Survey point calculation

Two simple calculations included. The first is calculation of distance and bearing between two given survey points (E,N). The second is calculation of the position of a second point (E,N) given the first point, offset and bearing. Handy for setout of roads, buildings etc on site.

Calculation Reference

Using a Compass

Geometry

Surveying

To calculate the distance and bearing between two given survey points (E,N), we can use the following steps:

Step 1: Subtract the Easting (E) and Northing (N) coordinates of the two points to get the differences in Easting (dE) and Northing (dN).

dE = E2 - E1 dN = N2 - N1

Step 2: Calculate the distance (D) between the two points using the Pythagorean theorem:

D = sqrt(dE^2 + dN^2)

Step 3: Calculate the bearing (B) from the first point to the second point using trigonometry:

B = atan2(dE, dN) * (180/pi)

where atan2 is a function that calculates the inverse tangent of two arguments, and pi is the mathematical constant equal to approximately 3.14159.

Note that the bearing is measured clockwise from the north direction.

2. To calculate the position of a second point (E,N) given the first point, offset, and bearing, we can use the following steps:

Step 1: Convert the bearing (B) to radians:

B = B * (pi/180)

Step 2: Calculate the Easting (E2) and Northing (N2) coordinates of the second point using the first point (E1, N1), offset distance (D), and bearing (B) as follows:

E2 = E1 + D * sin(B) N2 = N1 + D * cos(B)

Note that sin and cos are trigonometric functions that calculate the sine and cosine of an angle, respectively.

The resulting (E2, N2) coordinates give the position of the second point relative to the first point, at the specified offset distance and bearing.