Calculations

Calculations

• Solar table triangle normal

  A flat-shaded triangle with its normal.

  n = (b − a) × (c − a) ÷ |…|

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

  • CivilCraft
  32-bit, display only

• Pit scene in project units

  Converts a pit's ramp and bench outlines from meters back to project units for the 3D view.

  coordinate ÷ k, where k is meters per project unit

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

  • CivilCraft
  32-bit, display only

• Bone data for the card

  Packs the bone matrices (or dual quaternions) for the kernel.

  Skinning on the graphics card anim/skin-gpu.js

  • ModelCraft
  32-bit, display only

• Skinned points read back

  Runs one skin on the card and reads the points back.

  Skinning on the graphics card anim/skin-gpu.js

  • ModelCraft
  32-bit, display only

• Render buffers of a definition

  The triangles of a definition's shown faces as position, normal and texture-coordinate buffers.

  Scene handed to the renderer render-mc.js

  • ModelCraft
  32-bit, display only

• Height from a baked displacement map

  The displacement height at a texture coordinate.

  bilinear blend of the four texels round (u, v), wrapping at the edges, read at texel centers

  Scene handed to the renderer render-mc.js

  • ModelCraft
  32-bit, display only

• Displaced mesh point

  Moves a mesh point along its averaged normal by the material's height times its scale, for the render.

  p′ = p + n̂ × height(u, v) × scale

  Scene handed to the renderer render-mc.js

  • ModelCraft
  32-bit, display only

• A placement's surface in world coordinates

  Every triangle corner of the selected object with its normal and UV, in world coordinates, for the bake.

  Texture bake inputs ws-shading.js

  • ModelCraft
  32-bit, display only

• Bake ray distance and widths

  The ray distance, curvature width and cage distance handed to the bake.

  dist = given, or 0.25 × bounding box diagonal; width = percent ÷ 100; cage = percent ÷ 100

  Texture bake inputs ws-shading.js

  • ModelCraft
  32-bit, display only

• Where a load is drawn on a belt

  The distance along a belt at which a load is drawn at a given time.

  accumulating: s = min(v × t + c, S); stopping belt: s = D(t) − D at entry; drawn at max(0, s) + L ÷ 2

  Material flow drawing and playback addons/flow/lib/playback.js

  • ModelCraft
  32-bit, display only

• Where a vehicle is drawn

  A vehicle's point on its path segment at a given time.

  f = (t − t₀) ÷ (t₁ − t₀); point = path at f × length

  Material flow drawing and playback addons/flow/lib/playback.js

  • ModelCraft
  32-bit, display only

• Belt strips

  The boxes drawn for a conveyor between points sampled along its path.

  pieces = max(4, ceil(|angle| ÷ 10)) for a curve, else 1; length = √(run² + Δz²); turn = atan2(Δy, Δx)

  Material flow drawing and playback addons/flow/view.js

  • ModelCraft
  32-bit, display only

• Loads and vehicles as instanced boxes

  Sets the position, turn and size of each load and vehicle box for one frame.

  Material flow drawing and playback addons/flow/view.js

  • ModelCraft
  32-bit, display only

• Line buffer

  The positions of a polyline in the host's units, for drawing.

  Drawing NURBS curves and surfaces nurbs-ui/display.js

  • ModelCraft
  • PartCraft
  32-bit, display only

• Surface mesh buffers

  The positions, normals, parameters and colors of a surface's triangles, for drawing.

  Drawing NURBS curves and surfaces nurbs-ui/display.js

  • ModelCraft
  • PartCraft
  32-bit, display only

• Streamlines

  Traces lines along the flow from seed points for drawing.

  x ← x + ds × v(x + ½ ds v̂) ÷ |v|

  Simulation and flow result plots flow.js

  • PartCraft
  32-bit, display only

• Slice of a field

  Copies one layer of cells of a field for the cut-plane picture.

  Simulation and flow result plots flow.js

  • PartCraft
  32-bit, display only

• Field for coloring

  Picks the values and the color range for the cut plane.

  Simulation and flow result plots flow-ui.js

  • PartCraft
  32-bit, display only

• Plot mesh

  Splits the part's triangles until no edge is longer than the cell size, for drawing a field.

  midpoint = (a + b) ÷ 2

  Simulation and flow result plots fea.js

  • PartCraft
  32-bit, display only

• Smooth surface for display

  The limit positions of the refined cage as a triangle mesh.

