Axis
The dominant directional line. It can be longitudinal, radial, or crossed by a transept.
A = {p₁ → p₂}
Sacred geometry / field atlas
Where stone
becomes a system.
A visual index of church architecture through the mathematics of its plans, sections, modules, axes, and enclosing forms.
99
geometry studies
03
drawing modes
04
reading profiles
Dataset status99 schematic · 00 measuredSchematic = illustrative proportions; not a measured survey.
The collection
Choose a geometry study
Illustrative proportions · metric units · v1.1
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Study 01 / Basilica
Basilica of Sant'Apollinare in Classe
SCHEMATICData status: schematic; Illustrative proportions; not a measured survey.Envelope dimensions: 56 meters long, span 30 meters, height 18 meters; primary radius 15 meters.
Reference · Basilica of Sant'Apollinare in Classe
Source · UNESCO World Heritage Centre · Ravenna nomination ↗ · Real reference building: UNESCO describes the basilica as 56 m long by 30 m wide; the Atlas drawing dimensions, module, radius, and height are schematic readings, not a measured survey.
Data status · schematic
Illustrative proportions; not a measured survey.
Schema 1.1 · units: meters
Direct route · #atlas/basilica/plan/exterior/all
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Focus
Outside · Plan · all geometry · 100% zoom
The nave is read as a repeated bay module: length is a sequence, while the apse closes the axis with a single primary radius.
overall length
58.0 m
overall span
22.0 m
overall height
18.0 m
length / span
2.64 : 1
symmetry index
1.00
Derived reading
How the proportions behave
R = L ÷ span = 2.64
The nave is read as a repeated bay module: length is a sequence, while the apse closes the axis with a single primary radius.
floor area estimate1,276 m²supplied floor-area estimate
section ratio0.82H ÷ span
module / span0.33M ÷ span
radial reach11.0 mprimary radius
estimated volume14,239 m³schematic estimate
reading profile0 — 100 · interpretive score
These scores describe proportional tendencies, not empirical measurements. Basis: linearity = length ÷ span · verticality = height ÷ span · radiality = typology cue · repetition = bay count.
Proportion lab
The same questions, different answers
Relative readings · full collection
Compare the studies by the relationships that make a room feel directional, centered, compressed, or immense. The values are normalized from each study record; each row and envelope identifies its schema-defined data status.
Full collectionR = L ÷ spanlength-to-span ratio
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Select two or more studies with the + controls in the Atlas to create a focused comparison. Use a + control or the Add visible to compare action in the Atlas. Without a selection, the full collection is shown.
Selected for comparison
Schematic = illustrative proportions; not a measured survey. Measured = source-supported dimensions. Counts for the full collection: 99 schematic · 0 measured.
Direct route · #compare
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00 / collection geometry
Side-by-side envelopes
01 / linearity
Length : span
Scale 0 → 2.71 · active comparison maximum
A higher ratio reinforces a long processional reading.
02 / verticality
Height : span
Scale 0 → 1.53 · active comparison maximum
Vertical emphasis is compared with the widest enclosing dimension.
03 / repetition
Module and bay rhythm
Scale 0 → 11.5 m · active comparison maximum
Each line is one notional bay; group length is normalized to the largest module in the active comparison.
04 / interpretive profile
Reading profile
Scale 0 → 100 · interpretive reading score
These four scores describe proportional tendencies, not empirical measurements. Basis: linearity = length ÷ span · verticality = height ÷ span · radiality = typology cue · repetition = bay count.
Read the 99 study records as a table
Recorded dimensions, derived ratios, optional floor-area estimates with their basis, volume estimates with provenance, source notes, and the four interpretive reading-profile scores are available here and in the CSV or JSON export. Study names open in Atlas, with each curated study index kept visible in the row. The header actions download both formats. Both exports carry the study's curated index, schema version, unit system, published schema URL, active view route, data-status context, and self-describing reading-profile basis/note; each record also carries a direct study route.
Swipe horizontally on narrow screens · focus the table and use ← → or Home / End.
| Study / index | Axis | Status | Source / provenance | Length (m) | Span (m) | Length ÷ span | Height (m) | Height ÷ span | Bay count | Module (m) | Radius (m) | Symmetry index | Floor area estimate (m²) | Est. volume (m³) | Volume basis | Linearity (0–100) | Verticality (0–100) | Radiality (0–100) | Repetition (0–100) |
|---|
Reading the drawings
Geometry is a way of seeing
Notes on the atlas model
Open current studyDirect route · #method
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01 — 04
Every church is an argument between the line and the circle.
This atlas translates a building into a small vocabulary of geometric relationships: axes, modules, radii, envelopes, and proportions. Switch between outside and inside to see how the structural shell becomes a spatial sequence.
Module
A repeatable unit that sets the pace of bays, columns, windows, and structural spans.
M = L ÷ n
Envelope
The enclosing figure: rectangle, cross, ellipse, polygon, or a compound of simple forms.
E = {x, y, r, θ}
Symmetry
A reading of how closely the plan mirrors itself across its principal axes.
S = 1 − (Δ ÷ P)
Research key
How to read the derived values
These readings describe the proportional model; they are analytical aids, not measured survey results.
- Floor area reading
- Uses the supplied floor-area estimate when available; otherwise it displays a bounding area from length × span. The active reading labels which basis applies.
- Section ratio
- Height ÷ span. A larger value indicates a taller section relative to its widest enclosing dimension.
- Module / span
- Notional bay module ÷ span. It shows how much of the cross-width one repeated unit occupies.
- Radial reach
- The primary radius recorded for the study’s central, apsidal, oval, or other curved figure.
- Estimated volume
- An optional estimate. Its calculation basis and provenance are shown beside the value; missing estimates remain explicitly marked.
- Reading profile
- Four interpretive 0–100 scores. Linearity and verticality follow normalized length ÷ span and height ÷ span; radiality follows a typology cue; repetition follows normalized bay count. They describe proportional tendencies, not empirical measurements.
Evidence labels
How to read data status
The published schema defines 2 data statuses for 99 records; counts: 99 schematic · 0 measured; each record carries one label and a provenance note.
Illustrative proportions; not a measured survey.
Source-supported dimensions.
Dataset contract
What each record contains
JSON records and CSV rows describe the same study objects, while the published schema makes the contract reusable. Dimensions follow the schema unit system; optional estimates stay blank when a source does not supply them.
- Identity
id,index,name, andshortNameidentify a stable study and its display labels.- Context
typology,place,era,churchName,emphasis, andaxissituate the reading.- Envelope
length,span,height,envelope, andtypedescribe the enclosing figure.- Rhythm
bayCount,module, anddetailsrecord repetition, pace, and named geometric components.- Curvature & balance
radiusrecords the primary curved reach;symmetryis a normalized 0–1 reading.- Interpretation
surfaceNote,exteriorNote, andinteriorNotekeep the visual reading attached to each record.- Provenance
status,source,sourceUrl, andsourceNotestate the record’s data status, named-building reference, and provenance.- Optional estimates
floorAreaEstimate,volumeEstimate, andvolumeBasisare included only when supplied by the study; derived exports also identify the floor-area basis.
Derived in the interface and exports: length / span · height / span · module / span · floor area reading and basis · estimated volume · reading profile.
Important: The current collection is a schematic proportional study, not a measured survey or a claim about every church. Each record carries a status and provenance note. Replace the values in data/geometry.js with your own measured dataset to expand the atlas.