Doubts about how to use azimuth values from a Coordinate Object. Juan Antonio Breña Moral

Transcription

1 Douts out how to use zimuth vlues from Coordinte Ojet Jun Antonio Breñ Morl

2 # Definition An Azimuth is the ngle from referene vetor in referene plne to seond vetor in the sme plne, pointing towrd, (ut not neessrily meeting), something of interest. For exmple, with the se s your referene plne, the zimuth of the Sun might e the ngle etween due North nd the point on the horizon the Sun is urrently over. An imginry line drwn long the surfe of the se might point in the diretion of the Sun, ut would oviously never meet it. Soure: Wikipedi

3 # Prolem I hve stored GPS Point in street. I sve the sme GPS point severl times to void generting errors in the mesure proess. The point is: gol new Coordintes( , , ); I red vlues from GPS reeiver nd lulte the distne nd zimuth from urrent GPS vlue to gol. distne urrent.distne(gol); zimuth (int) urrent.zimuthto(gol);

4 distne urrent.distne(gol); zimuth (int) urrent.zimuthto(gol); //zimut in this se is 44 º //distne in this se is ~54.35m.? 44º 80 º 44º 90 º 0 º

5 Exmple: Gol: , Current: , º Compss nd Azimuth with the sme vlue, 44

6 Exmple: Gol: , Current: , ? 44º wth?v3na0v8rrpxu

7 # Prolem 54.35m. 44º Azimuth True North

8 # Prolem 54.35m. 44º GPS Referene Point X Azimuth

9 # Prolem Is it possile to lulte the tringle X--? To lulte α? 54.35m. 44º GPS Referene Point X Azimuth The north pole is the third point β 44º? α - β X α

10 #3 Questions I hve written some questions out how to use Coordintes ojet:. Is orret the wy to lulte zimuth? urrent.zimuthto(gol) [Current wy] or gol.zimuthto(urrent);?. If my wy is orret how to understnd the vlue 44º? How to mnge? 3. Tke look out video to understnd my prolem:. If you see, I wlk on the street while zimuth try to led to nother ngle out of the street (green line) 3. How to lulte red line?

11 Trigonometri rtios in right-ngled tringle opposite side sin hypotenuse B hypotenuse opposite side Bk to ontent A Adjent side C

12 Trigonometri rtios in right-ngled tringle djent side os hypotenuse B hypotenuse opposite side Bk to ontent A Adjent side C

13 Trigonometri rtios in right-ngled tringle opposite side tn djent side B hypotenuse opposite side Bk to ontent A Adjent side C

14 Simple trigonometri identities C B A os sin os Qsin Bk to ontent

15 Simple trigonometri identities Q sin os tn tn sin os A B C Bk to ontent

16 Simple trigonometri identities Q os sin(90 ) sin(90 ) os A 90 B C Bk to ontent

17 Simple trigonometri identities Q sin os(90 ) os(90 ) sin A 90 B C Bk to ontent

18 Simple trigonometri identities Q tn tn(90 ) tn(90 ) 90 B tn A C Bk to ontent

19 Trigonometri rtios of speil ngle 45 o Qx + x sin os 45 x tn Bk to ontent

20 Trigonometri rtios of speil ngle 30 o,60 o. Q y + y 3 y 3 sin 60 os 60 3 sin 30 os 30 tn 60 tn Bk to ontent y 3 60

21 Pythgoren Theorem ^ ^ + ^ ^ ^ - ^ ^ ^ - ^ Reltionship mong the lengths of sides. Side Side Side

22 Lw of Sines Sys: / Sin A / sin B / sin C Where A, B, nd C re interior ngles nd,, re lengths of sides. A C B

23 The Pythgoren Theorem If you squre the length of the two shorter sides nd dd them, you get the squre of the length of the hypotenuse , or dj + opp hyp hyp sqrt(dj + opp ) 5 sqrt(9 + 6)

24 There re few tringles with integer sides tht stisfy the Pythgoren formul nd its multiples (6-8-0, et.) re the est known 5--3 nd its multiples form nother set opp hyp dj

25 Drwing Turtle You wnt to move h units in the ngle α diretion, to (x, y ): hyp opp You re t: (x, y) dj So you mke right tringle... And you lel it... And you ompute: x x + dj x + hyp * (dj/hyp) x + hyp * os α y y - opp y - hyp * (opp/hyp) y - hyp * sin α This is the first point in your Turtle tringle Find the other points similrly...