Calculations

Calculations

• Origin of the cached paths

  The point the cached drawing paths are stored relative to.

  origin = middle of the extents of the visible objects; path point = point − origin

  2D drawing on screen view.js

  • CadCraft
  32-bit, display only

• Grid spacing

  The spacing of the background grid: 1, 2 or 5 times a power of ten, at least 14 pixels apart.

  target = 14 ÷ zoom; p = 10^⌊log₁₀ target⌋; step = first of p, 2p, 5p, 10p that is ≥ target; major = 5 × step

  2D drawing on screen view.js

  • CadCraft
  32-bit, display only

• Pixels per paper millimeter

  How many CSS pixels one millimeter of the sheet takes, used to draw lineweights at their paper width.

  √(T₀² + T₁²) ÷ (25.4 when the paper is in inches, else 1)

  2D drawing on screen view.js

  • CadCraft
  32-bit, display only

• Kept solids as screen meshes

  The vertex positions and edge lines of the kept 3D solids as drawn on the 3D tab.

  position = (P − corner) × k, stored as 32-bit

  3D tab drawing of the 2D lines and kept solids ws3d.js

  • CadCraft
  32-bit, display only

• 2D lines as screen lines

  The 2D drawing's line pieces as drawn on the ground of the 3D tab.

  position = (x − min x, y − min y, 0), stored as 32-bit

  3D tab drawing of the 2D lines and kept solids ws3d.js

  • CadCraft
  32-bit, display only

• Triangles of a panel outline

  Cuts a panel's outline into triangles for drawing.

  ear when (b − a) × (c − a) > 1e-9 and no other point is inside the triangle

  Cabinets as 3D viewport bodies addons/cabinetcraft/lib/bodies3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  32-bit, display only

• Room coordinates to viewport coordinates

  A point of the room in the viewport's axes and millimeters.

  k = 25.4 (inch job) or 1; (x, y, z) → (x·k, z·k, −y·k)

  Cabinets as 3D viewport bodies addons/cabinetcraft/lib/bodies3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  32-bit, display only

• Member lines for the picture

  The 3D end points of every member, for drawing.

  Truss layout 3D picture addons/trusscraft/lib/view3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  32-bit, display only

• View projection

  Turns 3D points into picture coordinates for a view direction.

  x′ = x cos A − y sin A; y′ = −(z cos E + (x sin A + y cos A) sin E)

  Truss layout 3D picture addons/trusscraft/lib/view3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  32-bit, display only

• Picture output

  Scales the projected lines to the picture size and writes them as SVG.

  Truss layout 3D picture addons/trusscraft/lib/view3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  32-bit, display only

• Deflected shape

  The members' deflected shape, enlarged so it can be seen.

  drawn point = point + scale × displacement; scale = 0.015 × model size ÷ largest displacement

  Analysis results drawn on the model frame/frame-draw.js

  • CadCraft
  • BimCraft
  • DetailCraft
  32-bit, display only

• Force diagram beside a member

  A filled diagram of one internal force drawn square to each member, with its largest value labeled.

  height = value × 0.08 × model size ÷ largest value

  Analysis results drawn on the model frame/frame-draw.js

  • CadCraft
  • BimCraft
  • DetailCraft
  32-bit, display only

• Plate contours

  Each plate as two triangles colored by its corner values, with the largest values labeled.

  color = ramp(|value| ÷ largest |value|); kN·m/m = N·mm/mm ÷ 1000

  Analysis results drawn on the model frame/plate-draw.js

  • CadCraft
  • BimCraft
  • DetailCraft
  32-bit, display only

• Smooth shading normals

  The normal at each corner of faces joined by soft edges.

  n = normalize(Σ n_f × area_f) over the joined faces that meet at the corner

  Smooth shading and texture placement m3d/model.js

  • CadCraft
  • ModelCraft
  32-bit, display only

• Fitting a texture to a face

  The map from a point on a face to its place on an imported image.

  u = U · p + u₀, v = V · p + v₀, with U · n = 0 and V · n = 0

  Smooth shading and texture placement m3d/model.js

  • CadCraft
  • ModelCraft
  32-bit, display only

• Texture coefficients as stored

  The eight numbers of a texture's placement as they are kept in the face's paint.

  text = x rounded to 7 significant digits

  Smooth shading and texture placement m3d/model.js

  • CadCraft
  • ModelCraft
  32-bit, display only

• Normal per corner

  A unit normal for every corner of every face.

  n = normalize(Σ N_f) over the faces of a smooth group

  Polygon mesh: shading normals m3d/mesh.js

  • CadCraft
  • ModelCraft
  32-bit, display only

• Mesh buffers for the graphics card

  The vertex positions, normals and colors of a definition's faces as the arrays the graphics card draws.

  3D view drawing m3d/view3d.js

  • CadCraft
  • ModelCraft
  32-bit, display only

• Box of a placement as drawn

  The world-space box of one placed definition, used to frame the view and place the lights.

  3D view drawing m3d/view3d.js

  • CadCraft
  • ModelCraft
  32-bit, display only

• Overlay line clipped to the near plane

  A 3D line cut at the camera's near plane and projected to screen points for the 2D overlay.

  cut at depth 1.01 × near: a′ = a + (b − a) × (near′ − da) ÷ (db − da)

  3D view drawing m3d/view3d.js

  • CadCraft
  • ModelCraft
  32-bit, display only

• Mass prism mesh

  The triangles of the walls and roof of a mass.

  Building mass mesh for the 3D view massing.js

  • CivilCraft
  32-bit, display only

• Ground mesh with elevation bands

  The triangles, normals and colors of a ground surface, cut at the elevation band levels.

  position = (x + dx, y + dy, (z − origin z) × exaggeration); normal = normalized sum of face normals

  3D site view scene site3d.js

  • CivilCraft
  32-bit, display only

• Map picture coordinates on the ground

  Where each ground vertex falls in the map picture draped over it.

  u = (x + origin x − min x) ÷ width; v = (y + origin y − min y) ÷ height

  3D site view scene site3d.js

  • CivilCraft
  32-bit, display only

• Road body mesh

  The lanes, shoulders, curbs and walks of a corridor as triangles between neighboring sections.

  3D site view scene site3d-landscape.js

  • CivilCraft
  32-bit, display only

• Rail mesh

  Each rail as a swept I-shaped outline along the track's sections.

  3D site view scene site3d-rail.js

  • CivilCraft
  32-bit, display only

• Positions and indices from an accessor

  Reads a primitive's vertex positions and triangle indices from the file's binary chunk.

  Plant 3D models for the 3D view landscape/glb.js

  • CivilCraft
  32-bit, display only

• Node transform

  The 4×4 matrix of a node from its matrix, or from its translation, rotation and scale.

  M = T · R(q ÷ |q|) · S

  Plant 3D models for the 3D view landscape/glb.js

  • CivilCraft
  32-bit, display only

• Transform to the model's frame, Y up to Z up

  Applies each node's transform to its vertices and gathers all triangles into one mesh.

  p′ = M·p; (x, y, z) → (x, −z, y)

  Plant 3D models for the 3D view landscape/glb.js

  • CivilCraft
  32-bit, display only

• Scale a model to the unit box

  Centers a model in plan, sets its base at zero and scales it to one unit wide and one unit tall, with a normal per triangle.

  x′ = (x − cx) ÷ w; z′ = (z − z min) ÷ h; n = (b − a) × (c − a) ÷ |…|

  Plant 3D models for the 3D view landscape/symbols.js

  • CivilCraft
  32-bit, display only

• Model point to screen

  Where a model point is drawn on the canvas.

  Erection movie player erection-html.js

  • DetailCraft
  32-bit, display only

• Where a pick is at a given minute

  The offset of a lifted piece from its final place while the movie plays.

  Erection movie player erection-html.js

  • DetailCraft
  32-bit, display only

• A part's solid for drawing

  The mesh of a part: its profile extruded, with copes cut.

  3D view view3d.js

  • DetailCraft
  32-bit, display only

• Mitre ends on the mesh

  Moves the end vertices of a mesh onto the mitre's cut plane.

  3D view view3d.js

  • DetailCraft
  32-bit, display only

• The part under the pointer

  Which part a click hits and where the ray meets it.

  3D view view3d.js

  • DetailCraft
  32-bit, display only

• Open or closed surface

  The elements of a batch whose triangles do not close.

  key = round(x × 1e4), round(y × 1e4), round(z × 1e4); open if any edge count is odd

  Section caps: which elements are closed solids caps-closed.js

  • BimCraft
  32-bit, display only

• Elements split over several batches

  Checks again, over all its parts, an element that is drawn in more than one batch.

  Section caps: which elements are closed solids caps-closed.js

  • BimCraft
  32-bit, display only

• Adding tile results to the picture

  The sums of red, green, blue and sample count of every pixel after a pass.

  out[pixel] += tile[pixel]

  Rendered picture: sample sums and color tables compute/cpu-render.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Mean radiance of each pixel

  The picture as the average of its samples.

  color = Σ ÷ n

  Rendered picture: sample sums and color tables compute/cpu-render.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Color through a .cube table

  A color after the table's 1D and 3D look-ups.

  x = clamp((r − lo) ÷ (hi − lo)); trilinear: c = c₀ + (c₁ − c₀) × d along each axis in turn

  Rendered picture: sample sums and color tables exr/cube.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Table rows read from a .cube file

  The entries of a color table as they are held in memory.

  Rendered picture: sample sums and color tables exr/cube.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Numbers written to a .cube file

  A table entry as text in a saved color table.

  text = Number(v.toPrecision(7))

  Rendered picture: sample sums and color tables exr/cube.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Filmic tone curve

  Maps scene brightness to screen brightness for the filmic view transform.

  h(x) = (x (0.15 x + 0.05) + 0.004) ÷ (x (0.15 x + 0.5) + 0.06) − 0.02 ÷ 0.3; output = h(2 c) ÷ h(11.2)

  Real-time view and render bench rt/rt-post.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Baked probe light

  Collects the bounce light at each probe and removes the sky's own part.

  shᵢ,ₖ = bakedᵢ,ₖ − skyₖ (k = 0…11)

  Real-time view and render bench rt/rt-gi.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Mean radiance per pixel

  Averages the accumulated samples of each pixel for the bench and the parity comparison.

  mean = Σ samples ÷ n

  Real-time view and render bench render/bench-kernels.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Scene for the standalone viewer

  Packs the drawn scene into the viewer's file.

  Real-time view and render bench rt/rt-export.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Part geometry for the view

  Builds the triangles and feature lines of a part for drawing.

  Manual scene in the 3D view illustrate/scene3d.js

  • PartCraft
  32-bit, display only

• Cut faces lifted off the section plane

  Places the filled cut faces so they are not hidden by the plane that cut them.

  Manual scene in the 3D view illustrate/scene3d.js

  • PartCraft
  32-bit, display only

• Old and new sheet mixed per pixel

  The color of each pixel of the compare picture, and counts of removed, added and unchanged pixels.

  Sheet compare picture compare.js

  • MarkupCraft
  32-bit, display only

• Bench rim line segments

  Segment pairs for the rim of each bench.

  Pit and solar table meshes in the 3D view site3d-pit.js

  • CivilCraft
  32-bit, display only

• Haul ramp ribbon

  A road-wide ribbon on the pit walls for the haul ramp.

  offset = (−dy, dx) ÷ length × width ÷ 2; lift = 0.02 × width

  Pit and solar table meshes in the 3D view site3d-pit.js

  • CivilCraft
  32-bit, display only