Calculations

Calculations

• Binary STL

  Writes each triangle's unit normal and three corners.

  normal = n ÷ |n| from the winding; every number written with setFloat32

  STL and 3MF files for the printer print3d.js

  • ModelCraft
  • PartCraft
  32-bit in part

• A coordinate as 3MF text

  Formats one coordinate for the 3MF file.

  0 if |v| < 10⁻¹²; else v rounded to 10 significant digits

  STL and 3MF files for the printer print3d.js

  • ModelCraft
  • PartCraft
  64-bit

• 3MF vertex list

  Writes every corner of the mesh as a vertex element.

  STL and 3MF files for the printer print3d.js

  • ModelCraft
  • PartCraft
  64-bit

• 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

• Flat area per color

  The total area of level, upward faces of each color, largest first.

  s = ∛|m₀·(m₅·m₁₀ − m₆·m₉)|; area = Σ face area × s²; shown = round(area × 100) ÷ 100

  Areas of flat upward faces by color render-mc.js

  • ModelCraft
  64-bit

• Sunrise, sunset and solar noon

  The clock hours of sunrise, sunset and solar noon and the sun's highest altitude on a day.

  hᵢ = min(0.05·i, 23.99), i = 0 … 480; rise = first hᵢ with altitude > 0 after one ≤ 0; noon = hᵢ of the highest altitude

  Time of day, date and exposure from plain words scene-say.js

  • ModelCraft
  64-bit

• Clock hour for a named time

  The hour that stands for dawn, morning, noon, afternoon, golden hour, dusk or night on a given day.

  dawn = rise + 0.3; morning = rise + 0.45·(noon − rise); afternoon = noon + 0.55·(set − noon); dusk = set − 0.1; night = set + 2; hour = round to 0.01

  Time of day, date and exposure from plain words scene-say.js

  • ModelCraft
  64-bit

• The look for the choices made

  Combines time, date or season and weather into the sun's date and hour and the render's exposure.

  month, day = round(given); exposure = round((weather + time of day) × 100) ÷ 100

  Time of day, date and exposure from plain words scene-say.js

  • ModelCraft
  64-bit

• Places things can stand on

  Top-level placements and large flat faces with their box, top height, height and area.

  placement area = Δx × Δy of its box; face area from the model kernel; every number rounded to 0.001

  Placing scene trees and people scene-entourage.js

  • ModelCraft
  64-bit

• Point inside a face outline

  Whether a plan point lies inside a polygon.

  count edges with (y_a > y) ≠ (y_b > y) and x < (x_b − x_a)·(y − y_a) ÷ (y_b − y_a) + x_a; inside if odd

  Placing scene trees and people scene-entourage.js

  • ModelCraft
  64-bit

• The ground a request names

  The region to scatter over, the height things stand at, and the boxes to keep clear.

  on a placement: its box in plan, z = top of the box; on a face: its outline, z = first point's z; avoid boxes with top > z + 0.3 and bottom < z + 2.5

  Placing scene trees and people scene-entourage.js

  • ModelCraft
  64-bit

• Planting trees

  Places a number of trees over the region, each with a random turn and a size within 10% of the library's.

  minimum distance = max(0.5, 0.9 × crown width); yaw = rand × 2π; scale = 0.9 + 0.2 × rand

  Placing scene trees and people scene-entourage.js

  • ModelCraft
  64-bit

• Placing people

  Places figures over the region; along a line they face along it, half each way.

  heading = atan2(Δy, Δx) of the line; yaw = heading + π ÷ 2 (+ π for half of them) + (rand − ½) × 0.3; scale = 0.97 + 0.06 × rand

  Placing scene trees and people scene-entourage.js

  • ModelCraft
  64-bit

• Scattering points with a minimum spacing

  Seeded points inside a rectangle or along a line, none closer than the minimum distance to another.

  rectangle: x = x₀ + margin + rand × w, y likewise; line: p = a + (b − a) × i ÷ (count − 1) + normal × jitter; kept x, y = round to 0.01

  Placing scene trees and people scene-say.js

  • ModelCraft
  64-bit

• Placement matrix

  The 4×4 matrix for a turn about the vertical axis, a uniform scale and a position.

  c = cos(yaw)·scale; s = sin(yaw)·scale; columns [c, s, 0], [−s, c, 0], [0, 0, scale], [x, y, z]

  Placing scene trees and people scene-say.js

  • ModelCraft
  64-bit

• Arc and circle as straight segments

  The ground segments for one traced line, arc or circle.

