معادلات في هندسة المساحة
مرحبا بكم مرة اخري في موضوع اخر وهو معادلات مهمة في هندسة المساحة وهي منقولة من الموقع للفائدة المعادلة الاولي Transformations" http://www.engineeringsurveyor.com/images/spacer.gifhttp://www.engineeringsurveyor.com/images/spacer.gif Introduction 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. Scale 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-ordinates Rotation 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 rotation Translation 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 factors Scale, 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) + N These 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 Factor k = (Distance between 2 points in new system) / (Distance between 2 points in old system) Rotation Angle θ = (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) |
رد: معادلات في هندسة المساحة
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رد: معادلات في هندسة المساحة
احمد المصرى
اتمنى يفيد الناس |
الساعة الآن 06:20 PM. |
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