Calculations

Calculations

• Distance from a point to a triangle

  The distance used to decide whether a point is inside a face's outline or on it.

  Snap points picked in the 3D view m3d/infer.js

  • CadCraft
  • ModelCraft
  64-bit

• Midpoint of an edge

  The middle of an edge, offered as a snap point.

  m = (a + b) × 0.5

  Snap points picked in the 3D view m3d/infer.js

  • CadCraft
  • ModelCraft
  64-bit

• Point on an edge

  The point of an edge nearest the cursor, offered when no end or midpoint is in reach.

  Snap points picked in the 3D view m3d/infer.js

  • CadCraft
  • ModelCraft
  64-bit

• Point along an axis from the start point

  The point on a red, green or blue line (or one parallel or square to an edge) through the start point.

  Snap points picked in the 3D view m3d/infer.js

  • CadCraft
  • ModelCraft
  64-bit

• Where an axis line meets an edge

  The point where the line from the start point along an axis meets the edge or guide under the cursor.

  Snap points picked in the 3D view m3d/infer.js

  • CadCraft
  • ModelCraft
  64-bit

• Point on a locked direction

  The point kept on a line when a direction is locked with Shift or an arrow key.

  p = from + d × ((q − from) · d) ÷ (d · d)

  Snap points picked in the 3D view m3d/infer.js

  • CadCraft
  • ModelCraft
  64-bit

• Distance along a line under the cursor

  The point on a line nearest the cursor and how far along it lies, used by push/pull and moves along an axis.

  Snap points picked in the 3D view m3d/infer.js

  • CadCraft
  • ModelCraft
  64-bit

• Newell normal of a mesh face

  The normal of a face with any number of corners; its length is twice the face's area.

  N = Σ ((y_a − y_b)(z_a + z_b), (z_a − z_b)(x_a + x_b), (x_a − x_b)(y_a + y_b))

  Polygon mesh: normals, areas, triangles and volume m3d/mesh.js

  • CadCraft
  • ModelCraft
  64-bit

• Unit normal of a mesh face

  The direction a mesh face points.

  n = N ÷ |N|

  Polygon mesh: normals, areas, triangles and volume m3d/mesh.js

  • CadCraft
  • ModelCraft
  64-bit

• Area of a mesh face

  The area of one mesh face.

  area = |N| ÷ 2

  Polygon mesh: normals, areas, triangles and volume m3d/mesh.js

  • CadCraft
  • ModelCraft
  64-bit

• Center of a mesh face

  The point used as a face's middle.

  c = Σ pᵢ ÷ n

  Polygon mesh: normals, areas, triangles and volume m3d/mesh.js

  • CadCraft
  • ModelCraft
  64-bit

• Is a mesh face flat

  Whether every corner of a face lies in one plane, which decides if it stays one face or becomes triangles.

  |(p − c) · n| ≤ tol, tol = 1e-6 m by default

  Polygon mesh: normals, areas, triangles and volume m3d/mesh.js

  • CadCraft
  • ModelCraft
  64-bit

• Triangles of a mesh

  The triangles every face is cut into for area, volume, ray tests and drawing.

  Polygon mesh: normals, areas, triangles and volume m3d/mesh.js

  • CadCraft
  • ModelCraft
  64-bit

• Area and volume of a mesh

  The surface area of a mesh and, when it is closed, the volume it encloses.

  A = Σ |u × v| ÷ 2; V = Σ a · (b × c) ÷ 6

  Polygon mesh: normals, areas, triangles and volume m3d/mesh.js

  • CadCraft
  • ModelCraft
  64-bit

• 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