  aₖ = a₀ + sweep × k ÷ n; pₖ = [cx + r·cos aₖ, cy + r·sin aₖ, 0]

  Traced sketch into model edges sketch-photo-mc.js

  • ModelCraft
  64-bit

• Picked points in millimeters

  The picked model points as the surfaces library receives them.

  v_mm = round(v × 1000 × 10⁶) ÷ 10⁶

  Points picked for surfaces surfaces-mc.js

  • ModelCraft
  64-bit

• Letter outlines from strokes

  The outline of the text: each stroke segment as a rectangle of the pen's width, each stroke point as a disc.

  r = height × weight ÷ 2; rectangle corners = a ∓ r·n̂, b ∓ r·n̂; disc corner = c + r·[cos(i·π ÷ 6), sin(i·π ÷ 6)]; line k at y − 1.6·k·height

  3D text text3d.js

  • ModelCraft
  64-bit

• Letters as faces or solids

  The component the app places: flat faces, or a closed solid from z = 0 to the depth.

  g6(v) = round(v × 10⁶) ÷ 10⁶ on every coordinate

  3D text text3d.js

  • ModelCraft
  32-bit in part

• Did another program change the points

  Decides whether a definition's native USD points still match the model's own.

  changed if any fround(own coordinate) ≠ file coordinate, or the counts differ

  USD save, open and import usd-modelcraft.js

  • ModelCraft
  Exact

• Mesh from the native points

  Rebuilds a definition that was changed elsewhere from the file's native points and faces.

  USD save, open and import usd-modelcraft.js

  • ModelCraft
  64-bit

• Was a placement moved elsewhere

  Decides whether a placement's matrix in the file differs from the model's and takes the file's if so.

  moved if any |mₖ(file) − mₖ(own)| > 10⁻⁷ × max(1, |mₖ(own)|)

  USD save, open and import usd-modelcraft.js

  • ModelCraft
  64-bit

• Placements through the stage's frame

  Brings a placement matrix from the file's units and up axis into meters with Z up.

  M′ = F · M · F⁻¹

  USD save, open and import usd-modelcraft.js

  • ModelCraft
  64-bit

• Imported mesh points

  The points of an imported mesh in meters with Z up.

  p′ = F · p (rotation, scale and translation of the frame)

  USD save, open and import usd-modelcraft.js

  • ModelCraft
  64-bit

• Lamp output from a USD light

  The lumens of an imported lamp when the file does not carry ModelCraft's own value.

  area = width × height × scale² or 4π·(radius × scale)²; lumens = intensity × 2^exposure × 683 × max(area, 10⁻⁶) × π

  USD save, open and import usd-modelcraft.js

  • ModelCraft
  64-bit

• Round starting size

  Rounds a size to 1, 2, 5 or 10 times a power of ten.

  p = 10^⌊log₁₀ x⌋; m = x ÷ p; result = (1 if m < 1.5, 2 if m < 3.5, 5 if m < 7.5, else 10) × p

  Sizes for new curves and meshes, remesh grid ws-curve.js

  • ModelCraft
  64-bit

• Text as a curve object

  The letters' outlines as closed flat splines, filled and given a thickness.

  extrude = height × 0.05; each outline point [x, y] becomes a spline point [x, y, 0]

  Sizes for new curves and meshes, remesh grid ws-curve.js

  • ModelCraft
  64-bit

• Voxel remesh grid size

  Suggests a voxel size and counts the grid cells the typed size would need.

  suggested = niceSize(largest extent ÷ 40); cells = Π (⌈(extentₖ + 4·voxel) ÷ (voxel ÷ 2)⌉ + 1)

  Sizes for new curves and meshes, remesh grid ws-mesh.js

  • ModelCraft
  64-bit

• Size of a new mesh shape

  The size given to a new plane, cube, cylinder, sphere or torus.

  s = niceSize(view height ÷ 5); radius = s ÷ 2; torus tube = s ÷ 8

  Sizes for new curves and meshes, remesh grid ws-mesh.js

  • ModelCraft
  64-bit

• Volume and size of a placed solid

  The volume of a closed group or component and its width, depth and height as placed.

  k = ∛|det M₃ₓ₃|; volume = V × k × k × k; size_q = (max_q − min_q) × |column q|; retyped size → L ÷ |column q|

  Entity info: volume, size, angle and area modelcraft.js

  • ModelCraft
  64-bit

• Volume and size of a placed mesh

  The volume of a closed mesh and its size as placed.

