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Triangulate a mesh

Triangulation builds a surface mesh from a point cloud. Phytograph offers five methods; pick based on your data and what you want to do with the result.

Quick decision

Your data Use
Dense scan of a leaf or other roughly-flat surface Delaunay
Branch surfaces, consistent density Ball Pivot
Dense whole-plant scan, need a watertight surface Poisson
Concave shapes you want to wrap tightly Alpha Shape
Multi-scan TLS data with scanner positions Helios

This page uses the short names above. In the Method dropdown they appear in full as Bailey & Mahaffee / Helios (recommended), Ball Pivoting, Poisson (not recommended for leaf angle), Alpha Shape (not recommended for leaf angle), and Delaunay (2D) (not recommended for leaf angle) — the "not recommended for leaf angle" tags flag methods that resample or smooth the surface, which distorts the leaf-orientation statistics.

The Triangulation modal

All five methods live in one Triangulation Setup modal:

  1. Click Triangulate (triangle icon) — the modal opens. It's available whenever at least one scan exists in the scene; you don't need a scan selected first. Any scans you do have selected are pre-ticked in the modal's Scans picker (step 3) as a convenience.
  2. Method — pick the algorithm from the dropdown. The parameters and options below update to match. The default is Helios when any listed scan carries scan parameters, otherwise Ball Pivot.
  3. Scans — tick which scans to triangulate. Each row shows the scan's color, point count, and (when it has parameters) its scanner origin. Use All / None to select in bulk. To change a scan's parameters, edit it from the Scans panel before opening this modal.
  4. Output (non-Helios methods) — choose Triangulate each scan separately (one mesh per scan) or Merge selected scans into one mesh (their points are fused before meshing). Helios always fuses its selected scans, so this toggle is hidden for it.
  5. Set the method-specific Parameters (below).
  6. Click Triangulate.

While the mesh builds, a small progress pill appears at the top of the viewer for every method (not just Helios). It names the current stage — Reading points, Estimating normals, Meshing, Cleaning up mesh, Computing surface area — and shows a bar with the percentage. When you triangulate several scans separately the label is prefixed with the scan count (e.g. [2/3] Meshing), and a Helios run reports Triangulating scan N of M. Click the ✕ on the pill to cancel a run in progress; no mesh is added and nothing else changes.

Method-specific parameters:

  • Auto radius (default on) — the ball-pivot radius is computed from the median nearest-neighbour spacing of the cloud.
  • Untick it to set the radius manually (in meters). A good value is ~1.5–2× the average point spacing.
  • Grid — optionally pin the mesh to a voxel box (the same selector the Helios method uses). Pick Auto — fit to all points (no pin) for an ordinary mesh, or a voxel box to crop the points to it before meshing and make the mesh re-usable for the leaf-area inversion. A pinned, per-scan mesh records which grid and scan produced it, so the LAD tool can inject it directly instead of re-triangulating. A merged mesh (see Output below) can't be pinned for LAD — it has no single source scan — so the selector warns you; triangulate each scan separately to keep it LAD-re-usable. The Meshes panel shows whether a ball-pivot mesh is "re-usable for leaf-area inversion" or why it isn't.
  • Octree depth — higher = more detail and slower. Default 8 is a good starting point for whole-plant scans.

If Poisson fails, just run it again

Poisson occasionally fails with "Poisson reconstruction crashed inside Open3D". This is an intermittent bug in the underlying Open3D library, not a problem with your cloud or your settings — it hits a small fraction of runs regardless of input. Simply triangulating again almost always succeeds; if you'd rather not retry, Ball Pivot or Alpha Shape on the same cloud avoids it entirely. The reconstruction runs in a separate process, so a failure only affects that one triangulation — the app and the rest of your scene are unaffected.

  • Auto Alpha (default on) — alpha is chosen automatically.
  • Untick it to set the alpha radius manually: smaller alpha = tighter to the points, more holes; larger alpha = smoother surface, more bridging across gaps.
  • No parameters — the points are projected to a plane and triangulated. Best for a single roughly-flat surface.

