Formulario di topografia

Materie:Appunti
Categoria:Topografia
Download:1059
Data:08.03.2007
Numero di pagine:2
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Testo

Teorema sull‘INTERSEZIONE
Tg (AB)= XB-XA/ YB-YA
AB¯=XB-XA/ sen(AB)
γ= 180-(α+β)
APˉ=ABˉ/ senγ·senβ
BPˉ= ABˉ/ senγ·senα
(AP)=(AB)-α
(BP)=(AB)±180+β
(XP)A=APˉ·sen(AP)
(YP)A= APˉ·cos(AP)
(XP)B=BPˉ·sen(BP)
(YP)B= BPˉ·cos(BP)
XP=XA+(XP)A
YP=YA+(YP)A
XP=XB+(XP)B
YP=YB+(YP)B

Teorema di SNELLIUS
Tg(BA)=XA-XB/YA-YB
Tg(BC)=XC-XB/YC-YB
BAˉ= XA-XB/sen(BA)
BCˉ= XC-XB/sen (BC)
ω=(BA)-(BC)
PÂB=x
PĈB=y
x+y/2=180-½ (α+β+ω)
x-y/2=inv tg[tg x+y/2 ·cotg (θ+45)]
θ=inv tg AB¯·senβ/BC¯·senα
x=M+N
y=M-N
ω1=180-(α+x)
ω2=180-(β+y)
AP¯=AB¯/senα·senω1
CP¯=BC¯/senβ· senω2
BP¯=BC¯/senβ·seny
BP¯=BA¯/senα·senx
(AP)=(BA)±180+x
(BP)=(BC)+ ω2
(CD)=(BC)±180-Y
(XP)A=AP¯·sen(AP)
(YP)A= AP¯·cos(AP)
(XP)B=BP¯·sen(BP)
(YP)B= BP¯·cos(BP)
(XP)C=CP¯·sen(CP)
(YP)C= CP¯·cos(CP)
XP=XA+(XP)A
YP=YA+(YP)A
XP=XB+(XP)B
YP=YB+(YP)B
XP=XC+(XP)C
YP=YC+(YP)C

Teorema di HANSEN
α1=APQ α2=AQP β1=BPQ β2=BQP
Tg (AB)= XB-XA/ YB-YA
AB¯=XB-XA/ sen(AB)
x+y/2=90- ½ (α1-β1)
x-y/2=inv tg[tg x+y/2 ·cotg (θ+45)]
θ=inv tg senα2·senβ1+β2/senβ2·senα1+α2
x=M+N
y=M-N
(AP)=(AB)+x
(AQ)=(AP)-[180-(α1+α2 )]
(BP)=(AB)±180-y
(BQ)= (BP)-[180-(β1+β2 )]
AP¯=AB¯/sen (α1- β1)·sen y
BP¯= AB¯/sen (α1- β1)·sen x
AQ¯= AB¯/sen (β2- α2)· sen y+180-(β1+β2 )
BQ¯= AB¯/sen (β2- α2)· sen x-180-(α1+α2 )
(XP)A=AP¯·sen(AP)
(YP)A= AP¯·cos(AP)
(XQ)A=AQ¯·sen(AQ)
(YQ)A= AQ¯·cos(AQ)
(XP)B=BP¯·sen(BP)
(YP)B= BP¯·cos(BP)
(XQ)B =BQ¯·sen(BQ)
(YQ)B= BQ¯·cos(BQ)
XP=XA+(XP)A
YP=YA+(YP)A
XQ=XA+(XQ)A
YQ=YA+(YQ)A
XP=XB+(XP)B
YP=YB+(YP)B
XQ=XB+(XQ)B
YQ=YB+(YQ)B

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