Step 4: 2D Geometry Analysis¶

Purpose¶

This step performs the main two-dimensional geometric interpretation of the segmented vault data. It takes the projection image and segmentation masks produced in Steps 2–3 and works towards a bay-plan — the network of intrados lines (rib centre-lines) that defines the vault's planimetric design.

Medieval vault plans were conceived as intersecting patterns of ribs, laid out through iterative geometrical operations on a rectangular bay.¹ Vault Analyser replicates this logic computationally: it establishes the bay rectangle, locates the bosses (rib junctions), tests which geometric template best explains their positions, and reconstructs the rib network.

Sub-stages¶

2D Geometry Analysis is consisted of four sequential sub-stages, labelled 4A–4D in the interface:

Sub-stage	Name	Key action
4A	ROI and Bay Proportion	Define the analysis region and compute the bay's aspect ratio
4B	Reference Points	Review and adjust the boss and corner nodes used by later stages
4C	Cut-Typology Matching	Score each boss against starcut and circlecut templates to identify the best-fit design typology
4D	Bay-Plan Reconstruction	Infer the rib network as a graph of nodes and edges

Each sub-stage saves results before the next can run, so the data flow is strictly sequential: ROI → nodes → matching → reconstruction.

Interface layout¶

Key concepts¶

ROI (Region of Interest) : A rotatable rectangle that isolates one vault bay on the projection image. Later geometry is measured relative to this frame.

Boss : A raised keystone or junction where ribs meet. Bosses are represented as point nodes for later matching and reconstruction.

Cut typology : The family of geometric templates used to explain boss positions within the bay.

Bay plan : The final graph of nodes and edges representing the vault's 2D rib pattern.

Expected result¶

• a saved ROI with sensible bay proportions
• a reviewed set of reference points
• a credible matching result
• a reconstructed bay plan that agrees with the visible rib pattern