No post-triangulation filter on cloud methods

The Lmax / aspect filter is Helios-only. Each cloud method already applies its own length scale while reconstructing — the ball-pivot radius, alpha-shape alpha, Poisson octree depth — so the long bridge triangles the Helios filter trims never survive into the returned mesh. Re-filtering by edge length afterwards would do nothing (and the "auto Lmax" you'd see on a cloud method is just the auto-computed radius, not an independent estimate). Set the length scale through the method's parameter (e.g. the ball radius) instead.

Sky/miss returns are skipped

If the cloud is a multi-return / full-waveform scan, its sky/miss points — rays that hit nothing, recorded far out at the scanner's max range — are excluded automatically before triangulation. They aren't surface points, so meshing them would only span a phantom shell far from the real geometry (and slow Ball Pivot to a crawl). This is why the points used shown on the mesh row can be lower than the cloud's total point count.

The resulting mesh appears in the Scene panel's Meshes list, named after the method and source cloud — e.g. "Poisson triangulation (tree.xyz)" — so triangulation results are distinguishable at a glance from imported meshes, plant models, and each other. If two share the same auto-name, the later one is numbered — "… (2)", "… (3)". The source cloud is auto-hidden when the mesh lands so the result isn't buried in a sea of points; it stays in the scene and can be re-shown (eye icon).

Manage a mesh in the Meshes list

Each mesh row supports a few quick edits:

  • Rename — double-click the mesh name to edit it in place. Press Enter to commit or Esc to cancel; clearing the field restores the default name (method + source filename for a triangulated mesh, with a "(2)"-style suffix if it would otherwise duplicate another row; plant type/age for a plant).
  • Inspect parameters — expand the row (chevron ▸) to see how the mesh was reconstructed: the triangulation method and its method-specific parameters. For cloud methods that's the Poisson octree depth, alpha-shape radius, or ball-pivoting radii, plus the normal-estimation settings and the number of points used (which reflects any downsampling of a large streamed cloud). For a Helios mesh it's Lmax, the max aspect ratio, and how many scans were fused. Once you apply the triangle filter to a Helios mesh, the readout also shows the filter breakdown (candidates / kept / dropped).
  • Recolor — click the color swatch to the left of the name to open a color picker. Pick a color or type a hex value. The color applies to the mesh surface; texture-mapped meshes ignore it and keep drawing their texture, so the swatch is only shown for untextured meshes.
  • Transform — click the ⤢ (double-arrow) button on the mesh's row to open its Transform panel, where you can type an exact position, rotation (degrees), and per-axis scale, or toggle the on-screen translate/rotate gizmos. The Blender-style shortcuts T (translate), S (scale), and R (rotate) still work with a mesh selected; lock an axis with X/Y/Z. See Keyboard shortcuts.

Large (streamed) clouds are capped

Clouds imported from large XYZ scans are streamed from an on-disk octree rather than held in memory. When you triangulate one, it is downsampled to the Triangulate max points limit (default 5,000,000) before meshing, which bounds memory use. If a cloud is downsampled you'll see a warning toast telling you how many points were used. Raise the cap in Settings (open it from the app menu — Phytograph → Settings… on macOS, File → Settings on Windows/Linux, or press ++cmd+comma++ / ++ctrl+comma++) under Performance → Triangulate max points for more surface detail at the cost of more memory.

Plot leaf angles (any method)

The Leaf angles… tool works on every triangulated mesh — the cloud methods (ball-pivoting, Poisson, alpha-shape, Delaunay) as well as Helios. The Filter controls (Lmax / aspect) are Helios-only — see Helios method below. Expand a mesh's row to reach the tool:

  • Leaf angles… — opens the leaf-angle distribution plot (inclination PDF, azimuth rose, and a de Wit archetype + Beta fit). It reads the mesh's triangle normals directly, area-weighted, so it works on any triangulated surface. A mesh built with a voxel grid splits the distribution per cell; a mesh with no grid (every cloud mesh, and an auto-grid Helios mesh) shows a single Whole mesh distribution. See Estimate leaf area density for the related per-voxel inversion.

Helios method

The Helios method uses the scanner geometry to triangulate only the rays that actually returned, producing more accurate branch surfaces than cloud-only methods. Every selected scan must carry both point data and scan parameters (the scanner origin); scans missing parameters are listed but can't be selected, with a note telling you to add them.

