Calculations

Calculations

• Rounding a total

  Cuts a sum to 12 significant digits so that binary noise such as 0.1 + 0.2 does not show.

  tidy(n) = Number(n.toPrecision(12))

  Quantity totals and schedules from IFC properties ifc-qto.js

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• Totals by group

  Counts elements and sums the chosen number fields for each combination of group values and for the whole selection.

  sum = Σ vᵢ over the elements with a number; counted = how many had one

  Quantity totals and schedules from IFC properties ifc-qto.js

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• Spaces schedule totals

  The total floor area and volume of the listed rooms.

  Quantity totals and schedules from IFC properties ifc-qto.js

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• Is a property value the same in both versions

  Decides whether a number or text property changed between two versions of a model.

  same when |a − b| ≤ 1e-9 × max(1, |a|, |b|)

  Quantity totals and schedules from IFC properties ifc-compare.js

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• Number shown in Properties

  How a property or quantity value from the file is written out in the Properties panel.

  shown = round(x × 10⁴) ÷ 10⁴

  Quantity totals and schedules from IFC properties ifc-model.js

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• Placement of an item relative to its story

  The location and X direction written to the file for a placed item.

  (lx, ly) = W⁻¹ × (x ÷ unit, y ÷ unit, story z); direction = W⁻¹ rotation × (cos r, sin r)

  Placing and pasting elements in an IFC model ifc-place.js

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• Position and rotation read back from a placement

  The x, y and rotation of each placed item as listed in the equipment schedule and used by copy and paste.

  x = W[12] × unit; y = W[13] × unit; rot = round(atan2(W[1], W[0]) in degrees × 1000) ÷ 1000

  Placing and pasting elements in an IFC model ifc-place.js

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• An item's body in the file's unit

  Writes a library item's mesh or box as IFC geometry in the file's length unit.

  coordinate in file units = millimeters ÷ (millimeters per file unit)

  Placing and pasting elements in an IFC model ifc-place.js

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• Plan outline as polylines

  Turns the lines, arcs, circles, ellipses and bulged polylines of an item's plan into the straight segments written as its footprint.

  arc: n = max(4, ⌈sweep ÷ 10°⌉) segments; bulge: θ = 4 atan(b), r = chord ÷ (2 sin(θ ÷ 2))

  Placing and pasting elements in an IFC model ifc-place.js

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• Viewer point to model millimeters and back

  Converts a point between the viewer's Y-up meters and the model's Z-up millimeters.

  model = (x × 1000, −z × 1000, y × 1000) of C⁻¹ × v; viewer = C × (x ÷ 1000, z ÷ 1000, −y ÷ 1000)

  Placing and pasting elements in an IFC model ifc-place.js

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• Move and turn of pasted elements

  The matrix that carries copied elements to where they are pasted, with a turn about a point and a change of story.

  M = T(about + d) × Rz(rot) × T(−about); dz = elevation of target story − elevation of source story

  Placing and pasting elements in an IFC model ifc-elements.js

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• Placement written for a pasted element

  The location, Z axis and X axis of the new placement, from its matrix.

  location = round to 6 decimals; axis = column ÷ its length, rounded to 9 decimals

  Placing and pasting elements in an IFC model ifc-elements.js

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• Wall faces in plan

  The two long faces of each wall as plan segments in model millimeters, with a normal pointing away from the wall.

