Resources

Numerical accuracy

The calculations in our apps: the policy each one is under, the precision it runs at, and the code itself.

  • 941 calculation policies
  • 6,917 calculations in 1,248 source files
  • 143 exact
  • 6,286 in 64-bit
  • 335 with a 32-bit step
  • 437 open items
  • Last reviewed

Calculation policies

A policy says how one family of calculations keeps its precision. Open one to see its calculations, by source file, and their code.

  • Area markup with cut-outs, and clipboard placement

    The area and perimeter of an area markup less its cut-outs, whether cut-outs fit, and where pasted markups land.

    • MarkupCraft
    64-bit, direct
    6 calculations in 2 files
    64-bit
  • Area, perimeter and length

    Works out the area and perimeter of circles, polylines and hatches and the length of lines, arcs, polylines and splines.

    • CadCraft
    64-bit, direct
    5 calculations
    64-bit Open item
  • Areas of flat upward faces by color

    Adds up the area of the level, upward-facing faces on screen for each color, in square meters, for the wet-surface look.

    • ModelCraft
    64-bit, direct
    1 calculation
    64-bit Open item
  • Arithmetic on typed lengths

    Works out a length typed as an expression, such as 4+7/16 or 2*450mm, wherever a length is asked for.

    • CadCraft
    • ModelCraft
    • MarkupCraft
    • TakeoffCraft
    • CivilCraft
    • DetailCraft
    64-bit, direct
    4 calculations
    64-bit
  • As-built points compared with the drawing

    Brings the drawing's design points and surveyed as-built points to the same units, compares them against a tolerance, and marks and reports the differences.

    • CadCraft
    64-bit, direct
    3 calculations
    64-bit
  • Assembly drawing sheet and mesh exports

    Lays out the assembly drawing (view scale, positions on the sheet, bill of materials masses) and writes the placed assembly as one mesh for STL or as a 3MF file.

    • PartCraft
    32-bit step, flagged
    5 calculations
    32-bit in part Open item
  • Assembly joints and part placement

    Works out where each part of an assembly sits from its joints: mate frames on faces, the motion each joint allows, and the chain of transforms from the grounded part.

    • PartCraft
    64-bit, direct
    7 calculations
    64-bit Open item
  • Asset service life and maintenance due dates

    Stores an asset's service life in the IFC file and reads it back in years, and marks maintenance as overdue or due soon from its next date.

    • BimCraft
    64-bit, direct
    4 calculations
    64-bit
  • Assistant and window read-outs of radio link and coverage

    The numbers the assistant tools return for radio links and coverage, and the coverage read-out in the geotechnical and telecom window.

    • CivilCraft
    32-bit step, flagged
    4 calculations in 2 files
    32-bit in part Open item
  • Assistant answers: fire ratings and room areas

    Answers two questions a connected assistant asks of the open model: which walls have a given fire rating, and which rooms are under or over a given area.

    • BimCraft
    64-bit, direct
    3 calculations
    64-bit
  • Assistant answers: what is above an element

    Lists the elements whose bounding box starts within a distance above an element's top and overlaps its footprint, nearest first, with the gap in meters.

    • BimCraft
    32-bit step, flagged
    1 calculation
    32-bit in part Open item
  • Automatic constraints and dimension conversion

    Finds ends that meet and lines that are level or upright and constrains them, and turns a plain dimension into a constraint on the objects it measures.

    • CadCraft
    64-bit, direct
    2 calculations
    64-bit
  • Automatic dimensions

    Chooses what to dimension from the level and plumb edges, openings, circles and grid lines of a drawing and places chains, overall dimensions and diameters.

    • CadCraft
    64-bit, direct
    6 calculations
    64-bit Open item
  • Automatic mesh refinement of tetrahedral studies

    Decides which elements to refine after a solve, how small to make them, refines the mesh and stops when the estimated error meets the target.

    • PartCraft
    64-bit, stated limit
    5 calculations
    64-bit
  • Automatic plan dimensions

    Chooses the points an automatic row of dimensions measures between: the building's overall size and the stops along each outside edge.

