Calculations

Calculations

• Newmark time stepping

  The floor displacements, velocities and accelerations at every time step of the record.

  K* = K + c₁ M + c₂ C, c₁ = 1 ÷ (β Δt²), c₂ = γ ÷ (β Δt), β = 1/4, γ = 1/2; C = a₀ M + a₁ K

  Earthquake time-history of a building hazard.js

  • BimCraft
  64-bit

• Peak drift, floor acceleration, base shear and roof displacement

  The largest values over the run that the person reads.

  drift = uᵢ − uᵢ₋₁; floor acceleration = ü + a_g; base shear = k₀ u₁ (shear building) or Σ m (ü + a_g) (full matrix)

  Earthquake time-history of a building hazard.js

  • BimCraft
  64-bit

• Sway under static floor forces

  Floor displacements and story drifts under static sideways forces, used for the wind sway.

  shear building: driftᵢ = (Σ F above) ÷ kᵢ, u = running sum of drifts; full matrix: K u = F

  Earthquake time-history of a building hazard.js

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  64-bit

• Floor heights from the frame's nodes

  Groups the frame's nodes into floors by height and takes the lowest group as the base.

  nodes whose heights differ by ≤ tol join one group; floor height = mean of the group

  Earthquake time-history of a building hazard-frame.js

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• Inverse of the flexibility table

  Turns the floors' flexibility table into their stiffness matrix.

  Earthquake time-history of a building hazard-frame.js

  • BimCraft
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• Floor stiffness of a frame

  The stiffness the frame gives each floor sideways, and one stiffness per story for the drift check.

  F[i][j] = (mean sideways move of floor i under 1000 N on floor j) ÷ 1000 ÷ 1000; K = F⁻¹; k_story = V ÷ drift under forces ∝ height

  Earthquake time-history of a building hazard-frame.js

  • BimCraft
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• Floor masses from the frame

  The mass on each floor: half of each member's weight at each end, plus a load per square meter over the floor's plan box.

  member mass = ρ × A × L × 1e-9; floor area = (x extent ÷ 1000) × (y extent ÷ 1000); m = max(1, self + area × load)

  Earthquake time-history of a building hazard-frame.js

  • BimCraft
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• Placing each vertex of an element

  Moves an element's vertices and normals from its own axes into the scene with its placement matrix.

  p′ = M × p; n′ = (rotation part of M) × n ÷ |…|

  Measuring on the IFC view's mesh ifc-model.js

  • BimCraft
  32-bit in part

• Storing the mesh

  Turns the collected positions, normals, indices and element runs of a batch into typed arrays.

  Measuring on the IFC view's mesh ifc-model.js

  • BimCraft
  32-bit in part

• Area of a picked flat face

  The flat face a picked triangle belongs to and its area.

  area = Σ |(b − a) × (c − a)| ÷ 2 over the triangles in the picked plane

  Measuring on the IFC view's mesh measure.js

  • BimCraft
  32-bit in part

• Distance between two picked points

  The straight-line distance Measure reports.

  d = √(Δx² + Δy² + Δz²)

  Measuring on the IFC view's mesh measure.js

  • BimCraft
  32-bit in part

• Distance split along the IFC axes

  The measured difference as ΔX, ΔY and ΔZ in the file's Z-up axes.

  ΔX = Δx; ΔY = −Δz; ΔZ = Δy (the viewer is Y up)

  Measuring on the IFC view's mesh measure.js

  • BimCraft
  32-bit in part

• Room floor area and volume from its shape

  The floor area and volume of a space measured from its triangles, used when the file states neither.

  area = Σ −n_y ÷ 2 over triangles with n_y ÷ |n| < −0.5; volume = |Σ a · (b × c) ÷ 6|

  Measuring on the IFC view's mesh ifc-qto.js

  • BimCraft
  32-bit in part

• Room area and volume in the spaces schedule

  Chooses the file's stated value or the measured one for each room, and rounds the measured one.

  measured value kept as Number(value.toFixed(4))

  Measuring on the IFC view's mesh ifc-qto.js

  • BimCraft
  32-bit in part

• Bounding box of each element in a shared frame

  The box and triangle count of every element of a model, in coordinates both versions share.

  Measuring on the IFC view's mesh ifc-compare.js

  • BimCraft
  32-bit in part

• How far an element moved, and whether its shape changed

  The move of an element between two versions and a yes or no on a change of size or triangle count.

  moved = |center of box B − center of box A|, reported when > tolerance; reshaped when a box side differs by > tolerance

  Measuring on the IFC view's mesh ifc-compare.js

  • BimCraft
  32-bit in part

• Bounding box of chosen elements

  The smallest box round the vertices of the chosen elements.

  Measuring on the IFC view's mesh ifc-vis.js

  • BimCraft
  32-bit in part

• Reading a property value

  Turns an IFC property or quantity value into the number or text the index, the totals and the comparison use.

  number kept = round(x × 10⁶) ÷ 10⁶

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

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• 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

  • BimCraft
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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

  • BimCraft
  64-bit

• 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

  • BimCraft
  32-bit in part

• 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

  • BimCraft
  32-bit in part

• 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

  • BimCraft
  32-bit in part

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
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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

  • BimCraft
  32-bit, display only

• 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

  • BimCraft
  32-bit, display only

• 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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  64-bit