Calculations

Calculations

• A saved alignment applied

  A model point moved to the site by the alignment kept in the file.

  (x′, z′) = (x cos yaw − z sin yaw + t_x, x sin yaw + z cos yaw + t_z)

  AR on site: lining the model up with the building xr/xr-core.js

  • BimCraft
  • ModelCraft
  64-bit

• Re-check on a later visit

  How far the first reference point is from where the saved alignment puts it, and what to do about it.

  offset = √(Δx² + Δz²); keep < 0.05 m ≤ move < 0.5 m ≤ align again

  AR on site: lining the model up with the building xr/xr-core.js

  • BimCraft
  • ModelCraft
  64-bit

• Placing a reference point

  Takes the site point under the phone's center mark and runs the fit or the re-check with it.

  t_y = (w₁_y + w₂_y) ÷ 2 − (m₁_y + m₂_y) ÷ 2

  AR on site: lining the model up with the building xr/xr-session.js

  • BimCraft
  • ModelCraft
  64-bit

• Camera jitter per pass

  Moves the camera by less than a pixel each pass so that the sum of passes is anti-aliased.

  j_x = (h₂(i) − ½) × 2 ÷ w; rows 0 and 1 of the projection += j × row 3

  Rendered pictures render/render-core.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Section cut for the path tracer

  Clips every triangle of the scene against the section planes before the picture is traced.

  new corner = a + (b − a) × d_a ÷ (d_a − d_b)

  Rendered pictures render/render-pt.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Tiling fractal noise

  The noise value behind the library's brick, wood, stone and concrete textures.

  Σ ampₒ × noise(u fₒ, v fₒ) ÷ Σ ampₒ, f doubling and amp × gain per octave

  Rendered pictures render/textures.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Normal map bytes

  Turns a baked material's normal layer into the texture three.js reads.

  x = (byte − 128) ÷ 127; z = √(1 − x² − y²); out = (x ÷ 2 + ½) × 255

  Rendered pictures render/three-mats.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• 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

• Probe light as spherical harmonics

  Sums a small traced panorama into the four coefficients per color the view shades with.

  c = Σ L × Y × dΩ, dΩ = (2π ÷ w)(π ÷ h) sin θ

  Real-time view rt/rt-probes.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Cube faces to a 360° picture

  Builds the equirectangular panorama from six rendered faces.

  direction from (longitude, latitude); face = largest d·a; color = bilinear mix of four pixels

  Real-time view rt/rt-pano.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Display chain for one pixel

  Turns a linear color into the color shown: white balance, exposure, highlight knee, contrast, view transform.

  c ← max(0, WB c) × 2^stops; c ← 0.18 × (c ÷ 0.18)^(1 + contrast)

  Real-time view rt/rt-look.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Standing and falling in walk mode

  Keeps the walker's eye at eye height above the floor below, stepping up or falling as the floor changes.

  v ← v − 9.81 Δt; height ← max(floor + eye height, height + v Δt)

  Real-time view rt/rt-walk.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Target area and the count asked for

  The area of the faces a scatter set covers and the number of items its density asks for.

  area = Σ ½ |e₁ × e₂|; asked = min(2,000,000, round(area × density)); paint: Σ max(1, round(π r² × density))

  Scattered plants, rocks and people: how many and where rt/rt-scatter.js

  • BimCraft
  • ModelCraft
  64-bit

• A random point on the target

  Picks a triangle in proportion to its area and a point inside it.

