The problem
Small projects on level sites rarely need sections at all. Large projects, or sites with retaining structures, embankments, cuttings or changes in finished levels, often need several, drawn through the areas where the relationship between trees and proposed levels is hardest to judge from the plan alone.
Drawn by hand in CAD, a section is slow to produce and slower to keep up to date. Each crown has to be measured off the schedule, scaled, positioned against a ground line and redrawn whenever the survey or the section position changes. The result depends on the patience of whoever drew it, and two sections through the same trees rarely agree with each other in the detail.
Everything needed to draw a section properly is already in the survey: the position of every stem, its recorded height and crown clearance, the canopy outline built from its four measured spreads, and a terrain model for the ground. What was missing was a way to cut through all of that along a line of our choosing.
What this is not: the crown silhouettes are modelled, not measured profiles. Height, crown clearance and the width of each crown either side of the line come directly from the survey; the curve between them is a consistent, realistic shape rather than a record of that particular tree. The sections are drawn for illustration and context, to show trees in relation to levels and proposals. They are not intended for measuring clearances from, which should always be taken from the survey data.
One: drawing the line
In QGIS, a section line is drawn by clicking its two ends on the map, with a preview following the cursor between clicks. Lines are lettered in order (A, B, C), and if one is deleted the next line drawn takes the vacant letter, so a set of sections never skips a letter on the drawings. Each line keeps its own buffer distance: any tree whose stem falls within that distance of the line is included in the section.
Each included tree is then projected straight onto the plane of the section. Its position along the line sets where it stands in the elevation, and the ground level at its stem is read from the terrain model. Drag either end of the line below, and widen or narrow the buffer.
Interactive
From plan to elevation
Drag the A markers at either end of the section line, or select one and use the arrow keys.
Elevation (same scale horizontally and vertically)
Outlines are drawn heavier for trees close to the line and lighter for those further away, so the eye reads depth in a drawing that is otherwise flat. The ground here is an invented surface with a gentle fall and a hollow; in use it is sampled from a terrain model, or drawn level where none is supplied.
How each tree is placed on the section
For a section line from point A to point B, with unit direction l along the line and unit normal n across it, each stem at s is resolved into two distances:
The ground level at the stem is sampled from the terrain model, and the ground line itself is sampled at close intervals along the full length of the section, with the terrain model clipped to a margin around the trees so that sampling stays quick.
Crown width is not taken from an average spread. Every vertex of the tree's drawn canopy outline is projected onto the line, and the furthest reach on each side is kept separately:
Because the projection reads the finished canopy outline, any rotation already applied to it on the plan (see competition-derived canopy orientation) carries straight into the section.
Heights, crown clearance and stems
The crown is drawn from the recorded crown clearance up to the recorded height, both measured from ground level at the stem. Where a crown clearance was not recorded, one third of the height is used and the substitution is written to the processing log, so it is never silent.
The stem is drawn as a rectangle at its recorded diameter, from the ground to the crown base. Tree references are written below the ground line.
Outline weights run from 0.35 mm for trees close to the line down to 0.13 mm for those at the edge of the buffer. Where a fill is used, outlines are drawn at a uniform 0.30 mm instead, since the fill already separates overlapping crowns.
Two: the crown shape
The survey records a crown's height, its clearance and its spread, but nothing about the shape of the crown between them. A shape therefore has to be chosen, and it has to suit trees in general without looking manufactured. It took four attempts.
The first borrowed the gentle taper used in our tree shadow modelling, which is right for shadows and wrong for drawings: it narrowed the crown to 88% of its width at the top and looked like a rectangle. Straight lines to and from a widest point gave a visible corner. Curves fixed the corner but, pushed hard enough to narrow the top, drew the crown to a point like a teardrop. The shape settled on combines a sine curve for the lower crown with a half-ellipse for the upper crown.
Interactive
Four attempts at a crown
Step through the versions. The final shape can be adjusted; the faint outline behind the earlier versions is the final shape for comparison.
The target is correctly described as pyriform: widest in the lower third of the crown, narrowing to a rounded top. An ovoid shape would put the widest point near the middle, and broadleaved crowns seen in elevation are consistently fuller low down. The final version is widest 27% of the way up the crown, starts at 72% of full width at the crown base, and at a third of the way from the widest point to the top is still at about 95% of full width.
The crown shape formulas
Height within the crown is expressed as z, running from 0 at the crown base to 1 at the top. The crown's width at each height is its full width multiplied by a scale factor, with P the height of the widest point and B the width at the base.
Values as built: P = 0.27, B = 0.72, k = 2.0. The earlier versions are shown in the demo from their recorded formulas: a linear taper of 0.12; straight lines through P = 0.30, B = 0.55; and cosine quarter-waves with P = 0.35, B = 0.50, where raising the upper curve to a power to narrow the top collapsed it to a point well before the apex.
