Calculations

Calculations

• 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

• Corners and edges an element offers to Measure

  Collects an element's feature edges and corners in world space for the pointer to snap to.

  p_world = M × p_local; corners merged by round(coordinate × 1e4)

  Points and faces picked for 3D measuring viewer3d.js

  • BimCraft
  32-bit in part

• Area of the face under the pointer

  The area of the flat face the pointer is on, in world units.

  area = region area × |det M|^(2 ÷ 3)

  Points and faces picked for 3D measuring viewer3d.js

  • BimCraft
  32-bit in part

• Bounding box of each element

  The world-space box of each element, over every loaded model.

  box = M × (min, max of the element's vertices)

  Points and faces picked for 3D measuring viewer3d.js

  • BimCraft
  32-bit in part

• Clipping planes of a section box

  Turns each section cell's planes into the viewer's clipping planes and draws the cell's frame a hair inside it.

  viewer normal = turn(−n_x, −n_z, n_y); frame inset = Σ sizes × 1e-5 + 1e-4

  3D view drawing viewer3d.js

  • BimCraft
  32-bit, display only

• Section frame turned with the building

  Rotates a viewer point about the vertical through the model's center into the section frame.

  x′ = c_x + x cos a + z sin a; z′ = c_z − x sin a + z cos a

  3D view drawing viewer3d.js

  • BimCraft
  32-bit, display only

• Model bounds in the section frame

  The bounds of every drawn vertex in the turned section frame.

  box = min and max of turned vertex positions

  3D view drawing viewer3d.js

  • BimCraft
  32-bit, display only

• 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

• Solid of revolution

  Turns a profile of radius and height points into a closed triangle mesh about the vertical axis.

  vertex = (r × cos(2π i ÷ 24), r × sin(2π i ÷ 24), z), i = 0 … 23

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Elliptical head profile

  The outline of a 2:1 elliptical vessel head from the tangent line to the pole.

  (r × cos a, z₀ ± (r ÷ 2) × sin a), a = (π ÷ 2) × i ÷ 6

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Vessel capacity

  The capacity in cubic meters of a vessel or column: a cylinder and two 2:1 elliptical heads.

  V = (π (d ÷ 2)² L + (4 ÷ 3) π (d ÷ 2)² (d ÷ 4)) ÷ 10⁹

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Tank capacity

  The capacity in cubic meters of an atmospheric tank.

  V = π r² h ÷ 10⁹

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Signed volume of a mesh

  The volume enclosed by a triangle mesh in cubic millimeters, positive when the triangles face outward.

  V = Σ p · (q × r) ÷ 6 over the triangles

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Dimensions accepted for a piece of equipment

  Takes the dimensions a person typed, builds the solids and returns their bounding box, nozzles and capacity.

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Equipment moved and turned

  Moves a piece of equipment to a point and turns it about the vertical axis by an angle in degrees.

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

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Zone solid in millimeters

  Turns a hazard or consequence zone given in meters into a closed solid in millimeters for the model.

  vertex (mm) = vertex (m) × 1000

  Plant equipment solids, capacity and placement addons/plant/lib/engineering.js

  • BimCraft
  64-bit

• Pipe run handed to the pipe stress input

  Takes the model's pipe run with the most points and gives its points and total length to the pipe stress calculator.

  length = Σ √(Δx² + Δy² + Δz²) over the legs

  Plant equipment solids, capacity and placement addons/plant/lib/engineering.js

  • BimCraft
  64-bit

• Nozzle port size

  The outside diameter in millimeters stored on a nozzle's port, from its nominal pipe size.

  size = round(od (in) × 25.4 × 10) ÷ 10

  Plant equipment solids, capacity and placement addons/plant/lib/place.js

  • BimCraft
  64-bit

• Capacity property in the model

  The capacity in cubic meters written to the CadCraft_Plant property set of the placed equipment.

  CapacityM3 = round(V × 1000) ÷ 1000

  Plant equipment solids, capacity and placement addons/plant/lib/place.js

  • BimCraft
  64-bit

• Number written to the file

  Formats a coordinate, direction component or property value as STEP text.

  num(v) = round(v × 10⁴) ÷ 10⁴

  Plant equipment written as an IFC file addons/plant/lib/ifc-out.js

  • BimCraft
  64-bit

• Placement of an item

  The position and the turn about the vertical axis of a piece of equipment in the file.

  X direction = (cos a, sin a, 0), a = rot × π ÷ 180

  Plant equipment written as an IFC file addons/plant/lib/ifc-out.js

  • BimCraft
  64-bit

• Reference direction of a nozzle port

  A unit vector square to a nozzle's outward direction, used as the X axis of the port's placement.

  x = (d × a) ÷ |d × a|, a = (1, 0, 0) or (0, 1, 0)

  Plant equipment written as an IFC file addons/plant/lib/ifc-out.js

  • BimCraft
  64-bit

• Capacity property

  The capacity in cubic meters written to the CadCraft_Plant property set.

  CapacityM3 = round(V × 1000) ÷ 1000

  Plant equipment written as an IFC file addons/plant/lib/ifc-out.js

  • BimCraft
  64-bit

• Isometric projection

  The position on the drawing of a 3D point, before fitting to the sheet.

  u = (x − y) × cos 30°; v = z + (x + y) × 0.5

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Length text

  Turns a length in millimeters into the text on the drawing: whole millimeters, or feet and inches to 1/8 inch.

  mm: round(L); inches: round(L ÷ 25.4 × 8) eighths

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Point at a distance along a run

  The 3D point and direction at a given distance along a pipe run, used to place valves and spool balloons.

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Bill of materials quantities

  Pipe length per size and spec, the count of elbows by angle, valves and welds.

  pipe = Σ leg lengths; elbow angle = round(acos(u · v ÷ (|u| |v|)) × 180 ÷ π); welds = 2 × bends + 2 × valves

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Fit to the sheet

  The single scale and offset that place the projected runs inside the drawing area of the sheet.

  scale = min(availW ÷ bw, availH ÷ bh)

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit