بسم الله الرحمن الرحيم
مرحبا بكم مرة اخري في موضوع اخر وهو معادلات مهمة في هندسة المساحة
وهي منقولة من الموقع للفائدة
In our work, it may sometimes be necessary to transform a set of co-ordinates from one cartesian system to another. The following formulae may be used to transform a set of (e, n) co-ordinates into a set of (e', n') co-ordinates.
A simple scale change, for example changing feet to metres or applying a meteorological scale factor, may be applied thus:e' = k e
n' = k n
where e, n = original (old) co-ordinates: k = scale factor: e', n' = new co-ordinatesRotation
For a rotation of axis about an angle θ, which may be given or derived from known co-ordinates in both systems:e' = e cos θ - n sin θ
n' = e sin θ + n cos θ
where e',n' = new co-ordinates: e, n = original co-ordinates: θ = angle of rotationTranslation
For a change of origin by factors E and N:e' = e + E
n' = n + N
where e',n' = new co-ordinates: e, n = original co-ordinates: E & N = shift factorsScale, Rotation and Translation
If the transformation parameters are known(i) e' = k (e cos θ) - k (n sin θ) + E
(ii) n' = k (e sin θ) + k (n cos θ) + NThese formulae work for all cases.
If no scale factor is required, substitute k = 1.
If no rotation is needed then substitute θ = 0.
Similarly, if no Translations are required E & N = 0 as required.
If the transformation parameters are NOT known
In this case, two points in each system must be known (preferably as far apart as possible).
The following parameters may be calculated:
Scale Factork = (Distance between 2 points in new system) / (Distance between 2 points in old system)Rotation Angleθ = (Bearing between 2 points in new system) - (Bearing between same 2 points in old system)Translation
If (e, n) = 1 point in old co-ordinate system and (e', n') = same point in new system:E = e' - k (e cos θ) + k (n sin θ)
N = n' - k (e sin θ) - k (n cos θ)Further points may now be transformed by applying these parameters into the above formulae (i) and (ii).
من مواضيع دفع الله حمدان هجو :
هدفنا خدمة مهندس المساحة والطرق