  P = A + a (B − A) + b (C − A), (a, b) reflected when a + b > 1

  Scattered plants, rocks and people: how many and where rt/rt-scatter.js

  • BimCraft
  • ModelCraft
  64-bit

• Dropping a point onto the target

  Where a vertical ray from a brush dab meets a target triangle.

  t = (e₂·q) ÷ det, det = e₁·(d × e₂)

  Scattered plants, rocks and people: how many and where rt/rt-scatter.js

  • BimCraft
  • ModelCraft
  64-bit

• Slope and height limits

  Drops a candidate that stands on too steep a face or outside the height range.

  keep when n·up ≥ cos(slope) − 1e-9 and min ≤ p·up ≤ max

  Scattered plants, rocks and people: how many and where rt/rt-scatter.js

  • BimCraft
  • ModelCraft
  64-bit

• Values to texture bytes

  Stores a value from 0 to 1, or a normal component from −1 to 1, as one byte of a texture layer.

  byte = ⌊255 x + ½⌋; normal byte = ⌊127 x + 128.5⌋

  Material graphs baked to textures shading/bake.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Tiling value noise

  The smooth noise that procedural textures are built from.

  a + (b − a) f_x + (c − a) f_y + (a − b − c + d) f_x f_y, f = t² (3 − 2t)

  Material graphs baked to textures shading/lib.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Ambient occlusion of a texel

  The share of directions above a surface point that are not blocked nearby.

  open ÷ rays, directions (√u₁ cos 2πu₂, √u₁ sin 2πu₂, √(1 − u₁)) about the normal

  Material graphs baked to textures shading/texbake-job.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Decal geometry

  The triangles under a decal, clipped to its box and lifted off the surface.

  corner = o + x u + y v + z n + 0.0005 × face normal

  Material graphs baked to textures shading/decal.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• 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

• Unit changes on reading

  Standard Surface values converted to the app's units.

  thin film thickness ÷ 1000; emission ÷ 0.02; opacity = (r + g + b) ÷ 3

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

  • BimCraft
  • ModelCraft
  64-bit

• Tile size from uvtiling

  The material's tile size in meters from the uvtiling shared by a file's images.

  width = 1 ÷ tiling_u; height = 1 ÷ tiling_v

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

  • BimCraft
  • ModelCraft
  64-bit

• Mean of an input that varies over the tile

  The single value given to a shader input the renderers and the file cannot vary across the surface.

  mean = Σ f(uᵢ, vⱼ) ÷ 64², a 64 × 64 grid of texel centers

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

  • BimCraft
  • ModelCraft
  64-bit

• Rounding of spoken numbers and angles

  Turns a number or an angle into the short text that is spoken.

  num(v) = round(v × 100) ÷ 100; deg(θ) = num(round(normAngle(θ) × (180 ÷ π) × 100) ÷ 100)

  Spoken lengths, directions and extents access.js

  • CadCraft
  64-bit

• Direction as one of eight words

  Which of the eight directions (right, up-right, up and so on) leads from one point to another.

  index = round(atan2(Δy, Δx) ÷ (π ÷ 4)) mod 8

  Spoken lengths, directions and extents access.js

  • CadCraft
  64-bit

• A move in words

  The distance, angle and the two components of a move from one point to another.

  d = √(Δx² + Δy²); angle = atan2(Δy, Δx)

  Spoken lengths, directions and extents access.js

  • CadCraft
  64-bit

• Length along an object

  The length of a line, circle, arc or polyline that is read out with the object.

  line: √(Δx² + Δy²); circle: 2πr; arc: r × ((a₁ − a₀) mod 2π); polyline: Σ |pᵢ₊₁ − pᵢ|

  Spoken lengths, directions and extents access.js

  • CadCraft
  64-bit

• Extents of the visible objects

  The width, height and corners of the box round everything visible, said with the object counts.

  w = maxX − minX; h = maxY − minY

  Spoken lengths, directions and extents access.js

  • CadCraft
  64-bit

• Objects within a radius

  The objects within a given distance of a point, nearest first.

  Spoken lengths, directions and extents access.js

  • CadCraft
  64-bit

• Distance and side of each nearby object

  For each object near the cursor: whether the cursor is on it, or how far away it is and on which side.

