Calculations

Calculations

• Point inside the room

  Whether a point lies inside the room outline.

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/layout.js

  • BimCraft
  64-bit

• Head in a partly filled cell

  Moves the head of a grid cell the room only partly fills to the middle of the part inside.

  position = mean of the cell's 6 × 6 sample points that lie inside

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/layout.js

  • BimCraft
  64-bit

• Uncovered share of the room

  The share of the room farther than 0.75 × the allowed spacing from every head.

  uncovered = samples with no head within 0.75 × maxS ÷ samples inside the room

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/layout.js

  • BimCraft
  64-bit

• Pipe length and rise

  The length in meters and the rise of each pipe of the network from its two end points.

  length = √(Δx² + Δy² + Δz²) ÷ 1000; dz = Δz ÷ 1000

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/layout.js

  • BimCraft
  64-bit

• Sprinkler properties in the model

  The K-factor, coverage, design density and hazard class written on each placed head.

  CoverageM2 = round(coverage × 100) ÷ 100

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/place.js

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  64-bit

• SI value of a file unit

  Meters per file length unit and radians per file angle unit.

  SI unit: 10^prefix; conversion-based unit: factor × factor of its base unit; by name: degree π ÷ 180, inch 0.0254, foot 0.3048

  IFC units and placements ifc/geo-ctx.js

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• Axis placement as a matrix

  The matrix of an IfcAxis2Placement3D, 2D or IfcAxis1Placement.

  columns = (x, z × x, z, origin), x = reference direction projected square to z

  IFC units and placements ifc/geo-ctx.js

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• First projection axis

  The X axis of a placement: the reference direction projected into the plane normal to Z.

  x = normalize(v − z (v · z))

  IFC units and placements ifc/geo-ctx.js

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• Cartesian transformation operator

  The matrix of an IfcCartesianTransformationOperator, uniform or not, in 2D or 3D.

  columns = (x s₁, y s₂, z s₃, origin)

  IFC units and placements ifc/geo-ctx.js

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• World matrix of a placement

  The position of an element in the model from its chain of relative placements.

  world = parent world × local

  IFC units and placements ifc/geo-ctx.js

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• Grid placement

  The point where two grid axes meet, with their offsets, as a placement.

  t = ((pB − pA) × dB) ÷ (dA × dB); point = pA + dA t

  IFC units and placements ifc/geo-ctx.js

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• Map conversion

  The matrix that takes model coordinates to map coordinates, with its rotation and scale.

  map = (E, N, H) + R(θ) · S · model; θ = atan2(ordinate, abscissa)

  IFC units and placements ifc/geo-ctx.js

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• Matrix product

  The product of two 4 × 4 matrices.

  IFC units and placements ifc/geo-math.js

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• Point through a matrix

  Transforms a point by a matrix.

  p' = M · (x, y, z, 1)

  IFC units and placements ifc/geo-math.js

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• Matrix inverse

  The inverse of a 4 × 4 matrix, or null when it has none.

  M⁻¹ = adjugate ÷ determinant

  IFC units and placements ifc/geo-math.js

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• Rotation about an axis

  The matrix that turns by an angle about an axis through the origin.

  R = c I + s [a]× + (1 − c) a aᵀ

  IFC units and placements ifc/geo-math.js

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• Polygon normal

  The normal of a 3D polygon, with a length of twice its area.

  n = Σ ((yₐ − y_b)(zₐ + z_b), (zₐ − z_b)(xₐ + x_b), (xₐ − x_b)(yₐ + y_b))

  IFC units and placements ifc/geo-math.js

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• Signed area of a 2D polygon

  The area of a profile outline, positive when counter-clockwise; used to orient outlines and holes.

  A = Σ (xₐ y_b − x_b yₐ) ÷ 2

  IFC units and placements ifc/geo-math.js

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• Positions and normals handed to the app

  Packs the mesh into the vertex and index arrays the apps read.

  vertices = Float32Array of (x, y, z, nx, ny, nz) per vertex

  Triangle mesh built from IFC geometry ifc/geo-mesh.js

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  32-bit in part

• Planar face

  Adds one planar face with holes as triangles, all with the face's normal.

  Triangle mesh built from IFC geometry ifc/geo-mesh.js

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• Mesh moved by a matrix

  Adds another mesh, transformed, with its normals turned to match.

  p' = M p; n' = normalize((M⁻¹)ᵀ n); a mirror swaps the winding

  Triangle mesh built from IFC geometry ifc/geo-mesh.js

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• Signed volume

  The volume enclosed by the mesh, positive when the triangles face outward.

  V = Σ a · (b × c) ÷ 6

  Triangle mesh built from IFC geometry ifc/geo-mesh.js

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• Shared vertices

  Merges vertices that fall in the same grid cell, for boolean operations.

  key = (round(x ÷ eps), round(y ÷ eps), round(z ÷ eps))

  Triangle mesh built from IFC geometry ifc/geo-mesh.js

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• Segments of an arc

  How many chords replace an arc of a given sweep.

  n = max(2, ceil(|sweep| ÷ 2π × 36))

  IFC curves and profiles as point lists ifc/geo-curve.js

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  Exact

• Arc through three points

  The circular arc of an indexed poly-curve from its start, middle and end points.

  center = a + ((|ab|² (ac × n)) + (|ac|² (n × ab))) ÷ (2 |n|²), n = ab × ac

  IFC curves and profiles as point lists ifc/geo-curve.js

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• Circle and ellipse points

  Points on a circle or ellipse between two parameters.

  p = M · (r₁ cos θ, r₂ sin θ, 0), θ = a₀ + sweep × i ÷ n

  IFC curves and profiles as point lists ifc/geo-curve.js

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• Trimmed curve

  The part of a line, circle, ellipse or other curve between two trims given as parameters or points.

