Calculations

Calculations

• Runs joined across doors and outside walls moved to their middle

  Joins two runs on one line with a door between them into one wall, and moves a wall that has points on one side only half its thickness outward.

  c = (c₁ + c₂) ÷ 2; outside when the emptier side has < 15% of the other's points; c ← c ± thickness ÷ 2

  Walls, doors and rooms proposed from a scan scan-propose.js

  • BimCraft
  64-bit

• Wall ends snapped to corners

  Moves a wall's end onto the line of a perpendicular wall when it is within the snap distance.

  end ← c_other when |c_other − end| ≤ 350 mm

  Walls, doors and rooms proposed from a scan scan-propose.js

  • BimCraft
  64-bit

• Proposed wall coordinates

  Turns each wall back into the slice's own axes and writes its two ends.

  a, b = round(coordinate × 10) ÷ 10

  Walls, doors and rooms proposed from a scan scan-propose.js

  • BimCraft
  64-bit

• Proposed door offset

  The distance from a wall's start to the near edge of a door in it.

  offset = Math.round(max(0, along − width ÷ 2 − wall start))

  Walls, doors and rooms proposed from a scan scan-propose.js

  • BimCraft
  64-bit

• Rooms closed by the proposed walls

  The rooms the proposed walls close, each with its area and middle.

  area (m²) = round(area_mm² ÷ 1e6 × 10) ÷ 10

  Walls, doors and rooms proposed from a scan scan-propose.js

  • BimCraft
  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

• 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

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  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

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• 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

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• 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

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• 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

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Distance from a point to a triangle

  The shortest distance from a point to a triangle, on a corner, an edge or the face.

  MEP clearances and openings through walls and slabs mep/structure.js

  • BimCraft
  64-bit

• Segment crossing a triangle

  Where along a straight piece of a run it passes through one triangle of a wall or slab.

  t = (e₂ · (s × e₁)) ÷ (e₁ · (d × e₂))

  MEP clearances and openings through walls and slabs mep/structure.js

  • BimCraft
  64-bit

• Clearance between an MEP element and the structure

  The gap reported when a pipe or duct is closer to a structural element than its insulation plus the typed clearance.

  need = (insulation + gap) ÷ 1000; gap = min over vertices p and triangles T of dist(p, T), both ways

  MEP clearances and openings through walls and slabs mep/structure.js

  • BimCraft
  32-bit in part

• Run center line as straight pieces

  The center line of a run, part by part, that is tested against walls and slabs.

  bend point k = center + (−n cos(θk ÷ 8) + d₁ sin(θk ÷ 8)) × R, k = 0 … 8

  MEP clearances and openings through walls and slabs mep/structure.js

  • BimCraft
  64-bit

• Opening size

  The width and height of the opening a run needs in a wall or slab.

  opening = outside size + 2 × insulation + 2 × gap

  MEP clearances and openings through walls and slabs mep/structure.js

  • BimCraft
  64-bit

• Where a run passes through an element

  The position of each opening on the run, its place in plan, and the length of run inside the wall or slab.

  s = s₀ + u × piece length; through = s_leave − s_enter; at = midpoint of the two crossings

  MEP clearances and openings through walls and slabs mep/structure.js

  • BimCraft
  32-bit in part

• Picked focus distance

  The distance from the camera to the clicked surface, measured along the view direction.

  focus = round(−(d · view axis ÷ |view axis|) × t × 100) ÷ 100

  Focus distance picked in the view render/ipr.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Linear picture to display values

  Each pixel's final red, green and blue from the linear picture and the post settings.

  AP1 × wb → Rec.709 × 2^exposure → vignette → highlights → contrast → view transform → sRGB → 8 bits

  Rendered picture: mixing, post and color render/pt-post.js

  • BimCraft
  • ModelCraft
  32-bit in part

• View transform

  The tone curve that brings scene light into the display's range.

  Rendered picture: mixing, post and color render/pt-post.js

  • BimCraft
  • ModelCraft
  64-bit

• Blur for bloom

  The wide blur of the picture that bloom blends back in.

  r = max(1, round(√(12σ² ÷ 3 + 1) ÷ 2)); three box blurs of radius r per axis

  Rendered picture: mixing, post and color render/pt-post.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Bloom

  The picture blended with three blurs of itself.

  out = img × (1 − a) + (0.5 b₁ + 0.3 b₂ + 0.2 b₃) × a

  Rendered picture: mixing, post and color render/pt-post.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Light group gains

  The color and brightness factor of each light group in a light mix.

  gain = color (linear AP1) × 2^stops

  Rendered picture: mixing, post and color render/pt-mix.js

  • BimCraft
  • ModelCraft
  64-bit

• Mixed picture

  The linear picture made by adding the light groups with their gains.

  pixel = Σ over groups of (group sum × gain) ÷ samples

  Rendered picture: mixing, post and color render/pt-mix.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Picture or lighting element from the sums

  The linear picture, light mix or one lighting element as a mean per pixel, handed to the post step.

  mean = Σ samples ÷ sample count

  Rendered picture: mixing, post and color render/pt-mix.js

  • BimCraft
  • ModelCraft
  32-bit in part

• ACES filmic curve

  The default tone curve.

  f(x) = (x (x + 0.0245786) − 0.000090537) ÷ (x (0.983729 x + 0.4329510) + 0.238081)

  Rendered picture: mixing, post and color render/pt-spec.js

  • BimCraft
  • ModelCraft
  64-bit

• sRGB encoding

  The curve from display-linear values to stored sRGB values.

  c ≤ 0.0031308: 12.92 c; else 1.055 c^(1 ÷ 2.4) − 0.055

  Rendered picture: mixing, post and color render/pt-spec.js

  • BimCraft
  • ModelCraft
  64-bit

• One pixel to 8 bits

  A pixel's mean color turned into display bytes with the default settings.

  byte = round(sRGB(ACES(Rec.709(AP1 × wb))) × 255)

  Rendered picture: mixing, post and color render/pt-spec.js

  • BimCraft
  • ModelCraft
  64-bit

• Sample sums on the graphics card

  The running sum of every sample's color for a pixel when the render runs on the graphics card.

