Finding a New GPS Coordinate Between Two Lines on a Sphere

In summary, the conversation discusses a problem involving three GPS coordinates and the desire to create a new line with a gradient between the two existing lines. The goal is to find a new coordinate that represents the new curve without using an equation. The speaker also mentions the need for all lines to maintain the GPS structure and not represent the curved nature of the sphere. The solution proposed involves creating a new midpoint between two of the coordinates and drawing a new line from the original coordinate to the midpoint. The conversation concludes with a suggestion to consider the problem of generating appropriate triangulations on the sphere.
  • #1
frostfat
2
0
Hi, I have an interesting problem.

I have three GPS coordinates, creating two lines across the surface of a sphere (assuming the Earth is spherical). I want to be able to create a new line (across the surface of a sphere) with a gradient that is in between the gradient of the two existing lines, and intersects with one of the coordinates.

On this new line, I want to find a new coordinate, which I can use to represent the new curve. The result should be the new coordinate, not the equation of the new curve.

https://docs.google.com/drawings/d/1p9P3dzvI_shRHTEI0rxvundkW5Mvij1CRsbIlx2uGAU/edit?usp=sharing, not representing the curved nature of the sphere. All lines are to be crossing the surface of the globe, and maintaining the GPS structure.

Thanks in advance for any help! :)
 
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  • #2
I am curious: three GPS coodinates will create three lines, not two - one for each pair of points.
Of the three, what makes the upper right point special?I'm going to label your points, clockwise from upper right.
x0y0, x1y1, x2y2.

To bisect lines x0y0, - x2y2 and x1y1 - x0y0,
simply create a point x3y3 midway between x1y1 and x2y2.
Now draw your new line from x0y0 - x3y3
 
Last edited:
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Likes jim mcnamara and frostfat
  • #3
This is exactly what I was looking for, thanks for such a simple but effective answer.
 
  • #4
I suggest you to consider the problem of generate appropriate triangulations on the sphere ...
 

1. How do you calculate the distance between two points on a sphere?

The distance between two points on a sphere can be calculated using the haversine formula, which takes into account the radius of the sphere, the latitude and longitude coordinates of the two points, and the central angle between them. This formula is commonly used in navigation and GIS applications.

2. Can you explain the concept of great circle routes?

A great circle route is the shortest distance between two points on a sphere, such as the Earth. It is the path that follows the circumference of a great circle, which is the largest circle that can be drawn on a sphere. This route is commonly used in air and sea travel to save time and fuel.

3. How do you find a new GPS coordinate between two lines on a sphere?

To find a new GPS coordinate between two lines on a sphere, you can use the midpoint formula. This involves finding the average of the latitudes and longitudes of the two lines, then calculating the central angle and distance between the two points. This method can also be used to find multiple points along the same line.

4. How does the curvature of the Earth affect GPS coordinates?

The curvature of the Earth must be taken into account when calculating GPS coordinates, as it can affect the accuracy of the coordinates. The Earth is not a perfect sphere, so different projection methods must be used to accurately represent the curved surface on a flat map. Additionally, GPS satellites orbit the Earth at a certain distance, so their signals must be adjusted for the curvature of the Earth.

5. What are some challenges in finding a new GPS coordinate between two lines on a sphere?

One challenge in finding a new GPS coordinate between two lines on a sphere is determining the appropriate projection method to use. Different projections have different strengths and weaknesses, so choosing the right one can greatly affect the accuracy of the new coordinate. Additionally, the haversine formula may not be as accurate for long distances, as it assumes a perfect sphere and does not account for the Earth's ellipsoidal shape.

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