    • BimCraft
    64-bit, direct
    6 calculations
    64-bit Open item
  • Automatic sheet layout

    Splits a drawing into parts, picks a paper size and standard scale, and places a viewport for every part on the sheet.

    • CadCraft
    64-bit, direct
    7 calculations
    64-bit
  • Average daylight factor of rooms

    Works out each room's average daylight factor from its windows, its inside surfaces and the angle of sky each window sees.

    • BimCraft
    64-bit, stated limit
    13 calculations
    64-bit
  • B-spline basis functions

    The basis functions and derivatives under every NURBS curve and surface.

    • ModelCraft
    • PartCraft
    64-bit, direct
    3 calculations
    64-bit
  • Back-outs clipped out of areas

    Works out how much of an area a back-out covers, so that part can be taken off the area's quantity.

    • TakeoffCraft
    64-bit, stated limit
    4 calculations in 2 files
    64-bit
  • Baked physics key times

    The times of the keys written when rigid body physics is baked to the timeline.

    • ModelCraft
    64-bit, stated limit
    1 calculation
    64-bit
  • Batch schedule and batch inventory

    Places a recipe's steps on the plant's vessels for a number of batches and reports start and finish hours, utilization, cycle time and batches per day; keeps a mole inventory of charges, transfers, reactions and discharges.

    • CadCraft
    • BimCraft
    64-bit, direct
    4 calculations
    64-bit
  • BCF viewpoint of a markup

    The camera position and view scale written to a BCF file for each markup, in meters of paper.

    • MarkupCraft
    64-bit, direct
    1 calculation
    64-bit
  • Bearings and degrees-minutes-seconds

    Reads typed quadrant bearings and degrees-minutes-seconds angles, and writes angles in decimal degrees, degrees-minutes-seconds, grads, radians or surveyor's bearings.

    • CadCraft
    64-bit, direct
    6 calculations
    64-bit
  • Beginner shapes, align and drop to ground

    Builds the 20 mm starter shapes (box, cylinder, cone, sphere, roof) and moves placements so their boxes line up or stand on the ground.

    • ModelCraft
    64-bit, direct
    6 calculations
    64-bit
  • Best route across the terrain

    Finds the least-cost path between two points on the ground within a steepest grade and a tightest curve, and reports its length, steepest grade, smallest radius and earthwork.

    • CivilCraft
    32-bit step, flagged
    5 calculations
    32-bit in part Open item
  • Bid packages and leveling

    Our own cost of each bid package, each subcontractor's bid leveled with plugs for the scope it leaves out, the low bid, and the base bid with the chosen bids in it.

    • TakeoffCraft
    64-bit, direct
    5 calculations
    64-bit
  • Blank pages: paper sizes and grid

    The size of a new blank page in PDF points and the positions of its grid lines or dots.

    • MarkupCraft
    64-bit, direct
    2 calculations
    64-bit
  • Block model, ultimate pit and mine schedule

    Estimates block grades from samples, values each block, finds the most valuable pit within a slope, and reports tonnes, grades, strip ratio and a discounted schedule.

    • CivilCraft
    64-bit, stated limit
    10 calculations
    64-bit
  • Board geometry and clearances

    Distances between tracks, pads and zones, point-in-shape tests, areas and pad positions on a printed circuit board.

    Every app 64-bit, direct
    10 calculations in 2 files
    64-bit Open item
  • Board placement and routing

    Where parts are placed and where tracks and vias run on a board, with the wire length reported.

    Every app 64-bit, stated limit
    8 calculations in 2 files
    64-bit Open item
  • Bodies: volume, move and scale

    Lists each body with its volume and box, and moves, copies or scales bodies.

    • PartCraft
    64-bit, direct
    4 calculations
    64-bit
  • Body move, scale and path pattern arithmetic

    Builds the matrices that move, rotate and scale bodies, and the positions of pattern copies along a path.

    • PartCraft
    64-bit, direct
    5 calculations
    64-bit
  • Bone frames and pose matrices

    Works out each bone's rest frame from its head, tail and roll, and the matrices that carry the mesh from rest to a pose.

    • ModelCraft
    64-bit, direct
    6 calculations in 2 files
    64-bit
  • Boolean modifier

    Unites, subtracts or intersects the mesh with another object and returns the result as a new mesh.

