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Calculations

Every calculation under our calculation policies: what it works out, its formula and the precision it runs at. Open one to see its code as it is in the released app.

  • 6,917 calculations in 1,248 source files
  • 143 exact
  • 6,286 in 64-bit
  • 335 with a 32-bit step
  • Last reviewed

  • Adding a layer

    Creates a layer of 1 to 16 numbers per element.

    Polygon mesh: attribute layers (UV, color, crease, weights) m3d/mesh.js
    • CadCraft
    • ModelCraft
    32-bit in part

  • Storing a value in a layer

    Writes the values of one element of a layer.

    Polygon mesh: attribute layers (UV, color, crease, weights) m3d/mesh.js
    • CadCraft
    • ModelCraft
    32-bit in part

  • Blending corner values onto new faces

    The values new face corners get when faces are cut or joined, as a weighted mix of old corners.

    out = Σ wᵢ × valueᵢ

    Polygon mesh: attribute layers (UV, color, crease, weights) m3d/mesh.js
    • CadCraft
    • ModelCraft
    32-bit in part

  • Layers in the mesh file

    The layer data as it is written into the file.

    Polygon mesh: attribute layers (UV, color, crease, weights) m3d/mesh.js
    • CadCraft
    • ModelCraft
    32-bit in part

  • 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

  • World triangles for export

    Every triangle of the model in world coordinates, with its normal.

    p_world = M · p; n = normalize((p₁ − p₀) × (p₂ − p₀))

    Export to glTF and STL m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • glTF vertex positions

    The vertex coordinates and normals stored in the binary part of a .glb file.

    Export to glTF and STL m3d/io.js
    • CadCraft
    • ModelCraft
    32-bit in part

  • glTF placement matrix

    The matrix that places each group or component in the .glb file.

    Export to glTF and STL m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • STL triangles in millimeters

    The triangles of a binary STL file.

    x_mm = x × 1000, stored as a 32-bit float

    Export to glTF and STL m3d/io.js
    • CadCraft
    • ModelCraft
    32-bit in part

  • OBJ number format

    How every coordinate and normal component is written in an OBJ file.

    text = x rounded to 6 decimals

    Export to OBJ and Collada m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • OBJ vertex

    A vertex of the model as it goes into the OBJ file.

    (x, y, z) → M · p → (x, z, −y)

    Export to OBJ and Collada m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • OBJ face normal

    The flat normal written for a face.

    N = Σ pᵢ × pᵢ₊₁, normalized

    Export to OBJ and Collada m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • OBJ vertex and normal lines

    The lines that carry the numbers.

    Export to OBJ and Collada m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Collada number format

    How every number is written in a Collada file.

    text = x rounded to 12 significant digits

    Export to OBJ and Collada m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Collada positions and normals

    The vertex positions and face normals of each definition in the Collada file.

    Export to OBJ and Collada m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Collada placement matrix

    The 4×4 matrix of each placement, written row by row.

    Export to OBJ and Collada m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Is a face convex

    Decides whether a face is written as one polygon or as triangles in Collada.

    every turn (b − a) × (c − b) ≥ −1e-12 × size²

    Export to OBJ and Collada m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Unit factor for DXF and DWG

    The factor that turns the model's meters into the drawing unit of the export.

    inches: 1 ÷ 0.0254; mm: 1000; cm: 100; m: 1

    Export of the 3D model to DXF and DWG m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Exported point

    A vertex of the model in the export's unit.

    p′ = (M · p) × k

    Export of the 3D model to DXF and DWG m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Placement as a block insert

    The insertion point, scale, rotation and extrusion direction that stand for a placement matrix.

    scale = column lengths; n = third unit column; rot = atan2(r₀ · a_y, r₀ · a_x); insertion = (T · a_x, T · a_y, T · n)

    Export of the 3D model to DXF and DWG m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • DXF number format

    How every coordinate, scale and angle is written in the DXF text.

    text = x rounded to 15 significant digits

    Export of the 3D model to DXF and DWG m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • DXF insert record

    The numbers of one block placement in the DXF text.

    rotation in degrees = rot × 180 ÷ π

    Export of the 3D model to DXF and DWG m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Numbers handed to the DWG writer

    The same faces, lines and inserts as objects for the DWG writer.

    Export of the 3D model to DXF and DWG m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • IFC number format

    How every coordinate, direction component and elevation is written.

    text = x rounded to 9 decimals

    Export to IFC m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Shared points

    The corner points of the faces, each written once.