Naturalising the outline
A mathematically smooth crown looks drawn by machine, so the outline is roughened using the same two-layer method that draws our plan canopies, which was calibrated against our earlier CAD software until the two were near indistinguishable.
Each side of the crown is described by 16 anchor points. Every anchor except the base, widest point and top receives a small random offset of up to ±0.5% of the spread, and five anchors on each side are pulled inward by about 3%, distributed in proportion between the lower and upper crown so that they never bunch. A smooth curve is then passed through the anchors. The base of the crown is broken into six points, each lifted or lowered by up to 0.19 m.
The random numbers are seeded from the tree reference. Running the same section twice draws exactly the same crowns, which matters when a drawing is reissued and nothing about the tree has changed.
Three: the hand-drawn line
Sections tend to sit on drawings beside architects' elevations, and a crisp CAD outline reads as more precise than a modelled crown deserves. An optional second layer overdraws each crown and stem with a looser line, in the manner of the sketchy line settings found in architectural software: each stroke runs slightly past its corners and bows gently between them, and the whole outline is traced more than once.
The effect is deliberate as well as decorative. A sketched crown signals to the reader that the shape is indicative, which is exactly what it is.
Interactive
Overdrawing the outline
The settings start at the tool's own defaults.
Push the simplification up and the crown turns into a handful of long strokes; bring it down and the strokes become too short to read as drawn. The default sits where each stroke is long enough to have a visible overshoot.
How the sketch layer is built
The smooth crown outline of around 180 points is first simplified with the Douglas–Peucker method, which removes any point lying closer than the simplification distance to the straight line between its neighbours. What remains is a short run of straight strokes that still follows the crown.
Each stroke is then redrawn independently, once per pass. It is extended past both of its ends by the overshoot, varied stroke to stroke by the overshoot variation, so that neighbouring strokes cross at the corners as a pencil line would. Its midpoint is pushed sideways by a small random amount, set by the bow, and the stroke is drawn as a gentle curve through it.
The sketch layer sits on its own drawing layer above the clean outline and any fill. Nothing is replaced, so it can be switched off in CAD without regenerating the section.
What comes out
Every section in a project is written to a single DXF file at 1:1 in metres, stacked one above another with the letter titles (SECTION A–A, SECTION B–B) above each, a vertical scale marked every 5 m, and tree references below the ground line. The gap between sections scales with their height, so a tall section is never crowded by the one below it. The file opens in AutoCAD ready to be placed on a sheet at whatever scale the drawing needs.
On the plan, the ends of each line are marked with lettered circles in the usual convention, and the lines are added to the QGIS project as their own layer, so that the plan and the elevations always refer to the same positions.
Image to follow: an exported section as it appears in AutoCAD.
Drawing layers
Layer names follow the same convention as our plan drawings, so sections and plans share a layer structure and can be styled together.
| Layer | Content | Lineweight |
|---|---|---|
| ARB_ELEV_GROUND | Ground line, or the terrain profile where a terrain model is supplied | 0.30 mm |
| ARB_ELEV_STEM | Stems, drawn at recorded diameter | 0.30 mm |
| ARB_ELEV_CROWN | Crown outlines, weighted by distance from the line | 0.13–0.35 mm |
| ARB_ELEV_CROWN_FILL | Crown fill, 50% transparent (optional) | – |
| ARB_ELEV_CROWN_SKETCH | Hand-drawn overdraw of crowns and stems (optional) | 0.09–0.13 mm |
| ARB_ELEV_LABEL | Tree references below the ground line | Default |
| ARB_ELEV_TITLE | Section titles | 0.35 mm |
| ARB_ELEV_SCALE | Vertical scale marks and figures | 0.18 mm |
Crowns can be left unfilled, filled dark green, or filled in the BS5837 category colours used on our constraints plans, each at 50% transparency so that crowns behind remain visible. The category fill lets a reader follow a tree from the plan to the section without reading its reference.
What this is not: a section is not a survey of the trees in it. It carries no information that is not already in the schedule, and if the two ever appear to disagree, the schedule is the record.
Why build it this way
The tool reads the same canopy outlines, heights and crown clearances that produce the tree constraints plan. Nothing is redrawn and nothing is keyed in twice. If a tree is remeasured, a canopy is corrected or a section needs to move a few metres, the section is simply drawn again, and it is guaranteed to agree with the plan it sits beside.
That dependence runs through our other work. The canopy outlines have already been turned to follow the way each crown actually grows, described in the note on competition-derived canopy orientation, and the section inherits that without further effort. The same outlines and heights decide which trees appear in which survey photograph, described in the note on reading a tree survey from its photographs.
For now the tool is kept separate from our main survey processing, so that it can be used alongside it on live projects and prove itself before the two are brought together.
Version
This note describes version 0.7 of the section tool. It is written and maintained by Tony Sorensen, and will be revised when the tool changes in a way that affects the drawings it produces.
| Version | Date | Changes |
|---|---|---|
| 1.0 | September 2026 | First publication, describing section tool version 0.7. |