Calculations

Calculations

• Stair from a sketched walking line

  Turns a walking line of one, two or three segments into a straight, L or U stair: its direction, width, gap, split and tread depth.

  n = max(2, ⌈H ÷ riser_max − 1e-9⌉); tread = max(50, line length ÷ (n − 1)); split = first leg ÷ total

  Stair risers, treads and stairwell stair-sketch.js

  • BimCraft
  64-bit

• Roof plane area in Properties

  The sloped area of a manual roof plane shown in its properties.

  area = |½ Σ (xᵢ yᵢ₊₁ − yᵢ xᵢ₊₁)| ÷ cos θ

  Figures shown in the residential panels and schedules res-ui.js

  • BimCraft
  64-bit

• Cut list schedule

  The lumber schedule's rows: size, stock length, pieces and board feet, with totals.

  board feet shown = bf.toFixed(1)

  Figures shown in the residential panels and schedules res-ui.js

  • BimCraft
  64-bit

• Board feet of a framing in Properties

  Shows the piece count and board feet of one framing.

  shown = Math.round(BoardFeet)

  Figures shown in the residential panels and schedules res-ui.js

  • BimCraft
  64-bit

• Cut and fill in Properties

  Shows the terrain's cut and fill volumes.

  shown = V.toFixed(1) m³

  Figures shown in the residential panels and schedules res-ui.js

  • BimCraft
  64-bit

• Direction and height of a new stair

  The direction a new stair runs, from its start point to the pointer, and the height it climbs.

  angle = atan2(Δy, Δx) × 180 ÷ π; height = elevation above − elevation here

  Figures shown in the residential panels and schedules res-ui.js

  • BimCraft
  64-bit

• Building width on an elevation (fallback)

  The overall width of the building across a view direction, used for the width note on an elevation when the wall-based width is not available.

  x = q · r ± t ÷ 2 over every wall end; width from min to max

  Figures shown in the residential panels and schedules res-ui.js

  • BimCraft
  64-bit

• Inverse of a level's placement

  Inverts a level's 4×4 world matrix to bring site coordinates back into the level's plan.

  R⁻¹ = Rᵀ; t⁻¹ = −Rᵀ t

  Figures shown in the residential panels and schedules res-ui.js

  • BimCraft
  64-bit

• Local origin and merging of points

  Moves every point to a local origin and makes points that fall on the same spot one vertex.

  origin = ⌊min x⌋, ⌊min y⌋; key = round(x ÷ 1e-4), round(y ÷ 1e-4)

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Coordinates handed to the triangulator

  Packs the local coordinates for Delaunator and runs the Delaunay triangulation.

  coords = (x, −y) per vertex

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Boundary clipped to the data and given elevations

  Clips the outer boundary to the convex hull of the data and takes each corner's elevation from a first surface built without it.

  z_corner = elevationAt(x, y) with a 1e-6 edge tolerance

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Triangles kept inside the boundary

  Drops the triangles whose center lies outside the boundary.

  keep when the centroid (Σx ÷ 3, Σy ÷ 3) is inside the boundary polygon

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Surface from given triangles

  Builds a surface from vertices and faces read from a file, keeping every triangle counter-clockwise.

  o = (x_b − x_a)(y_c − y_a) − (y_b − y_a)(x_c − x_a); swap b, c when o < 0

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Crossing of two breakline segments

  Finds where two segments properly cross, as a fraction along each.

  t = cross(c − a, s) ÷ cross(r, s); u = cross(c − a, r) ÷ cross(r, s)

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Vertex at a breakline crossing

  Places a new vertex where two breaklines cross and gives it an elevation.

  x = x_a + (x_b − x_a) t; z from the first breakline

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Side of a breakline a vertex is on

  Decides whether a vertex lies left of, right of, or on the line of a breakline being forced in.

  on the line when |orient| ÷ L < 1e-7 × (1 + L)

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Whether a diagonal can be flipped

  Tests that the two triangles on an edge form a strictly convex quadrilateral.

  orient(c, d, a) and orient(c, d, b) have opposite signs

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  Exact

• Whether an edge crosses a breakline

  Tests whether two segments properly cross during the flips that force a breakline in.

  each segment's ends lie on opposite sides of the other

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  Exact

• Long outer triangles removed

  Removes triangles on the outside whose outer edge is longer than a limit, working inward.

  remove when outer edge length > maxEdge

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Contour lines

  The contour lines of the surface at every multiple of an interval.

  level = base + k × interval; t = (L − zᵢ) ÷ (zⱼ − zᵢ); point = pᵢ + (pⱼ − pᵢ) t

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Triangle clipped at an elevation

  Keeps the part of a triangle above or below a level, for the elevation bands.

  t = f_p ÷ (f_p − f_q); new point = p + (q − p) t at z = L

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Convex hull

  The convex hull of a set of points, counter-clockwise.

  monotone chain; pop while cross(o, a, b) ≤ 0

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Polygon area

  The signed area of a polygon.

