Shapefile from heading and distance directions for property boundary

Question

I have a survey with heading and direction points describing the boundary for a rural property in Brazil. I am in correspondence with someone there who needs a shapefile (I believe he mentioned kml or kmz format file as well) of this boundary.

The format of the information is as follows:

Heading                 Distance            Alignment

NW 79º 41' 27"         170.08 meters         1-2 
NW 58º 27' 42"         119.83 meters         2-3 
...

The alignments I assume references points on some old maps I have of the property, beginning with a starting point described by some known area which has been marked in some way. Neither this map nor the survey has any lat/lon coordinates.

I know Python but do not have experience with GIS.

What terms can I search for, or what documentation would help me understand how to create the polygon he needs from the kind of information I have?

Is shapely or QGIS the tool I should familiarize myself with?

Is there a process for converting the kind of information into a polygon and what is the name of this process so I can familiarize myself with it?

---

There seems to be no way I could think of to ascertain the starting point considering it is described by surrounding landmarks but perhaps there is a way to create the general polygon and have a third party figure out how to orient it so to accurately overlay it on a map. The only other way is to contact the person living on the property and have them somehow use their smartphone to record the lat/lon of the starting point (maybe have them take a picture to send to me and I extract the coords from the exif data?).

Would this be helpful?

---

I attempted to create a polygon by accumulating points as suggested by @Spacedman (after converting the the bearing of deviation from N/S to degrees the python function I used for conversion are below) and the shape did not resemble the map boundary at all. As suggested by @MartinF perhaps I could invert some of the coords to try and see if I can make the shape more consistent with the map, but then I found a more recent map(2005).

Except now in this new map there seems to be some distances mixed in under the bearings column, I can't really make heads or tails of it.

(section)  (heading)       (distance)
Trecho     Rumo            Distancia (m)
1-2      R=1600.94m      D=138.36
2-3      56º02'14" SW    635.47
3-4      R=2900.00m      D=298.80
4-5      50º08'02" SW    187.45
5-6      R=10.00m        D=13.67
.....
17-18    38º28'17" NE    415.16
18-19    38º52'52" NE    305.91
19-20    40º11'22" NE    182.30
20-21    34º37'52" NW    122.53
...

At least I now know it is SAD-69 format and it contains zone and hemisphere info (although hemisphere is obvious) along with other UTM info.

Python functions to transform bearings to degrees:

def dms2dd(degrees, minutes, seconds):
    dd = degrees + (minutes/60) + (seconds/(60*60))
    return dd


def degree_from_bearing(bearing):
    # first transform from `NW 50º22'12"` to individual elements
    ns, we, deg, mins, secs = parse_dms(bearing)
    degree = dms2dd(deg, mins, secs)
    if ns == 'N':
        start = 0
        if we == 'W':
            start = 360
            degree *= -1
    elif ns == 'S':
        start = 180
        if we == 'E':
            degree *= -1
    else:
        raise ValueError(f'Heading must be North (N) or South (S), got "{ns}" instead.')
    result = start + degree
    assert result >= 0, f'Resulting degree is negative ({result}).'
    return result


def transform_data(data):
    # implementation of @Spacedman's algorithm
    x = y = 0
    coords = [(x, y)]
    for (heading, distance) in data:
        delta_x = distance * Decimal(math.cos(heading))
        delta_y = distance * Decimal(math.sin(heading))
        x += delta_x
        y += delta_y
        coords.append((x, y))
    return coords

Answer 1

Here's the algorithm you want in pseudocode:

set x=0, y=0 
output x,y
for each row of the data:
  delta_x = distance * cosine(heading)
  delta_y = distance * sine(heading)
  x = x + delta_x
  y = y + delta_y
  output x,y

This works by computing the offset in X and Y for each leg given the distance and direction.

Note the sines and cosines might be the other way round depending on your orientation. If your data is really in a text file in the format given you'll have to do some parsing in python to turn it into numeric fractional degrees and metres.

That algorithm starts from coordinate (0,0). If you want to start from some other lat-longitude point, you need to convert to a cartesian coordinate system for your area. You can use a UTM zone system for this. Convert the lat-long to UTM coordinates, and set the initial x and y to the UTM coordinates. Run the algorithm and get out a set of UTM coordinates for the region.

Answer 2

When you have land survey data – a sequence of bearings/azimuths and distances around a land parcel – but no starting point coordinates, the calculations you do are for the purpose of checking that the values are consistent, i.e., they define a closed polygon. The process is sometimes called map check.

If you do have starting point coordinates and a sequence of bearings/azimuths and distances, the calculations you do are for the purpose of calculating the coordinates of the other corner points, calculating a polygon "misclosure", and adjusting all values for perfect closure. The process is sometimes called map traverse.

There is a free Windows-based tool to do both map check and map traverse (and many other cogo calculations) called Copan. The results are text-based, so to get a KML or other popular text-based file, you'd have to find out the (or invent arbitrary) start-point coordinates, do the map traverse, then manually (or use a spreadsheet) to reformat the data.

Disclosure: I was a major developer of Copan.

Note: without further examples of your data it hard to say, but it is common for land survey directions to only be in the form N angle W or N angle E. In such cases – in order to keep each polygon side (survey mete) going consistently all clockwise or consistently all counter-clockwise – you will need to reverse the directions of some of them. For example, S 35 E is the exact opposite direction of N 35 W, and S 49 W is the opposite of N 49 E.