  Freeform bodies: display mesh form.js

  • PartCraft
  32-bit, display only

• Slider range of the section

  The lowest and highest value of n·p over the model's box, the two ends of the section slider.

  lo, hi = min, max of n · p over the 8 box corners

  Section view plane section.js

  • PartCraft
  32-bit, display only

• Section through a picked face

  The cutting plane through a flat face, placed by the instance matrix of an assembly.

  n = unit(M · n_face); c = n · (M · o_face)

  Section view plane section.js

  • PartCraft
  32-bit, display only

• Sketch coordinates to canvas pixels

  Maps a sketch point to its place on the canvas.

  x = w ÷ 2 + (u − c_x) × s; y = h ÷ 2 − (v − c_y) × s

  Sketch editor drawing sketchview.js

  • PartCraft
  32-bit, display only

• Dimension lines and label

  The lines, arcs, arrowheads and text of a dimension as drawn.

  label text = fmt(value, 3)

  Sketch editor drawing sketchview.js

  • PartCraft
  32-bit, display only

• Display mesh of a surface body

  The triangles used to draw each surface body.

  linear deflection = 2e-4 × diagonal; angular deflection = 2π ÷ 64

  Surface display meshes, curvature map and zebra stripes surface.js

  • PartCraft
  32-bit, display only

• Curvature per vertex

  The discrete Gaussian and mean curvature at each vertex of a triangle mesh, for the curvature map.

  K = (2π − Σ angles) ÷ A; H = |Σ (cot α + cot β)(pᵢ − pⱼ)| ÷ 4A, A = one third of the area of the triangles at the vertex

  Surface display meshes, curvature map and zebra stripes surface.js

  • PartCraft
  32-bit, display only

• Zebra stripe value

  Whether a surface normal reflects a light or a dark stripe.

  r = d − 2(d · n)·n; stripe = ⌊(atan2(r_x, r_z) ÷ π + 1) × stripes ÷ 2⌋ mod 2

  Surface display meshes, curvature map and zebra stripes surface.js

  • PartCraft
  32-bit, display only

• Triangle buffer for drawing

  Copies the part's mesh into the vertex buffer the GPU draws.

  3D view of the part view3d.js

  • PartCraft
  32-bit, display only

• Result colors on the part

  Spreads per-vertex or per-corner result colors onto the drawn triangles.

  3D view of the part view3d.js

  • PartCraft
  32-bit, display only

• What is under the pointer

  Finds the face, edge or plane under the pointer.

  3D view of the part view3d.js

  • PartCraft
  32-bit, display only

• Frame of the study's plane

  The origin and axes of the plane the result is drawn in.

  x = (helper × n) ÷ |helper × n|; y = n × x

  Magnetics add-on: the result drawn as display bodies addons/magnetics/lib/bodies.js

  • PartCraft
  32-bit, display only

• Triangle cut to the crop rectangle

  Cuts a field triangle to the rectangle that is shown.

  Magnetics add-on: the result drawn as display bodies addons/magnetics/lib/bodies.js

  • PartCraft
  32-bit, display only

• Field color bands

  The color band each triangle falls in.

  band = min(9, floor(|B| ÷ top × 10))

  Magnetics add-on: the result drawn as display bodies addons/magnetics/lib/bodies.js

  • PartCraft
  32-bit, display only

• Projection onto the picture

  A model point's place in the picture and its depth.

  orthographic: u = aspect ÷ 2 + q·right ÷ 2h; perspective: u = aspect ÷ 2 + q·right ÷ (2 tan(fov ÷ 2) × depth)

  Illustrate: projection, hidden lines and vector pictures illustrate/camera.js

  • PartCraft
  32-bit, display only

• Is a picture point hidden

  Decides whether a point of an edge is behind a triangle of another surface.

  barycentric l₁, l₂, l₃ in the picture; hidden when the triangle's depth < point depth − 10 eps

  Illustrate: projection, hidden lines and vector pictures illustrate/hlr.js

  • PartCraft
  32-bit, display only

• Feature edges

  The mesh edges drawn as lines: open edges and edges where two faces meet at more than an angle.

  drawn when open, or cos(face angle) < cos(angle)

  Illustrate: projection, hidden lines and vector pictures illustrate/edges.js

  • PartCraft
  32-bit, display only

• Numbers in the PDF

  How a coordinate is written into a PDF page.

  Illustrate: projection, hidden lines and vector pictures illustrate/pdf.js

  • PartCraft
  32-bit, display only

• Mesh buffers

  The item's box or mesh as geometry for drawing, turned from z up to y up.

  Library 3D preview library-3d.js Every app
  32-bit, display only

• Camera position

  Where the camera sits as the view is turned and zoomed.

  position = target + dist × (sin φ sin θ, cos φ, sin φ cos θ)

  Library 3D preview library-3d.js Every app
  32-bit, display only

• Variant body buffers

  The chosen variant's box or mesh as geometry for drawing.

  Library 3D preview library-configurator.js Every app
  32-bit, display only

• Vertex buffers for the 3D view

  Copies an object's triangles into a buffer for the graphics card.

  Drawing the 3D check view and CAD sheets on screen view3d.js

  • TakeoffCraft
  32-bit, display only

• Canvas paths for a CAD sheet

  Builds the canvas paths of one batch of lines and fills.

  Drawing the 3D check view and CAD sheets on screen cadset.js

  • TakeoffCraft
  32-bit, display only