  conic: angle = parameter × angle unit, or atan2 of the trim point in the conic's frame

  IFC curves and profiles as point lists ifc/geo-curve.js

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• B-spline curve points

  Points on a B-spline curve, rational or not, at 12 evenly spaced parameters per knot span.

  de Boor: d_j = (1 − a) d_{j−1} + a d_j, a = (u − k_i) ÷ (k_{i+p+1−r} − k_i); point = (x, y, z) ÷ w

  IFC curves and profiles as point lists ifc/geo-curve.js

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• Offset of a polyline

  A 2D polyline moved to its left by a distance, with mitered corners.

  p' = p + n × d ÷ max(0.2, n · n₁), n = normalized sum of the two edge normals

  IFC curves and profiles as point lists ifc/geo-curve.js

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• Circle and ellipse profiles

  The outline of a circular, hollow circular or elliptical profile.

  (r₁ cos a, r₂ sin a), a = 2π i ÷ 36

  IFC curves and profiles as point lists ifc/geo-profile.js

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• Fillets and edge radii

  Replaces corners of a profile outline with arcs of given radii tangent to both edges.

  d = r ÷ tan(half); center = corner + bisector × r ÷ sin(half), half = half the corner angle

  IFC curves and profiles as point lists ifc/geo-profile.js

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• I-shape outline

  The outline of a symmetric or asymmetric I-section with flange slopes, fillets and edge radii.

  inner flange face = thickness + tan(slope) × distance from the quarter point of the outstand

  IFC curves and profiles as point lists ifc/geo-profile.js

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• Closing an outline

  Drops repeated points of a profile curve and its closing point.

  IFC curves and profiles as point lists ifc/geo-profile.js

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• Straight extrusion

  The solid of a profile swept along a direction by a depth, with end caps and sides.

  top = bottom + direction × depth

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

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• Side face of a sweep

  Adds a four-sided face as one flat face or as two triangles.

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

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• Revolved solid

  The solid of a profile turned about an axis by an angle.

  p_k = o + R(axis, angle × k ÷ steps) · (p − o), steps = 36 per full turn

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

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• Frames along a path

  The tangent, normal and binormal at each point of a 3D polyline, and the miter stretch at each bend.

  tangent = normalize(t_in + t_out); miter = 1 ÷ max(0.25, t_in · tangent)

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

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• Normal carried round a bend

  Turns the section's normal by the rotation that takes the previous tangent to the next.

  angle = atan2(|a × b|, a · b); v' = R(a × b, angle) v, made square to b

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

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• Swept disk

  A round bar or tube along a path, such as rebar, with an optional inner radius and bend radius.

  section = 36-sided polygon of the radius; swept on the path's frames

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

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• Bends of a swept path

  Rounds the corners of a 3D polyline with arcs of a given radius.

  d = min(r ÷ tan(half), 0.999 × each leg); center = corner + bisector × r' ÷ sin(half)

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

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• Sphere

  The mesh of an IfcSphere.

  (r sin θ cos φ, r sin θ sin φ, r cos θ), θ = π i ÷ 12, φ = 2π j ÷ 24

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

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• Outer bound of a face

  Picks the largest loop of a face as its outer bound when the file marks none.

  size = |Σ ((yₐ − y_b)(zₐ + z_b), (zₐ − z_b)(xₐ + x_b), (xₐ − x_b)(yₐ + y_b))| (twice the area)

  IFC swept solids, primitives and faceted shapes ifc/geo-brep.js

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• Repeated points of a loop

  Drops consecutive points of a face loop that coincide, and a closing point equal to the first.

  IFC swept solids, primitives and faceted shapes ifc/geo-brep.js

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• Point on a clothoid

  The point at a length along a clothoid from its origin.

  x = ∫₀ˢ cos(k u²) du, y = ∫₀ˢ sin(k u²) du, k = sign(A) ÷ (2A²); Simpson's rule

  IFC alignment curves and stations ifc/geo-align.js

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• Points of a curve segment

  Samples one alignment segment from its parent curve and places it at the segment's start.

  n = max(2, min(400, ceil(|length| ÷ 2))); p_i = T · f(start + length × i ÷ n)

  IFC alignment curves and stations ifc/geo-align.js

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• Distance along the alignment

  The horizontal distance of each sampled point from the start.

  d_i = d_{i−1} + √(Δx² + Δy²)

  IFC alignment curves and stations ifc/geo-align.js

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• Height from the vertical profile

  The height of each horizontal point from the alignment's vertical profile.

  z = z_lo + (z_hi − z_lo) × (d − d_lo) ÷ (d_hi − d_lo)

  IFC alignment curves and stations ifc/geo-align.js

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• Point at a station

  The position and direction on a curve at a distance along it.

  p = p_{i−1} + (p_i − p_{i−1}) × (d − d_{i−1}) ÷ (d_i − d_{i−1})

  IFC alignment curves and stations ifc/geo-align.js

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• Placement along an alignment

  The matrix of an element placed at a station with lateral, vertical and longitudinal offsets.

  origin = p + left × lateral + (0, 0, vertical) + heading × longitudinal

  IFC alignment curves and stations ifc/geo-align.js

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• Solid between cross sections

  The solid of an IfcSectionedSolidHorizontal: cross sections placed across the alignment at their stations and joined.

  ring point = o + x × ((1 − f) a_x + f b_x) + y × ((1 − f) a_y + f b_y), f = (d − d₀) ÷ (d₁ − d₀)

  IFC alignment curves and stations ifc/geo-align.js

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