QGIS - tool to plot polygon from point with known bearings and distances

Question

Is there a tool that can convert a point dataset to a polygon based on some known parameters.

We will have

1- x,y

2. Azimuth

3.Distances in m for a- point in the direction of 2 (the azimuth) (200m), distance 180 degrees from 2 (25m), and distance -90/90 from the point (12m)

So the shapes will be something like this and be based on the point dataset.

We need to get the x,y for points lowercase a-d and then create a polygon based on these. If this is possible this can then be easily updated to have more points and create a better shape but the key question here is how can we create these points...

Is the only way to do this using spatial maths as in Creating points based on distance and bearing from survey point using QGIS?

Over the last year is there a plugin to achieve this?

Unfortunately, the Azimuth and Distance plugin works based on starting from a point and moving along that, whereas here I have multiple points and fixed dimensions.

The process to build a plugin/model to do this seems to be in http://www.portailsig.org/content/pyqgis-des-geometries-des-vecteurs-de-l-algebre-vectorielle-ou-des-cosinus-directeurs-exempl but I don't want to recreate the 'wheel' if I don't need to...

UPDATE Unfortunately, my result with Kazuhito's reply is and I get 2019-03-12T04:00:49 WARNING Cannot zoom to selected feature(s) : No extent could be determined. Working in WGS 84.

Answer 1

Probably you can do this in two steps:

[Step 1] Create a series of points layer (Pt1, Pt2, ...)

[Step 2] Build the polygon at each point geometry from [Step 1].

Let me try to provide an answer for the [Step 2] part... building the ship ... if I can call them ships.

Tool is Geometry by expression in the Processing Toolbox >> Vector geometry.

combine(
 combine(
  tapered_buffer(make_line(project($geometry, 175, radians("Angle_A2B")), 
                           project($geometry, 200, radians("Angle_A2B"))), 
                 start_width:=24, end_width:=0),
  buffer(make_line($geometry, project($geometry, 175, radians("Angle_A2B"))), 12)
  ),
 tapered_buffer(make_line($geometry, project($geometry, 25, radians("Angle_A2B"+180))), 
                start_width:=24, end_width:=20)
)

The above expression combines three parts (bow, body, and stern of the ship).

---

Details about the above expression:

[The bow] ... ... a tapered buffer (175m~200m from the point A)

tapered_buffer(make_line(project($geometry, 175, radians("Angle_A2B")), 
                           project($geometry, 200, radians("Angle_A2B"))), 
                 start_width:=24, end_width:=0)

[The body] ... ... a 175m long x 2*12m wide buffer (the point A is at the rear end)

buffer(make_line($geometry, project($geometry, 175, radians("Angle_A2B"))), 12)

[The stern] ... ... a tapered buffer (0m~25m toward the opposite side) The tail ends at 20m width. Please adjust as required.

tapered_buffer(make_line($geometry, project($geometry, 25, radians("Angle_A2B"+180))), 
                    start_width:=24, end_width:=20)

Because combine() can take only two geometries, I used it twice to combine three geometries (combine(bow, body) and then with stern).

NB - My expression in the picture is scaled by x10 times :)

I did not answer to [Step 1] but project($geometry, distance, azimuth()) will get you what you need.

---

[Update]

"if the width is 14m on one side and 18m on the other (L3/L4) - how do we change the body calc to deal with this?"

convex_hull(
  combine(
    make_line($geometry, project($geometry, 200, radians("Angle_A2B"))),
  combine(
  combine(
    offset_curve(make_line($geometry, project($geometry, 175, radians("Angle_A2B"))), 14),
    offset_curve(make_line($geometry, project($geometry, 175, radians("Angle_A2B"))), -18))
  ,
  combine(
    offset_curve(make_line($geometry, project($geometry, 25, radians("Angle_A2B"+180))), 7),
    offset_curve(make_line($geometry, project($geometry, 25, radians("Angle_A2B"+180))), -9))
)))