*(Using Blender 3.6.5 and Geometry Nodes)*

*NB: This answer is under work and has yet to be fully documented...*

#### Objective ####

Build Bezier curves connecting sets of two points on a sphere, controlling mid-point height.

#### Approach ####

[![GN Main graph, controls and results][1]][1]

The <i>GeometryNodes</i> modifier is added to the object made of vertices put at the targetted airports position (named <i>OtherAirports</i> in the demo file).<br> 
<b>1. </b>Sphere properties and hub airport (named <i>Schiphol</i> in the demo file) position are recovered from objects specified through the <i>Group Input</i> node (label <i>(7)</i>).<br>
<b>2. </b>A single edge per targetted airport (label <i>A</i>) is build to connect it to the hub airport (label <i>H</i>).<br>
<b>3. </b>The [perpendicular bisector][3] to those edges crossing the sphere centre is used to shift outward the mid-point. These points are collected as a point cloud.<br>
<b>4. </b>Edges and apex points are combined in broken lines made of three points and two edges.<br>
<b>5. </b>These sets of segments are converted to Bezier curves, which handles are modified to tune the flightpath shape.<br>
<b>6. </b>Control parameters are:<br>
<b>6.1. </b><i>Height</i>: Fraction of the circular arc connecting <i>H</i> to <i>A</i> used to shift the apex. A value of 0 puts apices on sphere.<br>
<b>6.2. </b><i>HubAngle</i>: Additional angle between the curve tangent and the edge connecting <i>H</i> to apex. Positive values increase "take-off" slope.<br>
<b>6.3. </b><i>ApexWeight</i>: Factor controlling the radius of curvature at apex. 0 is the default value. -1 makes a sharp angle. Positive values yield flatter curves.<br>
<b>6.4. </b><i>AirportAngle</i>: Additional angle between the curve tangent and the edge connecting apex to <i>A</i>. Positive values increase "landing" slope.<br>

#### Process data ####

[![GN Extract data graph][4]][4]

#### Build direct paths ####

[![GN Direct paths graph][5]][5]

#### Compute apices ####

[![GN Apex graph][6]][6]

#### Build over paths ####

[![GN complete paths graph][7]][7]

#### Build and adjust flight paths ####

[![GN convert to Bezier curves graph][8]][8]

#### Resources ####

[<img src="https://blend-exchange.com/embedImage.png?bid=Pb5OYsrM" />](https://blend-exchange.com/b/Pb5OYsrM/)


  [1]: https://i.sstatic.net/4grPI.jpg
  [2]: https://i.sstatic.net/jMRCb.jpg
  [3]: https://en.wikipedia.org/wiki/Bisection#Line_segment_bisector
  [4]: https://i.sstatic.net/73EGi.png
  [5]: https://i.sstatic.net/3WMwc.png
  [6]: https://i.sstatic.net/7ptqe.png
  [7]: https://i.sstatic.net/ymkpB.png
  [8]: https://i.sstatic.net/voxF2.png