Resources
Numerical accuracy
The calculations in our apps: the policy each one is under, the precision it runs at, and the code itself.
This device: processor, memory, graphics The standard Precision is not robustness
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.
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IFC units and placements
Reads the length and angle units of an IFC file and turns its placements, transformation operators, grid placements and map conversion into 4 × 4 matrices.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 13 calculations in 2 files
64-bit -
Inverse kinematics and joint trajectories
Joint angles that put a robot link at a target, and timed joint moves with their speeds, accelerations and peak torques.
Every app 64-bit, stated limit- 9 calculations in 2 files
64-bit -
KISS file: quantities, sizes and weights
Writes the bill of materials as a KISS file for fabrication software: quantities, sizes, lengths, weights and plate areas.
- DetailCraft
- 6 calculations
64-bit Open item -
Library 3D preview
The 3D view of an item on its Library page and on the configure page.
Every app Display only- 3 calculations in 2 files
32-bit, display only -
Library configurator sizes
The size and connection positions shown for the chosen variant on a Library item's configure page.
Every app 64-bit, direct- 2 calculations
64-bit -
Load flow and short-circuit currents
Bus voltages, branch flows and losses of an AC network, and fault currents by symmetrical components.
Every app 64-bit, stated limit- 12 calculations in 3 files
64-bit Open item -
Load reserve and escape route checks
Finds the load factor at which a design first reaches its limit, and the narrowest door on the best way out of every room.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 3 calculations
64-bit Open item -
Lumped system models
Operating point and response over time of electrical, thermal, hydraulic and mechanical networks built from lumped elements.
Every app 64-bit, stated limit- 12 calculations in 3 files
64-bit Open item -
Magnetic and electric field solvers
The field of wire segments, the mutual inductance of loops, and 2D finite-element magnetic and electric fields with energy, capacitance and force.
Every app 64-bit, stated limit- 12 calculations in 2 files
64-bit Open item -
Member axes and section properties
Works out each frame member's length and local axes, and the area, second moments and torsion constant of a section from its outline.
- CadCraft
- BimCraft
- DetailCraft
- 6 calculations
64-bit Open item -
Member frames and local coordinates
Turns a member's start point, end point and rotation into its own axes, and moves points between the model and a member's own coordinates.
- DetailCraft
- 5 calculations
64-bit -
Meshing a slab or wall into plates
Cuts a slab or wall outline into four-node plates and places their nodes in the frame model.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations in 2 files
64-bit -
Model points written to USD
Writes the vertices and edges of a model into USD meshes and curves.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 2 calculations
32-bit in part Open item -
Move, rotate and mirror
Moves, rotates and mirrors selected members, footings and stairs, and keeps each section facing the right way.
- DetailCraft
- 10 calculations
64-bit -
Number text in USD files
Writes numbers into .usda text and decides which attribute types are 32-bit and which are 64-bit.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 3 calculations in 2 files
32-bit in part Open item -
Numbers in a DWG file, read and written bit for bit
Reads and writes the number codes of a DWG file: full and compressed 64-bit values, whole numbers of several sizes and object handles.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 16 calculations in 2 files
64-bit -
Numbers in the frame analysis report
The values printed in the analysis and design report tables, which are also what the CSV and PDF downloads contain.
- CadCraft
- BimCraft
- DetailCraft
- 10 calculations in 5 files
64-bit Open item -
Numbers sent between people editing together
How a number in an edit is written into a Studio Live message and read back on the other side.
Every app 64-bit, direct- 5 calculations
64-bit -
Numbers typed into the property grid
Turns what a person types or drags in a Properties row into the number handed to the app.
Every app 64-bit, direct- 3 calculations
64-bit -
Parametric PCB footprints
Pad positions, pad sizes and the courtyard of standard-style footprints, worked out from pitch, row spacing and pin count.
Every app 64-bit, stated limit- 7 calculations
64-bit -
Pass or fail against a regulation limit
Decides whether a found value meets the minimum, maximum or range of a regulation rule.
- CadCraft
- BimCraft
- CivilCraft
- DetailCraft
- 1 calculation
64-bit -
People flow and evacuation time
How fast people pass doors, corridors and stairs, which way each room empties, and how long it takes everyone to reach an exit.
Every app 64-bit, stated limit- 6 calculations
64-bit -
Pipe, duct and gas networks
Heads, pressures, flows and velocities in a steady network of pipes, pumps and fittings.
Every app 64-bit, stated limit- 9 calculations in 2 files
64-bit Open item -
Piping in an IFC file as PCF components
Reads pipe segments, fittings and valves from an IFC file and gives their end points, bores, bend angles and center points in millimeters.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 4 calculations
64-bit -
Planar linkages (closed loops)
The pose of four-bars, slider-cranks and other planar linkages, their sweep, velocity ratios, mobility and Grashof class.
Every app 64-bit, stated limit- 9 calculations
64-bit Open item -
Plate element for slabs and walls
The stiffness of one four-node plate of a slab or wall, and the membrane forces, bending moments and shears inside it.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations
64-bit -
Polygon triangulation (ear clipping)
Splits a flat polygon with holes into triangles, for caps of extruded sections and faces with holes.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 9 calculations
64-bit -
Polygon triangulation by ear clipping
Splits a flat polygon with holes into triangles for IFC shapes.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 5 calculations
64-bit -
Protection curves and grading
Relay and fuse operating times, grading margins between devices, and the cable damage time.
Every app 64-bit, stated limit- 6 calculations
64-bit Open item -
Rebar congestion map of a footing
Shows how tight the openings between reinforcing bars are for concrete to pass, and reports the tightest place.
- DetailCraft
- 6 calculations
32-bit in part Open item -
Reference picture size and position
Places a copied area of a sheet in the model at its true size.
- DetailCraft
- 4 calculations
64-bit -
Regulation limits in force and how values are written
Gives an app's tools the tightest limit of a rule across the ticked regulation packs, and writes required and found values in problems and on the code summary sheet.
- CadCraft
- BimCraft
- CivilCraft
- DetailCraft
- 4 calculations in 2 files
64-bit Open item -
Reinforcing bars and the bending schedule
Places the bars in a pad footing and works out their bends, cut lengths, counts and weights for the bending schedule.
- DetailCraft
- 13 calculations
64-bit Open item -
Rigid-body dynamics of a mechanism
Joint torques for a given motion, the mass matrix, joint accelerations for given torques, energy, and a simulated motion over time.
Every app 64-bit, stated limit- 6 calculations
64-bit -
Rotations, transforms and small linear algebra (motion)
Rotation matrices, roll-pitch-yaw angles, rotation vectors, rigid transforms and the dense solve used by the robot and linkage calculations.
Every app 64-bit, direct- 7 calculations
64-bit Open item -
Schedule risk (Monte Carlo)
The finish at P10, P50, P80 and P90, how often each task is critical, and which durations drive the finish.
Every app 64-bit, stated limit- 3 calculations
64-bit -
Seismic loads and story drift to ASCE 7-22
The seismic base shear and story forces by the equivalent lateral force procedure, the building's period, the weight of each floor and the drift check.
- CadCraft
- BimCraft
- DetailCraft
- 11 calculations in 2 files
64-bit -
Settlement, flexible mats, pile groups and retaining walls
Estimates elastic settlement, analyzes a footing as a plate on springs, shares a load over a pile group and checks a cantilever retaining wall.
- DetailCraft
- 11 calculations
64-bit -
Single-part shop drawing
Draws one part with its holes, copes and section, and prints its dimensions, cut angles and weight.
- DetailCraft
- 5 calculations
64-bit -
Size of a copied area
Works out how big a copied area of a sheet is on paper and in the real world, the pixel size it is rendered at, and the scale and turn that fit it to two picked points.
- CadCraft
- BimCraft
- MarkupCraft
- DetailCraft
- 5 calculations
64-bit -
Spending on a person's own AI model
Adds up what calls to a person's own AI model have cost today and this month, and stops a call that could pass the limits the person set.
Every app 64-bit, stated limit- 4 calculations
64-bit -
Spread between coarse and refined results
States how far a coarse live result is from the refined one, as a fraction.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 1 calculation
64-bit -
Steel member checks on a solved frame
Runs the steel code checks along every member for every strength combination, finds the governing ratio, checks the deflection limit, and finds what gives way first.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations in 2 files
64-bit -
Steel member resistance to EN 1993-1-1
The design resistances of a rolled I or H section: classification, tension, bending, shear, buckling, lateral-torsional buckling and the combined checks.
- CadCraft
- BimCraft
- DetailCraft
- 11 calculations
64-bit Open item -
Steel member strength to AISC 360-16
The design strengths of a rolled I-shape in tension, compression, bending and shear, and the combined bending and axial check.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations
64-bit Open item -
Steel profiles: area, mass per meter and sizes
Looks up a steel section or builds a plate or custom profile, and gives its outline, area, mass per meter, width, depth and perimeter.
- DetailCraft
- 5 calculations
64-bit -
Steel section dimensions, areas and outlines
Gives the dimensions, published area and mass of every steel section in millimeters, the exact area from the dimensions, and the outline used to draw and sweep it.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 6 calculations
64-bit Open item -
Straight stair geometry
Works out the risers, treads, pitch and the stringer and tread parts of a straight steel stair from its rise, going and width.
- DetailCraft
- 4 calculations
64-bit -
Supplier stock and lead-time check
Reads a supplier's stock list and checks each quantity the model needs against it: how much is short, and how long the wait is.
- TakeoffCraft
- DetailCraft
- 12 calculations in 2 files
64-bit -
The model file and what it stores
Keeps members, grids, levels and loose bolts, and reads and writes the model file.
- DetailCraft
- 6 calculations
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
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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.
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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.
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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
What this browser can see of your machine. It is shown here only and sent nowhere; the desktop app reads the full hardware, a web page cannot.
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.
- Processor
- Memory
- Numbers in the apps
- Graphics processor (WebGL)
- WebGPU
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.
What makes geometry robust
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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.
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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.
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Stated tolerances
Where a tolerance is used it is written down, scaled to the size of the geometry and applied the same way everywhere.
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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.
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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.
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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.