
Where an alignment such as a tunnel has to pass through a series of points with the minimum clearance at each point then the optimum solution is done by performing a regression analysis to determine the line which results in the least possible clearance for all of the points.

Where an alignment such as a tunnel has to pass through a series of points with the minimum clearance at each point then the optimum solution is done by performing a regression analysis to determine the line which results in the least possible clearance for all of the points.

Surveyors regularly make multiple observations to a point under several different conditions. The mean of these can be used as a solution but a more accurate method is to use least squares regression analysis where the best fit is determined when the square of the residuals is least. The function however has many uses in mathematics and statistics.

Engineers building tunnels commonly want to know the precise centre and radius of the shape they have constructed. This is done by recording 3D coordinates around a cross section and then using a least squares analysis to determine the optimum circle that passes through each of the points. It is also used widely in designing road and railway alignments or simply to determine the centre of an object where measurements can only be taken to the perimeter.

CAD stands for ‘Computer Aided Design’ and we have used the term here to describe the fitting algorithms provided as Freeware.