  Wall faces and plan frames from element meshes ifc-place.js

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• Smallest rectangle round a wall's plan points

  The minimum-area bounding rectangle of a set of plan points.

  for each hull edge direction u: area = (max u − min u) × (max v − min v); keep the smallest

  Wall faces and plan frames from element meshes ifc-place.js

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• Snapping an item to the nearest wall face

  The position and rotation that put an item's back against the nearest wall face.

  t = clamp((p − a)·(b − a) ÷ |b − a|², 0, 1); q = a + t (b − a); position = q + n × maxY; rot = atan2(−n_y, −n_x) − 90°

  Wall faces and plan frames from element meshes ifc-place.js

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• Plan frame of copied elements

  The turn of the first copied element and the box of all copied meshes measured in those turned axes.

  rot = atan2(W[1], W[0]) in degrees, rounded to 6 decimals; box from orientedBox

  Wall faces and plan frames from element meshes ifc-place.js

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• Box of points in turned plan axes

  The bounds of a point list in plan axes turned by an angle, and the box center in model millimeters.

  u = x cos r + y sin r; v = −x sin r + y cos r; center = ((u₀ + u₁) ÷ 2, (v₀ + v₁) ÷ 2) turned back

  Wall faces and plan frames from element meshes ifc-place.js

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• Is this mesh a straight prism

  Checks that the mesh is closed and consistently wound, and picks candidate directions for the prism's axis.

  eps = tol × bounding-box diagonal, tol = 1e-6

  Turning a face mesh back into an extrusion ifc-solids.js

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• Depth, frame and outline of the prism

  The prism's depth, its origin and axes, and its outline and holes in the cap's own two axes.

  h = v · n; depth = max h − min h; (u, v) = ((p − origin) · x, (p − origin) · y)

  Turning a face mesh back into an extrusion ifc-solids.js

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• Removing collinear outline points

  Drops outline corners that lie on the line between their neighbors.

  drop b when |(b − a) × (c − b)| ≤ tol × max(1, |c − a|)

  Turning a face mesh back into an extrusion ifc-solids.js

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• Volume of a closed mesh

  The signed volume of a closed triangle mesh, used to check a conversion.

  V = Σ A · (B × C) ÷ 6

  Turning a face mesh back into an extrusion ifc-solids.js

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• Area of the prism's outline

  The outline's area less its holes; times the depth it is the prism's volume.

  area = |shoelace(outer)| − Σ |shoelace(hole)|

  Turning a face mesh back into an extrusion ifc-solids.js

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• Writing the prism into the file

  The IFC lines of the outline, its placement and the extrusion depth.

  each number written as toFixed(6)

  Turning a face mesh back into an extrusion ifc-solids.js

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• Degrees from degrees, minutes, seconds and millionths

  Reads an IFC compound angle as decimal degrees.

  deg = d + m ÷ 60 + (s + μ ÷ 10⁶) ÷ 3600

  Where an IFC model point is on the earth ifc-geo.js

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• File point to map grid

  Easting, northing and height in meters of a point of the file.

  [E, N, H] = (matrix × p) × meters per map unit

  Where an IFC model point is on the earth ifc-geo.js

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• Longitude and latitude from the site's reference point

  An approximate WGS 84 position of a file point from its offset east and north of the site's point.

  w = √(1 − e² sin² φ); N = a ÷ w; M = a (1 − e²) ÷ w³; lon = lon₀ + east ÷ ((N + h) cos φ); lat = lat₀ + north ÷ (M + h)

  Where an IFC model point is on the earth ifc-geo.js

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• Degrees to degrees, minutes and seconds

  Formats a latitude or longitude with its hemisphere letter.

  d = ⌊|deg|⌋; m = ⌊(|deg| − d) × 60⌋; s = (|deg| − d − m ÷ 60) × 3600, shown with 2 decimals

  Where an IFC model point is on the earth ifc-geo.js

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• Viewer point to the file's own coordinates

  Takes a point picked in the viewer back to the file's Z-up coordinates in its own length unit.

  y = C⁻¹ × (place⁻¹ × p); file = (y_x, −y_z, y_y) ÷ meters per file unit

  Where an IFC model point is on the earth ifc-geo.js

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• Feature edges of one element

  The edges of an element where its faces meet at more than the feature angle, plus its free edges.

  edge drawn when n₁ · n₂ ≤ cos(angle), or when only one triangle uses it

  Element outlines in the IFC view ifc-vis.js

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• Edge segments of a batch

  Collects every element's edges into one array of line segments with a run per element.