  k = ∛|det M₃ₓ₃|; volume = V × k³; size_q = (max_q − min_q) × |column q|

  Entity info: volume, size, angle and area modelcraft.js

  • ModelCraft
  64-bit

• Arc angle

  The angle an arc sweeps, in degrees.

  shown = round(sweep × 180 ÷ π × 100) ÷ 100

  Entity info: volume, size, angle and area modelcraft.js

  • ModelCraft
  64-bit

• Total area of selected faces

  The sum of the areas of the selected faces.

  total = Σ face area

  Entity info: volume, size, angle and area modelcraft.js

  • ModelCraft
  64-bit

• Print check size and volume

  The size in millimeters and the volume in cubic centimeters shown after a print check.

  shown size = round(mm × 10) ÷ 10; shown volume = round(mm³ ÷ 1000 × 10) ÷ 10 cm³

  Entity info: volume, size, angle and area modelcraft.js

  • ModelCraft
  64-bit

• Mirror plane for a flipped copy

  Puts the mirror plane on the far side of the selection's box so the copy lands beside the original.

  far = max over the box's 8 corners of (corner − c)·a; plane point = c + a × far

  Edits and settings from the main window modelcraft.js

  • ModelCraft
  64-bit

• Curve object from a drawn curve

  Makes a curve object from a drawn arc, circle, polygon or curve, flat when all its points share a height.

  closed if |first − last| < 10⁻⁹; flat if every |z − z₀| < 10⁻⁹, then z ← 0 and the placement carries z₀; bevel depth = max(10⁻⁴, length ÷ 100)

  Edits and settings from the main window modelcraft.js

  • ModelCraft
  64-bit

• Node meshes baked into the model

  Converts each baked mesh from millimeters to the model's meters.

  x_m = x_mm ÷ 1000

  Edits and settings from the main window modelcraft.js

  • ModelCraft
  64-bit

• Guessing storey heights

  Proposes a storey for each different height the top-level groups and components stand on.

  height = round(box min z × 100) ÷ 100

  Edits and settings from the main window modelcraft.js

  • ModelCraft
  64-bit

• Sun settings from the panel

  Reads month, day, hour, latitude, longitude and time zone from the Style panel into the model's sun.

  value = clamp(parseFloat(text), lo, hi); month, day = value | 0

  Edits and settings from the main window modelcraft.js

  • ModelCraft
  64-bit

• Room handed to add-ons

  The room made by the selected floor face, as add-ons receive it: outline in millimeters, height and area.

  z = round(room height × 1000); area (mm²) = area (m²) × 10⁶

  Edits and settings from the main window modelcraft.js

  • ModelCraft
  64-bit

• Scale of a photographed sketch

  Reads the 1 : n scale the person types for a sketch photo.

  n = round(Number(text)); accepted if 1 ≤ n ≤ 100 000

  Edits and settings from the main window modelcraft.js

  • ModelCraft
  64-bit

• Point and normal under the pointer

  The clicked point and the face normal in the face's own coordinates, and where on the material's tile the point lies.

  p = M⁻¹ × hit; n = (b − a) × (c − a), made unit; tile uv = planar uv ÷ tile size

  Decal placement and size ws-shading.js

  • ModelCraft
  64-bit

• Barycentric weights of a point in a triangle

  The three weights of a point against a triangle's corners and its distance from the triangle's plane.

  n = ab × ac; b = ((ap × ac) · n) ÷ |n|²; c = ((ab × ap) · n) ÷ |n|²; a = 1 − b − c; dist = |ap · n| ÷ |n|

  Decal placement and size ws-shading.js

  • ModelCraft
  64-bit

• Size of a new decal

  The width and height a new decal and its material tile are stored with.

  height = round(width × (picture height ÷ picture width) × 1000) ÷ 1000

  Decal placement and size ws-shading.js

  • ModelCraft
  64-bit

• Resize a decal

  A decal's new height and depth when its width is changed.

  h = round(w × size₁ ÷ size₀ × 1000) ÷ 1000; depth = max(0.01, min(w, h) ÷ 2)

  Decal placement and size ws-shading.js

  • ModelCraft
  64-bit

• Turn a decal a quarter turn

  The decal's new width direction and swapped sizes after a quarter turn about its normal.

  u′ = n × u; size′ = [size₁, size₀]

  Decal placement and size ws-shading.js

  • ModelCraft
  64-bit

• 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