Select the Helios method in the Triangulation modal to reveal its options (the per-scan/merged toggle is hidden — Helios always fuses the selected scans):

  1. Make sure each scan you want to include has scan parameters attached. If a scan only has data, click the radio icon on its row in the Scans panel to add parameters (or import a Helios scan XML that carries <origin> and <size> for each <scan>).

  2. In the Scans picker, tick two or more eligible scans. Each row shows the scan's origin read from its parameters — no manual entry. To adjust a scan's parameters, edit it from the Scans panel before opening this modal.

    Each scan is triangulated in the angular grid it was actually sampled in: its scanner origin, zenith/azimuth sample counts (Ntheta/Nphi) and angular bounds all come from that scan's own parameters. Edit them per scan in the Scans panel — they are no longer typed in once for the whole batch. 3. Filtering happens afterwards. There is no Lmax to set here — Phytograph triangulates unfiltered, keeping every candidate triangle, and the edge-length (Lmax) and aspect-ratio filter is applied as a live post-processing step in the mesh panel (next step). This means estimating a good Lmax is instant, and you can change it and watch the mesh update without ever re-triangulating. 4. Grid — the triangulation grid bounds the region that gets meshed: - Auto — fit to all points (default when you haven't made a box): Phytograph fits a single-cell grid around every point. A warning reminds you that all points are triangulated, so the ground and trunk should already be segmented or cropped away. - A voxel box: create one with Create Voxel Grid (it appears in the Meshes list), position and size it over the region you care about, and set its grid subdivisions in the mesh panel. It then appears in the Grid dropdown; selecting it uses the box's position, size, Nx×Ny×Nz cell counts, and azimuthal rotation as the grid — a box rotated about its vertical axis crops to that rotated footprint, not its axis-aligned bounding box. 5. Click Triangulate.

The mesh lands in the Meshes list named "Helios triangulation" (the word triangulation keeps it distinct from a Helios plant model). Expand its row to reach the Filter controls:

  • Lmax — maximum allowed edge length (meters). Triangles with a longer edge are hidden. Seeded automatically from the candidate edge-length distribution (see below); edit it and the mesh re-filters instantly.
  • Max aspect — drops mis-shapen triangles (max edge ÷ min edge; default 4).
  • Auto — re-applies the automatic Lmax estimate.

The auto-estimate inspects the spread of candidate edge lengths: valid triangles connect adjacent points on the same leaf or branch (short edges), while erroneous ones bridge separate surfaces (long edges). It places Lmax at the natural split between those two scales and reports two numbers (with a ? next to them that opens a short how-to-read explainer):

  • Separation (η) — how cleanly the edge lengths fall into two groups. High means a sharp valley between the short and long scales (the mesh is insensitive to Lmax); Medium/Low means they blur together (leaves close together relative to scan resolution) and the mesh is sensitive to Lmax.
  • Modes (×) — how far apart those two groups are. Genuine gap bridges sit many times above the surface spacing (High). A small ratio (Low) means both groups are really surface — sampled at different spacings, e.g. a coarse or strongly anisotropic scan — so cutting between them drops valid triangles and leaves holes.

Watch for High η with Low Modes: a confident split placed in the wrong spot. If the mesh looks holey there, raise Lmax. The filter breakdown above the controls (candidates / kept / dropped) updates as you adjust the filter.

Scans with near-coincident returns can produce a handful of degenerate triangles thousands of times smaller than the real surface. Those are excluded from the estimate — otherwise they would form the strongest split in the distribution and pull Lmax below every genuine triangle, leaving the mesh empty. The estimate is also never placed below the smallest real candidate, so Auto always yields at least one triangle.

Check point spacing

The edge-based auto-estimate has a blind spot: on a sparsely-sampled surface (a thin shell of points relative to the leaf size) the triangulation generates mostly bridge triangles spanning the gaps, so the candidate-edge distribution is dominated by bridges. The split can still look clean (η/Modes read Medium or even High) while Lmax lands several times too large — and an oversized Lmax bridges across the surface, tilting the reconstructed leaf normals and corrupting the leaf-angle distribution and G(θ) (you may see G(θ) far below the expected ~0.5 for a near-spherical canopy).

