Calculation example - Three Point Resection

Determine the coordinates of an unknown station P from three (3) previously coordinated reference points A, B and C visible from station P, only by measuring the angles subtended by lines of sight from station P to the three coordinated points. Resection technique is commonly implemented when the existing reference points are not accessible during a survey.

Known values: Angles a and c, Reference points A, B and C coordinates (Tienstra’s Method).

Solution: Station P coordinates.

 1. Calculate baselines AB, BC and CA bearing angles.

 Checking the sign value of all subtractions Dx and Dy above, the bearing angles of lines AB, BC and CA are calculated referencing the table below:

 2. Calculating angles A, B and C of the three coordinated reference points respectively:

Always add angles A, B and C for checking calculations: A + B + C = 200^g

 3. Checking on the "danger circle" observations error, thus estimating on whether all four points lie on (or sufficiently close to) the circumference of a circle or a straight line, which would lead to no or high risk of an erroneous solution.

 4. Calculating coefficients K₁, K₂ and K₃

 5. Calculating station’s P coordinates:

 6. Validating results: