Derivation constants and tolerances

Derivation constants are not defaults of the attribute ledger. The ledger fixes what may be written; these fix what is derived when nothing was written. Write a value and the written value always wins.

Tolerances are the numbers that decide how different two things must be to be different things. Coordinates are integer millimetres by default, so a length tolerance sits at half the integer step.

Both are published as DERIVATION_CONSTANTS and TOLERANCES, and a test binds the two tables on this page to the implementation.

Derivation constants — seventeen

Constant	Value	Unit	What it decides
WALL_T	100	mm	default wall thickness (t: overrides), distributed half to each side of the centre line
RAIL_T	60	mm	default thickness of a non-enclosing boundary (air:1); t: overrides
RAIL_T_MAX	80	mm	cap on the thickness of a non-enclosing boundary; whatever t: says, it stops here
RAIL_H	1100	mm	default top height of a non-enclosing boundary; the boundary's h: overrides
OPENING_HEAD	2000	mm	lintel height. A door rises to it; everything else drops from it
OPENING_H	1200	mm	default height of an opening that is not a door; the opening's h: overrides
CEILING_T	30	mm	face thickness of a ceiling
ROOF_T	200	mm	default roof slab thickness, and the amount stacked above the ceiling height on a top storey
CUT_HEIGHT	1200	mm	height of the plan cut above FL (the default input to derive)
DEFAULT_RISER_MAX	180	mm	maximum riser (riser: overrides). It decides the riser count
TREAD_TARGET	300	mm	target going used when the landing of a turning run is solved as the remainder (tread: overrides)
LANDING_MIN	1100	mm	minimum depth of an intermediate landing; a written landing: is raised to it too
ENTRY_LANDING	1100	mm	default depth of the entry floor band (entry: overrides)
LANE_ESCALATOR	1200	mm	default nominal width of one escalator unit (lane: overrides). It decides the unit count
TREAD_SOLID	200	mm	face thickness of a tread board (solids)
SLAB_T	200	mm	thickness of a landing slab and of the inclined slab of a ramp or escalator
STEP_MARK	400	mm	pitch of the escalator step marks in plan

Three dimensions are solved on the spot rather than held as constants. The lift car is inset min(300, side ÷ 6) on all four sides and stands from FL + 60 to FL + 2400. The escalator balustrade is min(140, unit width ÷ 8) wide and 100mm thick, raised 900mm above the tread surface. Each is defined relative to another value, so none of them is a constant of its own.

Tolerances — seven

No question may have two tolerances.

Tolerance	Value	Unit	What it permits
EPS	0.5	mm	edge axis-parallelism, facing, interval coincidence, gap in collinear merging, grid-reference overrun, opening overlap
AREA_EPS	1	mm²	whether what a cut leaves disappears; whether the left/right area difference counts as "no bias"; whether a roof tile survives
PROBE	5	mm	how far to probe either side of a drawn line. The lower bound on the resolution of shape
SPAN_EPS	1	mm	comparing the cut plane with a part's z; minimum length of a visible interval; matching twin frames; minimum length of an envelope hole; minimum length of a wall interval
CROSS_EPS	1e-6	—	the sign (cross product = twice the area) when cutting by a half-plane
PARALLEL_EPS	1e-9	—	parallelism between an infinite line and a segment; the range of the segment-side parameter
POINT_EPS	1	mm	the width within which a point counts as lying on a polygon edge (on the boundary counts as inside). Where a column stands is read this way

EPS is 0.5mm because that is half the integer millimetre step. AREA_EPS at 1mm² is a 1mm × 1mm sliver: if a half-plane cut leaves that or less, it is not counted as shape.

PROBE at 5mm is different in kind from the other six. It is not a rounding allowance but a floor on shape itself: a space narrower than 5mm can be assigned to neither side of the line, and its boundary yields no segment at all.

Why they live in one place

While these values sat module by module, the same 0.5 was written twice independently, a 1 appeared as a literal in four places, and the axis-parallel test used a literal 0.5 rather than the shared value. All the same numbers, so nothing broke. What was broken was that nobody could say what would move if one of them moved.

The same had happened to the wall thickness of 100mm — four separate literals, and fixing one left the other three untouched. Tolerances and constants are part of the rules of derivation, and rules that differ per consumer mean different buildings out of the same source.

Neighbouring pages

• Form — derive(model) and the four promises
• Matter — where the constants actually bite
• The arithmetic of vertical runs — the step-division constants
• attributes — the side that says what may be written
• defaults — the defaults of the notation itself