Because the candidate edges can't reveal this on their own, the Filter panel offers a Check point spacing button whenever the indicators aren't both High. It measures the actual nearest-neighbor spacing of the points inside the grid (an independent signal) and compares it to your current Lmax:

  • If Lmax is within a normal multiple of the spacing, it confirms bridging is unlikely.
  • If Lmax is much larger than the spacing (≳3×), it warns that the mesh is likely bridging and suggests lowering Lmax toward the point spacing.

The check only reports — it never changes Lmax for you. It can take from a moment to tens of seconds on a very large cloud (it builds a spatial index over the in-grid points), which is why it's an explicit button rather than automatic.

Merged multi-scan clouds

Helios triangulation assumes single-scan-position data — it uses one scanner origin per scan to reconstruct ray directions. If a scan is actually a registered merge of several scanner positions, the auto-estimate flags it (a toast and a note in the Filter panel): the triangulation would bridge surfaces seen from different origins, producing spurious triangles. Triangulate each scan position separately instead of meshing the merged cloud.

For most TLS data of stone-fruit trees the auto Lmax works; nudge it down (to ~5–10 cm) for finer branch surfaces, or up if your scan is sparse.

Very large scans

Full-resolution TLS clouds can produce several million candidate triangles — more than fits in a single response. When that happens Phytograph returns the densest few million triangles (a notice tells you how many of how many candidates were kept) and the Filter can only be tightened from there; loosening past that point means re-triangulating. Cropping to a voxel box or segmenting away ground/trunk first keeps the mesh — and the filter range — full.

Leaf area density

Helios triangulation is also the first step inside leaf area density estimation, where the mesh is used to derive the G-function rather than as the end product. If canopy density is what you're after, use that workflow instead of meshing directly.

Color a mesh by surface geometry

A triangulated mesh — one built by triangulating a point cloud, including Helios meshes — can be pseudocolored per triangle to inspect its surface, handy for checking a reconstruction or reading leaf/branch orientation. In the Meshes panel, click the chevron (▸) on the mesh's row to expand its Color by options (the chevron only appears on triangulation-generated meshes, not plants, shapes, or imported meshes):

  • Inclination — zenith angle of each triangle's normal, folded to 0–90° (a horizontal facet reads 0°, a vertical one 90°). Up- and down-facing facets read the same.
  • Azimuth — compass bearing the triangle's normal points, 0–360°. Triangulated surfaces have no consistent facet winding, so the outward direction must be inferred. For Helios meshes each facet's normal is oriented toward the scanner that saw it, giving the true outward bearing — so a scanned closed surface (e.g. a sphere) reads a continuous azimuth rather than flipping 180° between its upper and lower halves. For meshes with no scan provenance the normal is folded into the upper hemisphere instead (deterministic, but a closed surface will show a seam at its equator).
  • Triangle area — surface area of each triangle.
  • Source scan — (Helios meshes only) colors each triangle by the scan it was reconstructed from, using that scan's swatch color. Helios triangulates each scan independently, so every triangle belongs to one scan. A legend lists the contributing scans and their triangle counts.

For the scalar modes, pick the gradient with the colormap dropdown that appears below; a colorbar in the bottom-right shows the value range. The Source scan mode shows a per-scan legend instead. Choose Solid color to go back to the flat mesh color.

Plot the leaf angle distribution

For a Helios mesh, you can go beyond per-triangle coloring and plot the mesh's leaf angle distribution function — the statistical distribution of leaf orientations across the canopy. Expand the mesh's row in the Meshes panel and click Leaf angles…. It's offered for any triangulated mesh (DEM surfaces and fitted crowns excepted), though the Helios method gives the most faithful distribution. A plot window opens with:

  • Inclination PDF — the probability density of the leaf inclination (zenith) angle over 0–90°. Each triangle contributes its inclination weighted by its area, so a large leaf facet counts more than a sliver — the curve reflects leaf surface, not triangle count. A point is drawn at each bin center and joined by straight segments; the Bins dropdown changes the histogram resolution (9–90 bins, i.e. 10°–1° wide).
  • Azimuth distribution — a polar (compass) rose of the area-weighted azimuth, showing which directions the leaf surfaces face. North is up; the petal radius is the density in each 10° sector.