    • ModelCraft
    32-bit step, flagged
    2 calculations
    32-bit in part Open item
  • Boring logs and the soil profile between borings

    Cleans boring logs, corrects blow counts, places borings along a section line and joins their layers into a soil profile.

    • CivilCraft
    64-bit, direct
    6 calculations
    64-bit
  • Box tree for picking and collisions

    Finds which items have a box that a point range or a ray touches, for picking, snapping and collision checks.

    • CadCraft
    • ModelCraft
    • PartCraft
    64-bit, direct
    2 calculations
    64-bit
  • Buckling load factors and thermal stress setup

    Finds the lowest load factors at which a part buckles and their shapes, and sets up thermal loads for a stress study on the voxel model.

    • PartCraft
    64-bit, stated limit
    7 calculations
    64-bit
  • Building data for flood, wind and earthquake checks

    Takes room floor heights, opening sills, storey heights, areas, widths and masses from the model for the hazard checks.

    • BimCraft
    64-bit, direct
    3 calculations
    64-bit
  • Building mass areas, levels and base earthwork

    Works out a building mass's footprint area, gross floor area, height, floor levels, the ground under it and the cut and fill to set it on the slope.

    • CivilCraft
    64-bit, stated limit
    9 calculations
    64-bit
  • Building mass mesh for the 3D view

    Builds the walls and roof of a building mass as a triangle mesh for drawing.

    • CivilCraft
    Display only
    1 calculation
    32-bit, display only
  • Building masses as IFC

    Writes building masses as an IFC4 file: footprints, storey levels, heights and areas.

    • CivilCraft
    64-bit, stated limit
    6 calculations
    64-bit
  • Burn levels of an engraved picture

    Resamples a gray picture to the engraving grid and turns each cell into a burn level.

    • CadCraft
    • PartCraft
    32-bit step, flagged
    2 calculations
    32-bit in part Open item
  • Cabinet job cost estimate

    Prices a cabinet job from its sheets, edge banding, frame stock, hardware, countertops, labor and machine time, with markup and tax.

    • CadCraft
    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, stated limit
    10 calculations
    64-bit Open item
  • Cabinet job edits that change sizes

    Works out the sizes an edit puts into a cabinet job: the job in the other unit, a filler for a leftover, a gap at a door or window, and the notch of a new L or U room.

    • CadCraft
    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, stated limit
    4 calculations
    64-bit Open item
  • Cabinet job totals: linear stock and sheet count

    Adds up the hardwood to buy by length and counts the sheets a nested job uses.

    • CadCraft
    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, direct
    2 calculations
    64-bit
  • Cabinet material sizes, grooves and drill files

    Holds the thicknesses of the sheet materials and edge bands, derives the groove and sheet size from the picks, and writes the drill and G-code files.

    • CadCraft
    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, stated limit
    5 calculations in 2 files
    64-bit
  • Cabinet parts from a box and construction rules

    Turns a cabinet's width, height and depth and the shop's construction rules into the parts to cut: sides, bottom, top or rails, back, shelves, doors, drawer fronts and drawer boxes.

    • CadCraft
    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, direct
    6 calculations
    64-bit
  • Cabinet plan, elevation, section and 3D boxes

    Builds the drawing geometry of a cabinet job: each cabinet in plan, front view and section, the dimensioned shop drawings, and the boxes of the 3D view.

    • CadCraft
    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, direct
    13 calculations in 3 files
    64-bit Open item
  • Cabinet run layout and countertops

    Places every cabinet, filler and end panel along its wall or island, works out how runs meet at corners, and sizes the countertops.

    • CadCraft
    • BimCraft
    • ModelCraft
    • PartCraft
    64-bit, stated limit
    19 calculations in 2 files
    64-bit Open item

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

The standard

  • 64-bit everywhere

    Every calculation runs in 64-bit floating point (IEEE 754 double precision), from the number you type to the number you read.

  • 15 digits, always

    A 64-bit number keeps any 15-digit value intact and takes 17 digits to write out in full. Our rule for every calculation: carry all 17 between steps, and order the arithmetic so that avoidable rounding never costs one of the first 15.

