon towards north pole) of an event observed simultaneously by each > station. UTM is not needed here. No geodesics required at this time. > > I'm just trying to find a coord system or method that allows me to > position my view at each station to determine alt/az from the two > stations of two points on the path of an event, start and end. An event > occurs that has a path in the sky whose start is given by a lat/long and > vertical height above the surface of the (spherical) earth. The user > specifies a direction of the path from that surface point ccw from > north. The arc length of the path in degrees is specified to the last > point. One needs to then compute the lat/long below the end point, and > the height of the object at that point, assuming it's diving at some > given angle. > > The idea of the circle described above is just to get a start on this > problem by picking a start point on the earth's surface, center of the > circle in my example, and moving in a direction (angle ccw from north) > to a point on the circumference of the circle (end of ground track of > the event). I didn't really need the circle idea, but it just seemed > convenient for illustrating the simplistic part of what I was actually > doing. It gave me, I thought, a way to see if the rotation around the > "center" worked. You need to locate a point by the intersection of two azimuths and then convert to latitude and longitude ? Well, working with UTM coordinates the intersection of two directions is a simple law of sines calculation. Just inverse the UTM grid distance and direction between the two earth stations first and convert directions to interior angles. Once the intersection point is calculated then the UTM coordinates convert to latitude and longitude. Also a distance and vertical angle to the intersection point allows a height to be calculated. Now there is something I call an approximate-transverse-mercator if a simple conversion between lat,lon and rectangular coordinates is wanted. Search for KBH code on the web that was written for the HP35s. |