Per-cell overlays

If the mesh was triangulated inside a voxel grid (rather than the auto single-cell grid), the window splits the distribution per grid cell. Each cell's inclination curve is overlaid in its own color, with a checkbox list on the right. Untick a cell to drop it from both plots, or use All / None to toggle them in bulk — useful for comparing canopy layers (e.g. top vs. bottom voxels) or isolating one region. With the auto grid the list collapses to a single Whole mesh entry.

When more than 24 cells are visible (a fine grid quickly has hundreds of occupied voxels), the window shows a single combined curve over all visible cells instead of one line per cell — overlaying hundreds of curves is neither readable nor fast. Narrow the selection (untick cells, or click None and tick the handful you want) to ≤ 24 visible cells and the per-cell overlays, the per-cell parameters table, and the Show Beta fit option come back.

Canonical de Wit fit

The window also fits the six canonical de Wit leaf-angle distributions — planophile (mostly horizontal), erectophile (mostly vertical), plagiophile (mostly ~45°), extremophile (horizontal and vertical), spherical (random, as on a sphere's surface), and uniform — to the visible data and labels the closest match with a goodness-of-fit score (e.g. "Best fit: spherical (R²=0.94)"). The chosen curve is overlaid as a dashed line so you can see how well the canopy matches the archetype. Hiding cells re-fits to just the visible ones.

Same distributions feed the LAD G(θ) override

These de Wit families and the Beta (Goel–Strebel) fit below are exactly the distributions you can prescribe in the LAD tool's Supply G(θ) directly option to derive G(θ) without triangulating — useful when you know (or measured) the canopy's leaf-angle distribution. See Leaf-angle distributions and G(θ).

Beta-distribution fit (Goel–Strebel)

Below the inclination chart a fitted distribution parameters table reports, per cell, a continuous two-parameter Beta distribution fit to that cell's leaf inclination — the standard Goel & Strebel (1984) model. The shape parameters α and β are estimated by moment matching (the mean and variance of the normalized inclination t = θ/90), alongside the mean inclination mean θ in degrees, the fit R², the leaf-projection coefficient G(θ) (see below), and that cell's best de Wit archetype, so you can read every visible curve's parameters at a glance. A cell with no usable spread (all triangles coplanar) shows — for the Beta columns. (With more than 24 cells visible the table collapses to a single All visible row summarizing the combined distribution, matching the combined plot.)

Two export buttons in the window header write CSV files for analysis outside Phytograph, both reflecting the currently visible cells:

  • Parameters CSV — the fitted-parameters table exactly as shown: one row per visible cell (or the single All visible row in combined mode) with the α, β, mean θ, R², G(θ), and de Wit columns.
  • Distributions CSV — the empirical inclination probability density curves plotted in the chart: one row per visible cell (or a single combined row in combined mode), with one column per inclination bin (the column headers are the bin-midpoint angles in degrees). Densities are normalized so that the sum over bins × bin width equals 1.

Both files also include the cell's center and dimensions (each an (x, y, z) triple in metres) read from the triangulation grid, so every row is located in space. These are blank for a non-grid Whole mesh mesh and for the combined All visible row, which span no single grid box.

The G(θ) column is the area-weighted mean of |n̂ · v̂| over the cell's triangles, where n̂ is each triangle's face normal and v̂ is the beam direction — the leaf-projection coefficient Ross's G-function describes, here measured directly from the mesh geometry rather than assumed from a distribution. (It's the same quantity the leaf area density inversion reports per voxel.) When the mesh carries scan provenance the beam points from each triangle back to the scanner that saw it; for a mesh with no scan origins (e.g. a triangulated plant model) it falls back to the conventional nadir view (v̂ straight down), so G(θ) reduces to the area-weighted mean of |cos θ| and is defined for every mesh.

Tick Show Beta fit above the chart to overlay each cell's fitted Beta curve as a dashed line in the cell's color. It's off by default to keep the plot readable when many cells are visible, and is disabled while the combined view is active (more than 24 cells visible).

Produce a point cloud from a mesh

The inverse operation — turning a mesh or plant model back into a point cloud — is done with a true ray-traced scan, not random surface sampling. Place one or more scanners and run a synthetic LiDAR scan; the resulting cloud respects occlusion and scanner geometry, so it tests a reconstruction pipeline against a realistic (yet perfectly known) input.

What's next