Finding a New GPS Coordinate Between Two Lines on a Sphere

[frostfat]

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! :)

 

[DaveC426913]

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

 

[frostfat]

This is exactly what I was looking for, thanks for such a simple but effective answer.

 

[Ssnow]

I suggest you to consider the problem of generate appropriate triangulations on the sphere ...