Tracing an Optimal Route

To find the best route flare-timing constructs a graph and finds the shortest path connecting the nodes. It puts nodes on turnpoint cylinder arc boundaries and uses the competition specific math for working out distances on the Earth as the cost of connecting nodes in the network. It would be expensive to construct and evaluate a large network with the accuracy required so it is done iteratively. At each iteration the arc of the circle bounding a zone is shortened and the density of nodes is increased. For goal line zones the nodes are selected in pretty much the same way except that points on the arc are projected down onto the line.

This optimal path found on the Earth model for the competition is the edge to edge optimal route. Routes are shown with waypoints, segment distances [1] and total distance.

taskRoutes:
  edgeToEdge:
    distance: 159.373683
    legs:
    - 10.078208
    - 42.525217
    - 0
    - 64.949832
    - 41.820427
    legsSum:
    - 10.078208
    - 52.603424
    - 52.603424
    - 117.553256
    - 159.373683
    waypoints:
    - lat: -33.36047067
      lng: 147.93206999
    - lat: -33.43411056
      lng: 147.86878018
    - lat: -33.7159199
      lng: 147.55846831
    - lat: -33.7159199
      lng: 147.55846831
    - lat: -33.13199024
      lng: 147.57575486
    - lat: -33.35857718
      lng: 147.93468357

The naive way to measure task length would be to just connect the centers of each control zone. This is the point to point distance.

taskRoutes:
  pointToPoint:
    distance: 169.10714
    legs:
    - 57.427511
    - 69.547668
    - 42.131961
    legsSum:
    - 57.427511
    - 126.975179
    - 169.10714
    waypoints:
    - lat: -33.36137
      lng: 147.93207
    - lat: -33.75343
      lng: 147.52864998
    - lat: -33.12908
      lng: 147.57322998
    - lat: -33.36099999
      lng: 147.93149998

Knowing that FS uses a plane to work out the shortest route in two dimensions on the the Universal Transverse Mercator projection, we can also do that with our graph algorithm. We end up with waypoints, optimal on the plane but possibly sub-optimal on the sphere or ellipsoid model of Earth.

taskRoutes:
  projection:
    spherical:
      distance: 159.373683
      legs:
      - 10.078208
      - 42.525217
      - 0
      - 64.949832
      - 41.820427
      legsSum:
      - 10.078208
      - 52.603424
      - 52.603424
      - 117.553256
      - 159.373683
      waypoints:
      - lat: -33.36047067
        lng: 147.93206999
      - lat: -33.43411056
        lng: 147.86878018
      - lat: -33.7159199
        lng: 147.55846831
      - lat: -33.7159199
        lng: 147.55846831
      - lat: -33.13199024
        lng: 147.57575486
      - lat: -33.35857718
        lng: 147.93468357

taskRoutes:
  projection:
    planar:
      distance: 159.144781
      legs:
      - 10.065441
      - 42.4942
      - 0
      - 64.761082
      - 41.820427
      legsSum:
      - 10.065441
      - 52.559642
      - 52.559642
      - 117.320723
      - 159.14115
      mappedPoints:
      - easting: 586715.834
        northing: 6308362.198
      - easting: 580759.282
        northing: 6300248.47
      - easting: 551744.701
        northing: 6269201.551
      - easting: 551744.701
        northing: 6269201.551
      - easting: 553704.761
        northing: 6333932.964
      - easting: 586960.882
        northing: 6308569.955
      mappedZones:
      - latZone: H
        lngZone: 55

[1]	A zero leg distance indicates that the turnpoint was touched at one point only, the optimal route does not traverse the interior of the cylinder. The entry and exit waypoints are both shown but can be the same.