Modify the greatArcIntermediaryPoint function in util.ts

[HapDragon]

Modify the greatArcIntermediaryPoint function, because there may be some problem in calculating r.

Merge request checklist

• All lints and tests pass. If needed, new unit tests were added.
• If needed, the documentation has been updated.

[mistic100]

According to the linked article, the correct computation is

      // distance between points
        const Δφ = φ2 - φ1;
        const Δλ = λ2 - λ1;
        const a = Math.sin(Δφ/2) * Math.sin(Δφ/2)
            + Math.cos(φ1) * Math.cos(φ2) * Math.sin(Δλ/2) * Math.sin(Δλ/2);
        const δ = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));

no idea where your version come from

---

however I compared the results :

• current: [-1.877653919666705,-0.38152789807555176]
• new: [-1.877661200390654,-0.38152577113488884]

it only differs by 0.00001 rads

given is only used to comput the middle point of polylines which is only used for persistent tooltip placement, I will keep the current version which is less expansive.

[HapDragon]

According to the linked article, the correct computation is

      // distance between points
        const Δφ = φ2 - φ1;
        const Δλ = λ2 - λ1;
        const a = Math.sin(Δφ/2) * Math.sin(Δφ/2)
            + Math.cos(φ1) * Math.cos(φ2) * Math.sin(Δλ/2) * Math.sin(Δλ/2);
        const δ = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));

no idea where your version come from

however I compared the results :

• current: [-1.877653919666705,-0.38152789807555176]
• new: [-1.877661200390654,-0.38152577113488884]

it only differs by 0.00001 rads

given is only used to comput the middle point of polylines which is only used for persistent tooltip placement, I will keep the current version which is less expansive.

Hello, mistic100, the reason I find something maybe wrong is when I try to compute the midpoint of two point: such as :
poi1 :[longitude,latitude]: [6.160393754326874, -0.024855334829736897]
poi2 :[longitude,latitude] : [0.058584340850442264, 0.028657665309549385]
then the function: greatArcIntermediaryPoint(pos1,pos2,0.5) will give a mid point not in the line between poi1 & poi2, in fact it will be on the other side of the sphere.

So I look about the definition of this function, and the article link before the function: http://www.movable-type.co.uk/scripts/latlong.html, and find the paragraph below:

According to this, maybe is the problem, so I modify the code, after test, it shows, the problem above is removed.

[mistic100]

Ok then it is probably an error in the "greatArcDistance" function which does not handle well crossing 0/2Pi

[mistic100]

So I just tested it

var p1 = [6.160393754326874, -0.024855334829736897];
var p2 = [0.058584340850442264, 0.028657665309549385];

greatArcIntermediaryPoint(p1, p2, 0.5)
//  [-0.032108232961702045, 0.0019090099811879602]

this seems correct, the midpoint is not at the other side of the sphere

And when used to display permanent tooltips, it is correctly placed