    Export to IFC m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Is a placement rigid

    Decides whether a group is exported in its own coordinates with a placement, or in world coordinates.

    |column| = 1 ± 1e-9; columns square within 1e-9; determinant > 0

    Export to IFC m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Placement of an element

    Where each exported element sits relative to its level.

    location = (t_x, t_y, t_z − level elevation); axis = third column; ref direction = first column

    Export to IFC m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Level of an element

    Which level an element is listed under.

    the highest level with elevation ≤ z_min + 1e-6

    Export to IFC m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Precision stated in the file

    The precision value the IFC file declares for its geometry.

    Export to IFC m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Drawing unit factors

    The factor from the drawing's unit ($INSUNITS) to meters.

    in 0.0254; ft 0.3048; mi 1609.344; mm 0.001; cm 0.01; m 1; km 1000; yd 0.9144

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    Exact

  • Which unit factor is used

    Picks the factor for a drawing.

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Mirrored entities

    How an entity drawn in a flipped coordinate system is read.

    x → −x when the extrusion direction's z is negative

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Arc angles

    The start and end angles of a DXF arc.

    radians = degrees × π ÷ 180; mirrored: (a₀, a₁) → (π − a₁, π − a₀)

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Placing and scaling a segment

    Moves each line segment by the block placements above it and converts it to meters.

    x′ = a·x + c·y + e; y′ = b·x + d·y + f; then × k

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Arcs, circles and bulges as segments

    The points that stand for an arc, a circle or a polyline bulge.

    n = max(2, ⌈|sweep| ÷ (2π ÷ 48)⌉); pⱼ = c + r (cos aⱼ, sin aⱼ), aⱼ = a₀ + sweep × j ÷ n; bulge: sweep = 4 atan b

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Ellipse as segments

    The points that stand for an ellipse or an elliptical arc.

    p = c + major × cos t + minor × sin t, minor = major turned 90° × ratio

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Spline (NURBS) as segments

    The points that stand for a spline with control points.

    de Boor on homogeneous points (x·w, y·w, w); 12 samples per knot span

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Spline stored with fit points only

    The points that stand for a spline that carries fit points and no control points.

    centripetal Catmull–Rom, 12 samples per span

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Bulge arcs in hatch boundaries

    The points of a curved side of a hatch boundary given as a polyline bulge.

    center = chord midpoint + ((1 ÷ b − b) ÷ 2) × (chord turned 90°) ÷ 2; sweep = 4 atan b

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Block insert transform

    The transform that places a block, with its scale, rotation and array spacing.

    M = T(x, y) · R(rot) · S(s_x, s_y) · T(−base); array offset = R(rot) · (col × d_c, row × d_r)

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Hatch holes

    Which loops of a hatch are outlines and which are holes.

    area = ½ |Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|; a loop inside an odd number of larger loops is a hole

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • 3D face corners

    The corners of 3D faces and solids, which keep their heights.

    (x, y) placed by the block transform; all three × k

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Text line pitch

    The distance between lines of imported multi-line text, which is drawn as edges.

    pitch = height × 1.667 × spacing factor

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Edges of imported solids

    How the edges of an imported solid are matched to decide which ones show.

    key = round(x × 1e5), round(y × 1e5), round(z × 1e5)

    Import of DXF and DWG drawings into the 3D model m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • OBJ vertex

    A vertex line of an OBJ file.

    (x, y, z) → (x, −z, y)

    Import of OBJ, glTF and Collada models m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • glTF accessor values

    The numbers of a glTF buffer, such as vertex positions.

    Import of OBJ, glTF and Collada models m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • glTF node transform

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

    M = T · R(q) · S

    Import of OBJ, glTF and Collada models m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • glTF vertex in the model

    A glTF vertex moved by its node transforms and turned to Z up.

    p′ = M · p, then (x, y, z) → (x, −z, y)

    Import of OBJ, glTF and Collada models m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Collada numbers

    How lists of numbers in a Collada file are read.

    Import of OBJ, glTF and Collada models m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

  • Collada unit and up axis

    The change from the file's unit and up axis to Z-up meters.

    C = R_up · S(meter); node matrix → C · M · C⁻¹; point → C · p

    Import of OBJ, glTF and Collada models m3d/io.js
    • CadCraft
    • ModelCraft
    64-bit

A calculation is added only after its source was read. Each statement can be checked in the code shown on its policy's page; the app repositories are public. When a release changes a calculation, its page says so until it has been read again.