Curvilinear & Cartesian Conversions

In summary, the conversation discusses the creation of a program that calculates coordinates on ellipsoidal surfaces. The speaker is confused about converting between cartesian and curvilinear coordinates, specifically how to find the eccentricity and "N" value. They mention making progress but getting stuck in the equation and needing to take into account the height of the ellipsoid. They also mention being able to convert from curvilinear to cartesian, but struggling with the conversion back and finding the convergence value. They are seeking help and clarification on these calculations.
  • #1
G4CKT
12
0
I'm trying to create a program which will do these calculations. I am given Latitudes, Longitudes, and ellipsoidal heights for ellipsoids and another set of x, y, and z coordinates. I am so confused looking at how to convert these things. I know I need to iterate in order to go from cartesian to curvillinear I'm quite confused on the formulations though T_T.

Can anyone help me xD

PS: I need to take into account the height of the ellipsoid.

I made a bit of progress but I got stuck in the equation. I don't know how to find the eccentricity and the "N" value T_T

As well, I know I should be using these equations for the Curv -> Cart Transformation

X = (N+H) cos(phi) cos(lambda)
Y = (N+H) cos(phi) sin(lambda)
Z = [N(1-e^2)+H] sin(phi)

I just don't know how to get the "N" value or the eccentricity. I'm also still lost on the conversion back T_T
 
Last edited:
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  • #2
I figured out the curvilinear to cartesian conversion. Now I'm stuck on cartesian to curvilinear especially the convergence value T_T.
 

1. What is the difference between curvilinear and Cartesian coordinates?

Curvilinear coordinates are a system of coordinates that use curves or arcs to describe a point's location, while Cartesian coordinates use straight lines and right angles.

2. What are the advantages of using curvilinear coordinates?

Curvilinear coordinates are often used in physics and engineering because they can simplify the mathematical description of curved surfaces and make certain calculations easier.

3. How do you convert between curvilinear and Cartesian coordinates?

The conversion formula varies depending on the specific type of curvilinear coordinates being used, but generally involves using trigonometric functions and basic algebraic operations.

4. Can curvilinear coordinates be used in three-dimensional space?

Yes, curvilinear coordinates can be used in three-dimensional space to describe points on curved surfaces or in curved regions of space.

5. What are some real-world applications of curvilinear coordinates?

Curvilinear coordinates are commonly used in fields such as fluid mechanics, aerodynamics, and electromagnetism to describe the motion and behavior of objects in curved or irregular shapes.

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