Script 05: Volume

File: sql/scripts/main/05_calc_volume.sql
Reads from: {city2tabula_schema}.{lod_schema}_building
Writes to: {city2tabula_schema}.{lod_schema}_building (UPDATE)

---

Purpose

Estimates building volume using a simple bounding-box approximation: height × footprint area. Two estimates are computed, one from the eave height and one from the ridge height, giving a lower and an upper bound on the true volume.

This is a deliberate simplification. Computing the exact volume of a 3D building solid from CityGML would require expensive geometric operations. For the purposes of TABULA archetype matching (post script 02), a height × footprint approximation is sufficiently discriminating and much faster to compute.

---

What it does

UPDATE {city2tabula_schema}.{lod_schema}_building AS bf
SET
    min_volume = CASE
        WHEN bf.min_height IS NOT NULL AND bf.footprint_area IS NOT NULL
        THEN ROUND((bf.min_height * bf.footprint_area)::numeric, 2)
        ELSE bf.min_volume
    END,
    -- max_volume and the two unit columns follow the same shape
    ...
WHERE bf.building_feature_id IN {building_ids}

No CTEs are needed: both operands (min_height, max_height, footprint_area) are already columns in the same row, written by script 04.

Each assignment is wrapped in a CASE that guards against NULL inputs. When either operand is NULL, for example a building with no wall surfaces, the column keeps its previous value instead of being overwritten with NULL.

---

Volume semantics

Column	Formula	Interpretation
min_volume	min_height × footprint_area	Eave-height box, excluding the roof volume. Conservative lower bound.
max_volume	max_height × footprint_area	Ridge-height box, counting the full roof height as if it were a box. Liberal upper bound.

The true building volume lies somewhere between these two values. For a building with a flat roof, min_volume and max_volume are equal.

---

What comes next

Script 06 refines the storey count and overwrites the total floor area estimate.