Math Problem Statement

%Program to compute SLD99 values from accepted parameters of SLD99 report. %Coordinate Transformation From WGS84 To SLD99 system; %Entered Latitudes and Longitutes value in degrees, Minutes, Seconds formatin %a text file clc clear %Reading the text file format long [PI,PM,PS,LI,LM,LS,HI]=textread('wgsLP.txt','%f %f %f %f %f %f %f'); NPoints = min(length(PI)); for i=1:NPoints; phi=(PI(i)+(PM(i)/60)+(PS(i)/3600)); lambda=(LI(i)+(LM(i)/60)+(LS(i)/3600)); h=HI(i); % Constants for WGS84 ellipsoid a = 6378137.0; % semi-major axis in meters f = 1/298.257223563; % flattening e2 = (2*f-f^2); % square of first eccentricity b = a * (1 - f); % semi-minor axis

% Transformation parameters from WGS84 to Kandawala
deltaX =   0.2933; % Change in X (m)
deltaY = -766.9499; % Change in Y (m)
deltaZ =-87.713; % Change in Z (m)
delta_a = -860.655; % Change in semi-major axis (m)
delta_f = -0.2836136808*10^(-4); % Change in flattening


% Calculate radii of curvature
RM = a * (1 - e2) / (1 - e2 * sind(phi)^2)^(3/2);
RN = a / sqrt(1 - e2 * sind(phi)^2);

% Apply the transformation formulas
delta_phi = (1 / (RM + h)) * (-deltaX * sind(phi) * cosd(lambda) - deltaY * sind(phi) * sind(lambda) + deltaZ * cosd(phi) + ...
            (RN / a) * e2 * sind(phi) * cosd(phi) * delta_a  + ...
            sind(phi) * cosd(phi) * ((RN * b) / a + (RM * a) / b) * delta_f);
delta_lambda = (1 / ((RN + h) * cosd(phi))) * (-deltaX * sind(lambda) + deltaY * cosd(lambda));
delta_h = deltaX * cosd(phi) * cosd(lambda) + deltaY * cosd(phi) * sind(lambda) + deltaZ * sind(phi) - ...
          (a / RN) * delta_a + (RN * b) * (sind(phi)^2 / a) * delta_f;

% Calculate new coordinates in Kandawala
phi_kandawala = phi + rad2deg(delta_phi); % Convert back to degrees
lambda_kandawala = lambda + rad2deg(delta_lambda); % Convert back to degrees
h_kandawala = h + delta_h;




fprintf('\n %f %f %.3f  ',phi_kandawala,lambda_kandawala,h_kandawala);

end

Solution

The provided MATLAB script reads latitude and longitude values from a text file, transforms these WGS84 coordinates into the SLD99 coordinate system, and prints the transformed coordinates. Here’s an explanation of the key steps involved in the code:

Key Steps in the Code:

  1. Reading the Input File:

    • The script reads data from a file named wgsLP.txt containing latitude and longitude values in degrees, minutes, and seconds, along with a height (h) in meters. The file is expected to have 7 columns representing these values:
      • PI, PM, PS: Degrees, Minutes, and Seconds of latitude.
      • LI, LM, LS: Degrees, Minutes, and Seconds of longitude.
      • HI: Height in meters.
  2. Conversion of Latitude and Longitude:

    • Latitude (phi) and Longitude (lambda) are converted from degrees, minutes, and seconds format to decimal degrees using: ϕ=Degrees+(Minutes60)+(Seconds3600)\phi = \text{Degrees} + \left(\frac{\text{Minutes}}{60}\right) + \left(\frac{\text{Seconds}}{3600}\right) This formula is applied similarly for both latitude and longitude.
  3. Constants for WGS84 Ellipsoid:

    • The script uses WGS84 ellipsoid constants:
      • a: Semi-major axis.
      • f: Flattening.
      • e2: First eccentricity squared.
      • b: Semi-minor axis.
  4. Transformation Parameters:

    • Parameters for converting from the WGS84 ellipsoid to the SLD99 coordinate system (Kandawala Datum in Sri Lanka) are provided:
      • deltaX, deltaY, deltaZ: Translation shifts in meters.
      • delta_a: Change in the semi-major axis.
      • delta_f: Change in the flattening.
  5. Radii of Curvature:

    • The meridian (RM) and prime vertical (RN) radii of curvature are calculated based on the ellipsoid shape and latitude.
  6. Transformation Formulas:

    • The script calculates the changes in latitude (delta_phi), longitude (delta_lambda), and height (delta_h) using the transformation parameters and formulas based on the differences in ellipsoidal parameters and shifts.
  7. Convert Back to Degrees and Print Results:

    • The new latitude, longitude, and height values are converted back to degrees and printed in the format:
      • phi_kandawala, lambda_kandawala, h_kandawala

Explanation of Output:

The script outputs the converted coordinates for each point listed in the text file. Each line represents the transformed coordinates for one input point, providing the latitude and longitude in degrees, and the height in meters.

Improvements and Considerations:

  • Error Handling: The script does not handle cases where the input file wgsLP.txt is missing or formatted incorrectly.
  • Precision Control: If higher precision is needed, the format of the output can be adjusted.
  • Performance: For large datasets, MATLAB's vectorized operations can speed up the transformation.

Example Usage:

To use this script:

  1. Ensure you have a file named wgsLP.txt with the correct format in the same directory as the script.
  2. Run the script in MATLAB.

Do you have any questions or want to go deeper into any part of the code?

Relative Questions:

  1. How can you handle errors in reading the input file in MATLAB?
  2. What are the differences between the WGS84 and SLD99 coordinate systems?
  3. How do you convert coordinates between different ellipsoids in geodesy?
  4. What are the applications of converting between coordinate systems like WGS84 and SLD99?
  5. How can you optimize this script for larger datasets?

Tip:

To transform coordinates accurately, always check for any regional adjustments or specific parameters required for local datums.

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Math Problem Analysis

Mathematical Concepts

Coordinate Systems
Ellipsoid Geometry
Geodesy
Coordinate Transformation

Formulas

φ = Degrees + (Minutes/60) + (Seconds/3600)
RM = a * (1 - e2) / (1 - e2 * sin(φ)^2)^(3/2)
RN = a / sqrt(1 - e2 * sin(φ)^2)
Δφ, Δλ, Δh for coordinate transformation

Theorems

Ellipsoidal Geometry for Geodetic Datum Conversion
First and Second Eccentricity Formulas
Geodetic Coordinate Transformation Theorems

Suitable Grade Level

Undergraduate