Surveying I– coordinate account

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Calculation of coordinates of points of intersection with map frames

Figure 1. The intersection points 1 and 2 with map frames

Search:
1 (X₁, Y₁)
1 (X₁, Y₁)


Data:
A (X_A, Y_A)
B (X_B, Y_B)
X_R, Y_R

Intersection points of a control net with map frames are created when one side of the control net is at different sections of the map. The coordinates of these points we define as follows:

a) if the side of control net intersects with the map frame with known X_R coordinate (point 1), then X₁=X_R, and coordinate Y₁ we designate by the formula:

Y₁ = Y_A + (X_R – X_A) Y_B – Y_A X_B – X_A

b) if the side of control net intersects with the map frame with known Y_R coordinate (point 1), then Y₂=Y_R, and coordinate X₂ we designate by the formula:

X₂ = X_A + (Y_R – Y_A) X_B – X_A Y_B – Y_A

Control calculation::

For point 1:

Y_A – Y₁ X_A – X₁ = Y₁ – Y_B X₁ – X_B

For point 2:

Y_A – Y₂ X_A – X₂ = Y₂ – Y_B X₂ – X_B

Example

Calculate the coordinates of points 1 and 2, which lie at the intersection of the map frame.

Data:
A (900,00m; 1082,21m)
B (1084,22m; 990,60m)

SOLUTION

X₁= X_R= 1000,00m


Y₁ = Y_A + (X_R – X_A) Y_B – Y_A X_B – X_A

Y₁ = 1082,21 + (1000,00 – 900,00) -91,61 184,22

Y₁ = 1032,48m



Y₂= Y_R= 1000,00m


X₂ = X_A + (Y_R – Y_A) X_B – X_A Y_B – Y_A

X₂ = 900,00 + (1000,00 – 1082,21) 184,22 -91,61

X₂ = 1065,32m

Control

For point 1:

Y_A – Y₁ X_A – X₁ = 49,73 -100,00= -0,4973



Y₁ – Y_B X₁ – X_B = 41,88 -84,22= -0,4973

For point 2:

Y_A – Y₂ X_A – X₂ = 82,21 -165,32= -0,4973



Y₂ – Y_B X₂ – X_B = 9,40 -18,90= -0,4974