  ACC[pixel] += max(sample, 0)

  Rendered picture: mixing, post and color render/pt-wgsl.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Denoiser exposure scale

  The scale that brings the picture to the brightness the denoising network expects.

  scale = 0.18 ÷ 2^(mean of log₂ L over 16 × 16-pixel bins)

  Rendered picture: mixing, post and color render/pt-denoise.js

  • BimCraft
  • ModelCraft
  64-bit

• Denoiser input

  The color, albedo and normal values given to the denoising network.

  Rendered picture: mixing, post and color render/pt-denoise.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Denoiser output

  The denoised picture taken back to linear values.

  linear = inverse curve(x ÷ norm) ÷ scale

  Rendered picture: mixing, post and color render/pt-denoise.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Distance between two points

  The length a headset measurement reports.

  d = √(Δx² + Δy² + Δz²)

  Headset review: measuring, section cuts and issue cameras xr/xr-core.js

  • BimCraft
  • ModelCraft
  64-bit

• Snap to a corner

  The corner of the hit triangle nearest the hit, when it is within the snap radius.

  Headset review: measuring, section cuts and issue cameras xr/xr-core.js

  • BimCraft
  • ModelCraft
  64-bit

• Model to headset transform

  The matrix that places the model in the headset's space.

  M = T(anchor) · R_y(yaw) · S(scale) · T(−at)

  Headset review: measuring, section cuts and issue cameras xr/xr-core.js

  • BimCraft
  • ModelCraft
  64-bit

• Inverse of a rig or pose

  The inverse of a rigid motion with one uniform scale.

  M⁻¹ = [Rᵀ ÷ s², −(Rᵀ ÷ s²) t], s² = squared length of the first column

  Headset review: measuring, section cuts and issue cameras xr/xr-core.js

  • BimCraft
  • ModelCraft
  64-bit

• Section plane

  The plane of a section cut through what was pointed at.

  n = normal toward the eye; p = hit − n × depth; d = n·p

  Headset review: measuring, section cuts and issue cameras xr/xr-core.js

  • BimCraft
  • ModelCraft
  64-bit

• Issue camera

  The viewpoint, direction and up vector saved with an issue, in the app's coordinates.

  to app = M_up⁻¹ · M_rig⁻¹; eye = to app × head position

  Headset review: measuring, section cuts and issue cameras xr/xr-core.js

  • BimCraft
  • ModelCraft
  64-bit

• The point being pointed at

  The model point, surface normal and triangle under a controller's ray.

  Headset review: measuring, section cuts and issue cameras xr/xr-session.js

  • BimCraft
  • ModelCraft
  32-bit in part

• A measurement in the headset

  The length shown on the label between two picked points.

  d = |q − p|, shown through the app's length format

  Headset review: measuring, section cuts and issue cameras xr/xr-session.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Where an issue is placed

  The point and camera handed to the app with a new issue.

  Headset review: measuring, section cuts and issue cameras xr/xr-session.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Average and largest sample count

  The two numbers the render dialog states after an adaptive render.

  avg = round(10 × Σ nᵢ ÷ (w × h)) ÷ 10; max = largest nᵢ

  Samples per pixel reported after a render render/render-pt.js

  • BimCraft
  • ModelCraft
  32-bit in part

• A number as written to the file

  The text of every numeric value in the exported file.

  text = round(x × 10⁶) ÷ 10⁶

  MaterialX files: numbers written and read shading/mtlx.js

  • BimCraft
  • ModelCraft
  64-bit

• Tile size as uvtiling

  The repeat of every texture in the file, from the material's tile size in meters.

  uvtiling = round(10⁶ ÷ size) ÷ 10⁶

  MaterialX files: numbers written and read shading/mtlx.js

  • BimCraft
  • ModelCraft
  64-bit

• Shader parameters

  The constant inputs of the surface shader written to the file.

  Standard Surface: emission = luminance × 0.02; thin film thickness × 1000

  MaterialX files: numbers written and read shading/mtlx.js

  • BimCraft
  • ModelCraft
  64-bit

• Displacement height range

  The lowest height and the span of the height map, which set the displacement texture's levels and the scale written to the file.

  span = max h − min h; level = round(255 (h − min h) ÷ span); scale = displacement scale × span

  MaterialX files: numbers written and read shading/mtlx.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Displacement scale written

  The scale input of the displacement shader in the exported file.

  scale = round(10⁶ × displacement scale × span) ÷ 10⁶

  MaterialX files: numbers written and read shading/mtlx.js

  • BimCraft
  • ModelCraft
  32-bit in part

• A value read from the file

  The number or list of numbers in a value attribute.

  MaterialX files: numbers written and read shading/mtlx.js

  • BimCraft
  • ModelCraft
  64-bit