  Element outlines in the IFC view ifc-vis.js

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• Section of a run

  The outside diameter, wall and bend radius of a pipe from the size table, or the width and height of a duct, in millimeters.

  mm = inches × 25.4

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Run corners with the slope applied

  The corners of a run with its fall along the horizontal length from the first point.

  z = z₀ − slope × Σ horizontal leg length

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Bend radius of an elbow

  The center-line radius an elbow is built with.

  pipe: the table's radius; round duct: 1.5 × diameter; rectangular duct: its width for a turn in plan, its height for a turn up or down

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Elbow geometry at a corner

  The two tangent points, center and angle of the elbow where a run turns.

  θ = acos(d₁ · d₂); T = R × tan(θ ÷ 2); center = p₀ + n × R

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Where runs meet

  Finds run ends that touch another run's end or lie on another run's line, to make an elbow, reducer or tee there.

  end to end when |P − Q| ≤ max(tol_a, tol_b); tee when the foot of P on a leg is within the tolerance

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Elbow, reducer and tee allowances

  How much of each leg an elbow, a reducer or a tee takes.

  reducer length (duct) = max(150, max(|Δw|, |Δh|) ÷ 2 ÷ tan 15°); tee half length = max(25, 0.5 × branch + 0.25 × host)

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Straight pieces between fittings

  The start and end of every straight piece along each leg, after trims, tees, valves and weld cuts.

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Saving a run's definition

  The points, sizes, slope and flow kept in the run's property set.

  point = round to 3 decimals of a millimeter

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Length and surface written on each piece

  The length of a straight pipe or duct piece and a duct's outside surface, written as IFC quantities.

  L = |b − a|; perimeter = π w (round), π h + 2 (w − h) (oval), 2 (w + h) (rectangle); surface = perimeter × L

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Elbow written as a revolved section

  The axis and angle of the solid of revolution that an elbow is written as.

  axis at R to the side of the section; angle = θ

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Flat-oval outline

  The outline of a flat-oval duct with semicircular ends.

  r = H ÷ 2; c = W ÷ 2 − r; points at c + r cos a, r sin a

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Connecting ports that touch

  Joins a port to a port of another part that lies at the same place.

  connected when |p − q| < 0.6 mm

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Position along a run

  How far along a run a plan point lies, and how far off the line.

  t = clamp((p − a) · d, 0, L); s = Σ earlier legs + t

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Length of a run

  The length of a run's center line through its corners, with the slope applied.

  L = Σ |Vᵢ − Vᵢ₋₁|

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Pipe size for a flow and a velocity limit

  The smallest pipe of a material and class whose velocity stays at or under the limit.

  V = Q ÷ (π D² ÷ 4); first size with V ≤ V_max

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Duct size for a flow

  A duct sized by equal friction, returned in millimeters.

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Drain sizes by fixture units

  The smallest drain size that carries the fixture units reaching each sanitary run, never smaller than what flows into it.

  grow when needed nominal > drawn nominal + 1e-9

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Pipe and duct schedules

  Total length and piece count per pipe size, and length and surface per duct size.

  length = Σ stored piece lengths; surface = Σ perimeter × length

  Pipe and duct runs: layout, lengths and sizing mep-model.js

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• Friction rate of a round duct at the velocity limit

  The pressure drop per meter used to propose a duct size when the calculation ran by velocity.

  D = √(4 Q ÷ (π v)); rate = 0.02 × (1.204 ÷ D) × v² ÷ 2

  Pipe and duct runs: layout, lengths and sizing mep-calc.js

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• Proposed duct sizes

  The width and height proposed for each duct run that is too small or too fast.

  size for the largest flow in the run, rounded to 1 mm

  Pipe and duct runs: layout, lengths and sizing mep-calc.js

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