Zonge GDP-32 - Gradient

MATHEMATICAL ALGORITHMS
Section 15, Page 5 October 2002
GRADIENT
where:
m
1
A = √(Dy
2
+ Dx
2
)
n
1
A = m
2
A = √(Dy
2
+ (Dx+N
1*
a)
2
)
n
2
A = m
3
A = √(Dy
2
+ (Dx+N
2*
a)
2
)
n
3
A = √(Dy
2
+ (Dx+N
3*
a)
2
)
Dx = |Ax - Rx|
Dy = |Ay - Ry|
dx = |Ax - Bx| - Dx
m
1
B = √(Dy
2
+ dx
2
)
n
1
B = m
2
B = √(Dy
2
+ (dx-N
1*
a)
2
)
n
2
B = m
3
B = √(Dy
2
+ (dx-N
2*
a)
2
)
n
3
B = √(Dy
2
+ (dx-N
3*
a)
2
)
For these calculations, we are assuming numbers (coordinates) increase in value to the right and
up, (to the east and north, for example).
RHO
V
I
mA mB nA nB
=
−−+
2
1
1111
π **
West
Ax, Ay
East
Bx, By
Rx
,
R
y
Rx
,
R
y
m n
m n
running survey
west to east
running survey
east to west
Y
X
Dy
Dx
Dx dx
N= 1 2 3
N= -3 -2 -1