  Spoken lengths, directions and extents access.js

  • CadCraft
  64-bit

• Measure between two points

  The length, angle, Δx and Δy said back after a command takes a point.

  d = √(Δx² + Δy²); angle = atan2(Δy, Δx)

  Spoken lengths, directions and extents access.js

  • CadCraft
  64-bit

• Snap points near the cursor

  The snap points within a radius of a point, nearest first, for stepping from one to the next with a key.

  d = √((sx − px)² + (sy − py)²)

  Spoken lengths, directions and extents access.js

  • CadCraft
  64-bit

• Transform from point pairs

  The move, turn, scale and mirror that carry one to three source points onto their destination points.

  turn = atan2(d₂ − d₁) − atan2(s₂ − s₁); k = |d₁d₂| ÷ |s₁s₂|; M = T(d₁) · R(turn) · S(k) · T(−s₁)

  Align and distribute align.js

  • CadCraft
  64-bit

• Bounding boxes in the coordinate system in force

  Each selected object's bounding box, measured along the axes of the user coordinate system when one is set.

  with a UCS: box of R(−angle) · T(−origin) applied to the object

  Align and distribute align.js

  • CadCraft
  64-bit

• Edge or middle of a box

  The left, center, right, top, middle or bottom coordinate of a bounding box.

  center = (minX + maxX) ÷ 2; middle = (minY + maxY) ÷ 2

  Align and distribute align.js

  • CadCraft
  64-bit

• Moves that line objects up

  For each object, the vector that brings its chosen edge or middle onto the reference.

  d = ref − edge(box)

  Align and distribute align.js

  • CadCraft
  64-bit

• Moves that space objects evenly

  For each object between the first and the last, the vector that makes the middles or the gaps equal.

  centers: step = (mid_last − mid_first) ÷ (n − 1); gaps: gap = (span − Σ sizes) ÷ (n − 1)

  Align and distribute align.js

  • CadCraft
  64-bit

• Degrees, minutes, seconds to decimal degrees

  The decimal angle for text such as 45°23'30", 45d23'30" or, inside a bearing, 45-23-30.

  deg = d + m ÷ 60 + s ÷ 3600

  Bearings and degrees-minutes-seconds angles.js

  • CadCraft
  64-bit

• Bearing or DMS text to an angle

  The angle in degrees, counter-clockwise from east, for a typed bearing such as N45°23'30"E or a plain DMS angle.

  N…E: 90 − off; N…W: 90 + off; S…E: 270 + off; S…W: 270 − off

  Bearings and degrees-minutes-seconds angles.js

  • CadCraft
  64-bit

• Decimal degrees to degrees, minutes and seconds

  The degrees, minutes and seconds text for an angle at the chosen precision.

  n = round(deg × unit + 10⁻⁹); d = ⌊n ÷ unit⌋; m = ⌊rest ÷ (unit ÷ 60)⌋; s = (rest − m × unit ÷ 60) ÷ 10^secDec

  Bearings and degrees-minutes-seconds angles.js

  • CadCraft
  64-bit

• Angle to a surveyor's bearing

  Bearing text such as N45°23'30"E for an angle in degrees.

  a = deg mod 360; offset = |90 − a| (north half) or |270 − a| (south half)

  Bearings and degrees-minutes-seconds angles.js

  • CadCraft
  64-bit

• Angle in the drawing's angle format

  An angle written as decimal degrees, degrees-minutes-seconds, grads, radians or a bearing.

  grads = a × 10 ÷ 9; radians = a × π ÷ 180

  Bearings and degrees-minutes-seconds angles.js

  • CadCraft
  64-bit

• Bearing of a vector

  The bearing text for a direction given by its x and y components.

  angle = atan2(dy, dx) × 180 ÷ π

  Bearings and degrees-minutes-seconds angles.js

  • CadCraft
  64-bit

• Size in millimeters

  The width and height of the copied area, on paper or at the drawing's real size.

  paper: mm = pixels × ptPerPx × (25.4 ÷ 72); real: mm = pixels × mmPerPx

  Size of a copied area areaclip.js

  • CadCraft
  • BimCraft
  • MarkupCraft
  • DetailCraft
  64-bit