  • 32-bit gets a warning

    A 32-bit number keeps about 7 digits. Where a 32-bit step can reach a number you read, the calculation is flagged in the lists below, and the app will warn that the result can have less mathematical precision.

This device

The apps calculate in 64-bit on every device. Work handed to the graphics processor is the exception: browsers expose graphics processors as 32-bit calculators, which can provide less mathematical precision.

A browser reports a rounded or capped view of the machine, never a full inventory: it gives the number of processor threads (not the model), memory rounded down and capped at 8 GB (Chromium only), and one graphics adapter even when a machine has several. What the browser reports about graphics is a capability, not a measurement of the card. The size of a graphics card's memory bus (a 192-bit bus, for example) says how fast data moves, not how precisely it calculates. Most graphics cards can calculate in 64-bit natively, slowly, but WebGL and WebGPU do not offer it to web pages.

Approaches

Every policy takes one of five approaches to keeping its precision.

Exact values 8 policies
Constants and factors are held as exact fractions from their definitions. The arithmetic is ordered so that no rounded factor is ever used.
Exact predicates 1 policy
Coordinates are 64-bit. The yes-or-no decisions that shape the geometry (which side of a line, inside or outside a circle) are computed exactly, so rounding cannot flip one.
64-bit, direct 337 policies
Every value is a 64-bit number from input to result. Formulas are closed form or a direct solve, and every comparison uses a stated tolerance.
64-bit, stated limit 428 policies
The arithmetic is 64-bit, but the method or the data sets the accuracy: a solver tolerance, a mesh, a step size, a datum shift, a table. The limit is stated where the result is shown.
Display only 49 policies
Computed to draw the screen, often in 32-bit on the graphics processor. No number a person reads, saves or exports comes from it.
32-bit step, flagged 118 policies
One step stores or exchanges 32-bit values that reach a number a person reads. It is listed here with its open item, and the step is either moved to 64-bit or the app will warn where the number is read.

Precision is not robustness

Mathematical precision is how many digits a number keeps. Geometric robustness is whether a shape stays valid: every intersection found, every solid closed, every face joined to its neighbors. They are different properties, and a CAD system can have the first without the second.

Every geometric algorithm rests on yes-or-no questions. Is this point left or right of that line? Do these two edges cross? Is this point inside that circle? Each answer is the sign of a small expression. When three points are almost in line, the true value of that expression can be smaller than the rounding error of the arithmetic that computes it, and the sign comes out wrong. That happens at 15 digits as readily as at 7.

One wrong sign is not a small error in the last digit. It is a different decision: an intersection that is missed, two triangles that overlap, a face that points the wrong way, a solid with a gap in it. Every coordinate can be correct to 15 digits while the shape they describe is invalid.

A point C almost on the line from A to B. Magnified, C is a tiny distance to one side of the line. A B C C left or right?
C lies a rounding error away from the line through A and B. Which side it is on decides how the geometry is built.

What makes geometry robust

  • Exact predicates

    The yes-or-no questions are answered exactly. The fast 64-bit answer is used when it is safely away from zero. When it is not, the sign is computed again with as many digits as it takes.

  • Decide once

    A decision about a shape is recorded as topology, and every later step agrees with it. The same question is never asked twice with a chance of two answers.

  • Stated tolerances

    Where a tolerance is used it is written down, scaled to the size of the geometry and applied the same way everywhere.

  • Local origins

    Coordinates far from zero are moved to a local origin before the work, so the digits are spent on the geometry and not on the distance to the origin.

  • Valid by construction

    Algorithms whose result is guaranteed to be a closed solid, whatever the input, in place of ones that repair the result afterwards.

  • More than the language

    These choices matter more than the programming language. JavaScript, C++ and Rust all compute with the same 64-bit numbers: the same algorithm is as robust, or as fragile, in each.

Where our apps stand

The list on this page records both properties. Surface triangulation in CivilCraft and BimCraft uses exact predicates. Solid modeling in PartCraft runs on a kernel whose result is a closed solid by construction. The intersections in the CadCraft app use stated tolerances today, and exact tests for the near-parallel and near-tangent cases are an open item. Each policy says which approach it takes.