Texture resolution formula

The Demetrescu-d’Annibale texture resolution formula is the algorithm 3DSC uses to compute how many 4096 px texture atlases are needed to texture a segmented photogrammetric tile at a fixed, homogeneous ground resolution. It is the single source of truth for every place in the documentation that quotes the formula — the Metashape tool reference and the Digital Replica Phase 3 how-to both link back here.

The formula was published as Equation (1) in Demetrescu et al. 2026 (Remote Sensing 18(2):203, open access, CC-BY) and is implemented in the 3DSC for Metashape add-on (Supplementary Code S1 of that article).

The formula

For a tile of surface area \(A_{\text{tile}}\), the number of texture atlases required to hold the target texel density is:

\[n_{\text{tex}} = \operatorname{round}\!\left( \frac{A_{\text{tile}}}{100} \times \frac{(L_{\text{ref}} / r_{\text{target}})^2}{s_{\text{tex}}^2 \times r_{\text{uv}}} \right), \qquad n_{\text{tex}} \geq 1\]

Where:

  • \(n_{\text{tex}}\) = number of \(4096^2\) texture atlases required (minimum 1)

  • \(A_{\text{tile}}\) = actual surface area of the tile in m² (from chunk.model.area() in Metashape)

  • \(L_{\text{ref}}\) = 10 000 mm — side length of the reference 100 m² square (10 m × 10 m)

  • \(r_{\text{target}}\) = 1.26 mm²/texel — empirically determined target texture density

  • \(s_{\text{tex}}\) = 4096 px — texture atlas dimension

  • \(r_{\text{uv}}\) = 0.6 — UV-space utilization efficiency (photogrammetric UV atlasing leaves ~40 % of texture space unused)

  • \(\operatorname{round}(\cdot)\) = standard rounding (0.5 rounds up)

The formula operates in two conceptual steps.

Step 1 — Reference calculation

How many atlases a standard 100 m² tile needs:

\[n_{\text{ref}} = \frac{(10000\ \text{mm} / 1.26\ \text{mm}^2/\text{texel})^2} {4096^2 \times 0.6} \approx 6.26 \text{ textures per } 100\ \text{m}^2\]

Step 2 — Area scaling

Scale that reference proportionally by the actual tile area:

\[n_{\text{tex}} = \operatorname{round}\!\left( n_{\text{ref}} \times \frac{A_{\text{tile}}}{100} \right)\]

Worked example

A tile of \(A_{\text{tile}} = 50\ \text{m}^2\) needs \(6.26 \times (50/100) = 3.13 \rightarrow 3\) textures. A 55 m² tile gives \(6.26 \times 0.55 = 3.44 \rightarrow 3\); a 60 m² tile gives \(6.26 \times 0.60 = 3.76 \rightarrow 4\).

Using standard rounding (rather than always rounding up) optimizes texture memory: tiles slightly above a threshold receive an extra atlas, while those slightly below keep the lower count.

Reference table

Texture count per tile area, as published (Table 3 of Demetrescu et al. 2026), at 1.26 mm²/texel, 4096 px atlases, \(r_{\text{uv}} = 0.6\):

Tile area (m²)

Textures (4096 px)

0 – 16

1

16 – 33

2

33 – 49

3

49 – 66

4

66 – 83

5

83 – 100

6

Note

The published tiling standard caps the standard tile at 100 m² (6 atlases). The Metashape add-on additionally offers a Texturize Models (200 m² limit) mode that extends this to larger tiles and caps at 12 atlases; this is a tool convenience beyond the published standard, intended for oversized architectural features rather than the normal tile size.

Reference implementation

The formula is implemented in 3DSC_MS_GUI.py (method _compute_texture_pages) as:

numtex = pow((10000 / x_res_a_terra), 2) / (tex_size * tex_size * ratio)
numtex_x_area = (numtex * area_model) / 100
tex_num = max(1, round(numtex_x_area, 0))

Where the code variables map to the published notation as:

  • x_res_a_terra → \(r_{\text{target}}\) (default 1.26)

  • tex_size → \(s_{\text{tex}}\) (default 4096)

  • ratio → \(r_{\text{uv}}\) (default 0.6)

  • area_model → \(A_{\text{tile}}\), from chunk.model.area()

The constant 10000 is \(L_{\text{ref}}\) in mm.

Why these defaults

  • 1.26 mm²/texel (target density): empirically determined through iterative testing on Head Mounted Displays and desktop screens with domain experts. At this density (~0.67–0.87 texels per mm² of real surface) fine details — mortar texture, surface weathering, painted decoration — stay clearly visible during close-range immersive inspection while keeping rendering performance acceptable. Across the Amba Aradam digital replica the achieved density stayed within 1.15–1.32 mm²/texel (mean ~1.25).

  • 4096 px (\(s_{\text{tex}}\)): chosen for broad platform compatibility — deployable on web browsers, mobile devices and entry-level HMDs without exceeding memory limits. \(8192^2\) is feasible on high-end hardware.

  • 0.6 (\(r_{\text{uv}}\)): the median UV-space efficiency observed across the dataset; automatic UV parameterization in Metashape leaves ~40 % of the atlas unused (island spacing, seam allowances, packing). Adjust it if a different unwrapping strategy is used.

See also