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 performs a coordinate transformation from the WGS84 (World Geodetic System 1984) to the SLD99 (Sri Lanka Datum 1999) system by reading latitude, longitude, and height values from a text file (wgsLP.txt
) and applying a series of mathematical operations to convert the coordinates. Let's break down the program and the key components:
Key Sections of the Code:
-
Reading the Text File: The
textread
function is used to read latitudes, longitudes, and height data (in degrees, minutes, and seconds format) from a text file (wgsLP.txt
). The variablesPI, PM, PS, LI, LM, LS, HI
represent parts of latitude and longitude. -
Conversion from DMS to Decimal Degrees: The latitude (
phi
) and longitude (lambda
) values in Degrees, Minutes, and Seconds (DMS) format are converted into decimal degrees using: -
Constants for WGS84 Ellipsoid: The WGS84 ellipsoid is defined by:
a
: Semi-major axis (radius at the equator)f
: Flattening (difference between the semi-major and semi-minor axes)e2
: First eccentricity squared, derived from the flattening. The semi-minor axisb
is calculated as .
-
Transformation Parameters: These are the parameters for transforming coordinates from WGS84 to the SLD99 datum:
deltaX
,deltaY
,deltaZ
: Translation components in meters.delta_a
: Change in the semi-major axis.delta_f
: Change in the flattening.
-
Radii of Curvature:
RM
: Meridian radius of curvature.RN
: Prime vertical radius of curvature. These are used in geodetic transformations.
-
Coordinate Transformation Equations:
delta_phi
: Change in latitude.delta_lambda
: Change in longitude.delta_h
: Change in height. These values are calculated using transformation formulas, which involve trigonometric operations and depend on the translation parameters.
-
Calculate Kandawala Coordinates: After applying the transformation formulas, the new coordinates in the Kandawala system are:
phi_kandawala
: Transformed latitude.lambda_kandawala
: Transformed longitude.h_kandawala
: Transformed height.
-
Output: The transformed coordinates are printed out using
fprintf
, displaying the latitude and longitude in degrees and the height in meters.
Improvements and Considerations:
- Error Handling: If the text file contains incomplete or incorrect data, the script might crash. It would be useful to add error checks.
- Precision: The output may require specific precision handling depending on the coordinate system’s use case.
- Input File Format: Ensure the
wgsLP.txt
file has data correctly formatted for this script.
Do you have any questions or would you like further details? Here are 5 relative questions for expansion:
- How is the flattening parameter related to the eccentricity of the ellipsoid?
- What are the practical applications of converting from WGS84 to SLD99?
- How could the script handle larger datasets efficiently?
- Can this code be extended to other coordinate transformation systems, and how?
- How do translation parameters (deltaX, deltaY, deltaZ) affect the final coordinates?
Tip: Always check the ellipsoid and datum definitions carefully when transforming coordinates between systems, as small errors can lead to significant positional inaccuracies.
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Math Problem Analysis
Mathematical Concepts
Coordinate transformation
Geodesy
Ellipsoid geometry
Trigonometry
Formulas
φ = PI + (PM/60) + (PS/3600)
λ = LI + (LM/60) + (LS/3600)
RM = a * (1 - e²) / (1 - e² * sin²(φ))^(3/2)
RN = a / sqrt(1 - e² * sin²(φ))
Δφ, Δλ, Δh transformation formulas
Theorems
WGS84 ellipsoid definition
Datum transformation formulas
Suitable Grade Level
University/Advanced Geodesy
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