  A = ½ Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Point inside a polygon

  Tests whether a point is inside a polygon.

  count crossings of a ray to the right; odd = inside

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Polygon clipped by a convex polygon

  Clips a polygon to a convex polygon, used to keep a boundary inside the data's hull.

  inside when cross(b − a, p − a) ≥ −1e-9; t = cross(a − p, e) ÷ cross(d, e)

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Polygon clipped at a station or an offset

  Cuts a wall outline at an opening's edge or at a layer boundary.

  t = (at − a) ÷ (b − a); new point has the clip coordinate exactly

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Layer bands across a wall in plan

  The band of each wall layer across the wall, from the exterior face inward.

  off₀ = ±t ÷ 2; offᵢ₊₁ = offᵢ ∓ tᵢ

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Layer thicknesses against the wall thickness

  Checks that a wall's layers add up to its thickness before any layer is drawn.

  |Σ tᵢ − t| ≤ 0.005 mm

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Curved wall outlines as chords

  Maps a path from the wall's frame back to the plan, adding points along a curved wall so the chords stay close to the arc.

  step = 2 acos(max(−1, 1 − 0.002 ÷ radius)); n = ⌈|Δstation| ÷ R ÷ step⌉

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Boundary lines between layers

  Finds the stretches of a layer boundary that lie inside the wall's outline.

  x = x_a + (x_b − x_a) × (offset − y_a) ÷ (y_b − y_a)

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Outline of joined wall pieces

  Finds the outer edges of wall pieces that touch, so shared edges inside a joint are not drawn.

  t = cross(c − a, v) ÷ cross(d, v); parallel when |cross(d, v)| < 1e-12 × |d| × |v|

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Building width on an elevation

  The overall width of the building's walls across a view direction, for the width note on an elevation.

  x = p · right ± |n · right| × t ÷ 2 over every wall end

  Wall layers drawn in plans and sections wall-section-graphics.js

  • BimCraft
  64-bit

• Wall and opening edges for an elevation

  The edges of a straight wall's two faces, its ends and its openings, handed to the hidden-line view.

  P(s, t, h) = a + u s + n t at height h

  Wall layers drawn in plans and sections wall-section-graphics.js

  • BimCraft
  64-bit

• Walls of every level in one level's axes

  Moves every wall and opening into one level's plan and height, for a section through several levels.

  T = inverse(level) × level_wall; a′ = T a; z = T₁₄ + base offset

  Wall layers drawn in plans and sections wall-section-graphics.js

  • BimCraft
  64-bit

• Where a section cuts a wall

  The station along a wall at which the section plane cuts it, when the cut is square to the wall.

  s = ((o − a) · dir) ÷ (u · dir)

  Wall layers drawn in plans and sections wall-section-graphics.js

  • BimCraft
  64-bit

• Layer bands in a section cut

  The rectangle of each wall layer in a section, between the heights the openings leave.

  x = c + off × (n · right); offᵢ₊₁ = offᵢ ∓ tᵢ

  Wall layers drawn in plans and sections wall-section-graphics.js

  • BimCraft
  64-bit

• Corners of an item

  The four corners in plan of an item of given width, depth, position and turn.

  corner = (x₀ + x cos a − y sin a, y₀ + x sin a + y cos a), a = rot × π ÷ 180

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Access strips

  The strips beside each side of an item that must stay free, as turned rectangles.

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Overlap of two convex polygons

  Whether two items, or an item and an access strip or obstacle, overlap by more than a sliver.

  separated if maxA ≤ minB + tol or maxB ≤ minA + tol on any edge normal; tol = 1

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Distance from a point to a segment

  The shortest distance from a corner of one item to an edge of another.

  t = clamp(((p − a) · (b − a)) ÷ |b − a|², 0, 1); d = |p − (a + t (b − a))|

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Gap between two items

  The least distance between two items that do not overlap, compared with the minimum aisle width.

  gap = min over corners and edges of the point-to-segment distance

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Floor load of an item

  The weight of an item divided by its footprint area, compared with the floor load limit.

  load = weight ÷ (area ÷ 10⁶) in kg per m²; area = |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)| ÷ 2

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Footprint of Plant equipment

  The width, depth, height and center of a piece of Plant equipment for the layout, from its bounding box.

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Flow path length

  The length of the path through a sequence of items, measured center to center along X then Y.

  L = Σ (|Δx| + |Δy|)

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Openings and walls on a room's edge

  Finds the doors, windows and walls that lie on the outline of a room.

  t = clamp(((p − a) · (b − a)) ÷ |b − a|², 0, 1); d = |p − a − t (b − a)|; on the edge if d ≤ tolerance

  Rooms handed to add-ons with their doors, windows and walls addons/bimcraft-api.js

  • BimCraft
  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

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• 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

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• 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

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• 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

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• 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

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit