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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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 -
Outline checks: inside, crossing, cut-outs
Decides whether a point is inside an outline, whether an outline crosses itself, and whether a cut-out sits fully inside its area and clear of the other cut-outs.
- TakeoffCraft
- 6 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 -
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 -
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 -
Priced estimate
Each row's quantity with waste, its material and labor amounts, crew hours, and the totals of the estimate, of each bid area and of each alternate.
- TakeoffCraft
- 5 calculations
64-bit Open item -
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 -
Quantities sent in a bid package
Sends each scope line's quantity and unit to the bidding service.
- TakeoffCraft
- 2 calculations
64-bit Open item -
Rates exported as a price table
Writes each priced item's material and labor rates as a price table another app can read.
- TakeoffCraft
- 2 calculations
64-bit Open item -
Rates, percentages and extended amounts
Reads a typed unit rate and percentage, and works out quantity × rate to the cent.
- TakeoffCraft
- 6 calculations in 2 files
64-bit -
Revision overlay: lining up two sheets and moving the takeoff
Fits the move, turn and scale that lays an old sheet over its revision from two pairs of picked points, and carries the marks and the scale across.
- TakeoffCraft
- 7 calculations in 3 files
64-bit -
Revision overlay: what changed under a mark
Compares the pictures of an old sheet and its revision and flags the marks whose drawing changed.
- TakeoffCraft
- 4 calculations in 2 files
64-bit -
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 -
Roof pitch and slope factors
Reads a roof pitch and turns plan lengths and areas into lengths and areas along the slope.
- TakeoffCraft
- 4 calculations
64-bit -
Room outline by flood fill
Finds the room around a clicked point on a picture of the sheet and returns its outline as an area mark.
- TakeoffCraft
- 4 calculations in 2 files
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 -
Rounding for display and for money
Rounds a number to a fixed count of decimals, and writes a length in feet and inches to the nearest fraction of an inch.
- TakeoffCraft
- 4 calculations
64-bit -
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 -
Sheet scale read from the sheet's text
Finds scale notations in a PDF sheet's text and picks the listed scale to offer for the sheet.
- TakeoffCraft
- 3 calculations
64-bit -
Sheet scale: presets, calibration and drawing units
Sets how many real feet one unit on the sheet stands for: from a named scale, from two picked points and a typed distance, or from a DWG or DXF drawing's own units and viewport.
- TakeoffCraft
- 10 calculations in 4 files
64-bit Open item -
Snapping to and measuring the sheet's own linework
Reads the vector lines of a PDF page or a CAD sheet, snaps picked points to them, and measures a whole connected path or closed loop from one click.
- TakeoffCraft
- 11 calculations in 4 files
64-bit Open item -
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 -
Spline through fit points
Works out the control points and knots of a cubic spline that a drawing stores only by its fit points and end tangents.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- 5 calculations
64-bit Open item -
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 -
Takeoff lengths and areas
Lengths, perimeters and areas of measured runs and outlines, with arcs and cut-outs.
- TakeoffCraft
- 6 calculations
64-bit -
Takeoff quantities from marks
The length, area, perimeter and count each mark measures at its sheet's scale, and the totals per item and per sheet that a takeoff reports.
- TakeoffCraft
- 6 calculations
64-bit -
Triangle mesh built from IFC geometry
Holds every shape read from an IFC file as triangles, moves and joins them, and hands the result to the app.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 5 calculations
32-bit in part Open item -
Triangulation of faces with holes
Splits a flat face, with any holes, into triangles.
- CadCraft
- ModelCraft
- TakeoffCraft
- 9 calculations
64-bit -
Typed distances and coordinates while drawing
Places the next point of a run or outline from a typed distance, a distance and angle, or a pair of coordinates, and reads a typed spot elevation.
- TakeoffCraft
- 5 calculations in 2 files
64-bit -
Typed lengths and item units
Reads a typed length (feet-inches with fractions, decimal feet, inches, meters, centimeters, millimeters) into feet, and converts feet and square feet into an item's unit.
- TakeoffCraft
- 7 calculations
64-bit -
Unit conversion
Converts lengths, areas, volumes, angles and slopes between 57 units.
Every app Exact values- 4 calculations
64-bit -
Unit table: reading and writing values
Holds every unit's size as an exact fraction, reads typed values such as 12'6 1/2", 45°30'15" or 3:1, and writes values as feet and inches, degrees-minutes-seconds or decimals.
Every app Exact values- 8 calculations
64-bit -
USD mesh coordinates in saved and exported files
Writes the points of every mesh into a USD file and reads them back when a USD file is opened.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 7 calculations in 3 files
32-bit in part Open item -
USD transforms and placement
Works out where every object of a USD scene sits: each object's own transform, its place in the world, the change to meters with Z up, and the placement of instanced copies.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 11 calculations in 3 files
64-bit Open item -
Weibull life data
Weibull shape and scale fitted to failure times, with confidence bounds, mean life and B10 life.
Every app 64-bit, stated limit- 6 calculations
64-bit Open item -
Wire antenna (method of moments)
Input impedance, segment currents, radiation pattern and directivity of thin-wire antennas.
Every app 64-bit, stated limit- 8 calculations
64-bit
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.