This section describes the working of Turf.js module Along.

Purpose of this Turf.js module

This takes a LineString as an input and returns a point at a specified distance from the starting. For more information and its usage visit its official documentation page.

Pre-requisites for understanding this module

  • Haversine Formula and its Arctangent version

    • Basically, this formula calculates distance between two points over a spherical surface.

  • Measurement of angles in Radians

    • It is more natural to measure angles in radians than in degrees. Most of the calculations here are done in Radians.

  • Concept of Bearing

    • Bearing is the angle that a line segment AB (or BA) makes with the North direction (considered 0°). As in the figure, if Bearing from A to B is 45°, then bearing from B to A is 225°.

    Figure 1

Behind the scenes- Working of this module

Variables/Assumptions

  • Distance to travel from the starting point in KM = d
  • Total distance travelled since starting point in KM = t

Cases

There are various cases of this.

Case-1

  • Let us consider the following diagram.

  • Let say we have d = 4. At A, t=0. We travel from point A to point B and measure its distance using Haversine formula from A to B.

  • At B, distance from A to B = 2 KM, then we dont need any further calculation (because d=4 KM and the total travelable distance is just 2KM).

  • So, B is the point itself.

    Figure 2

Case-2

  • Now let us consider another diagram with point ABCD.

  • At B, we have travelled just 2 KM. If d > 2 KM, we need to go a little further. We travel from B to C and update the t.

  • At C, we have covered 4 KM. If d is more than 4 KM, we continue moving forward to another point.

    Figure 3

Case-3

  • Let’s revisit the Case-2. Here, lets say we have d=3.5 KM.

  • At C, we have already covered 4 KM. Thus, we need to go (4-3.5) KM back along CB at some angle. So what is that angle?

  • It is the bearing that we have going from C to B. As in the figure, if θ is the bearing from B to C, θ-180 is the bearing from C to B.

  • Note that, here bearing is considered only within the range -180 to + 180.

  • After that, we just traverse back 1.5 KM along the path CB, at bearing of θ-180 using interpolation (based on Haversine formula) to find the final point.

    Figure 4