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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Solar array shading
Works out, for each hour of each month's representative day, the share of a solar array's sample points that the model shades from the direct sun, and the share of the beam light lost.
- BimCraft
- CivilCraft
- 4 calculations
64-bit -
Solar array site and saved summary
The latitude and longitude kept for a ground PV array and the numbers the file keeps for its plan.
- CivilCraft
- 2 calculations
64-bit -
Solar string sizing
Works out how many modules go in a string and how many strings on an inverter from the module and inverter ratings and the temperatures given.
- BimCraft
- CivilCraft
- 6 calculations
64-bit Open item -
Solar yield estimate
Estimates the DC and AC energy a solar array gives in a year, month by month, with shading, temperature, losses and inverter clipping, and its performance ratio.
- BimCraft
- CivilCraft
- 8 calculations
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 -
Staking reports
Lists stakes along an alignment at stations and offsets, or survey points measured against it, each with its coordinates, design and ground elevations and cut or fill.
- CivilCraft
- 5 calculations
64-bit -
Storm drainage: rational method, pipe sizing and grade lines
Works out the runoff reaching each pipe, the pipe size that carries it, and the hydraulic and energy grade lines through the network.
- CivilCraft
- 9 calculations
64-bit Open item -
Storm hydrographs routed through the pipe network
Carries each catchment's runoff over time down the pipes and reports the peak flow, its time and the attenuation at every pipe and structure.
- CivilCraft
- 6 calculations
64-bit Open item -
Sun position
Works out where the sun is for a date, time and place: azimuth, altitude with refraction, declination and the equation of time.
- CivilCraft
- 3 calculations
64-bit -
Sun position and light on a tilted plane for solar
Gives the sun's direction for each solar hour and the direct, sky and ground-reflected light falling on a module plane, from a clear-sky model or typed monthly totals.
- BimCraft
- CivilCraft
- 8 calculations
64-bit -
Sun position for shadows
The sun's altitude and azimuth for a date, clock time, latitude, longitude and time zone, and the direction shadows are cast from.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- 5 calculations
64-bit -
Superelevation: runoff, runout and lane slopes
Works out where the lanes of a road rotate into and out of each curve and the cross slope of each lane at any station.
- CivilCraft
- 5 calculations
64-bit -
Surface exported as a GeoTIFF elevation grid
Samples a surface on a regular grid and writes it as a GeoTIFF with one elevation band.
- CivilCraft
- 4 calculations
32-bit in part Open item -
Surface triangulation
Builds a triangulated surface from survey points and breaklines, then its elevations, contours and slopes.
- BimCraft
- CivilCraft
- 6 calculations
64-bit -
Survey levels from text and the survey check
Reads spot levels written as text or block attributes into points with a height, and checks a surveyor's drawing for unit, origin, flat-contour, outlier and duplicate problems.
- CadCraft
- BimCraft
- CivilCraft
- 6 calculations
64-bit -
Survey network adjustment
Adjusts a survey network or a leveling run by least squares, closes a traverse by the compass rule, and reports residuals, the variance factor and error ellipses.
- CivilCraft
- 10 calculations
64-bit Open item -
Survey point files: reading and writing
Reads survey points from CSV or text files, counts them by description group, and writes them back as a PNEZD file.
- CivilCraft
- 3 calculations
64-bit -
Terrain import and GeoTIFF export settings
Works out the point spacing, the point count and the elevation scaling when an elevation grid or a LiDAR file is brought into a project, and the cell size offered when a surface is written as a GeoTIFF.
- CivilCraft
- 6 calculations
64-bit -
Thinning point clouds to a spacing
Keeps one point per grid cell when a large point cloud is imported, and estimates how many points an import will keep.
- CivilCraft
- 4 calculations
64-bit -
TIFF scan resolution
Reads the resolution of a scanned drawing from a TIFF file as dots per inch.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- PartCraft
- 2 calculations
64-bit -
Tracing a scan into lines and arcs
Turns the black-and-white pixels of a scanned drawing into lines and arcs, cleans them up, and offers their ends, middles, centers and crossings as snap points.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- PartCraft
- 10 calculations in 2 files
64-bit Open item -
Transition curves and sampled alignment geometry
Evaluates the six kinds of transition curve (clothoid, cubic parabola, Bloss, Helmert, sine half-wave, sine), finds the nearest point on one, and cuts curves into straight pieces for linework.
- CivilCraft
- 12 calculations
64-bit -
Traverse closure and compass adjustment
Runs a survey traverse from field angles or bearings and distances, reports its angular and linear misclosure and precision, and adjusts the stations by the compass rule.
- CivilCraft
- 4 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 -
Typed lengths, stations and unit text
Reads lengths and stations as typed, and writes stations, areas, volumes and bearings as text.
- CivilCraft
- 8 calculations
64-bit Open item -
Underground cable routes: cover, crossings, joints and trench quantities
Works out a cable route's length, its cover under the surface, its vertical separation from pipes and other routes it crosses, the joints it needs and the trench quantities.
- CivilCraft
- 10 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 -
Unsteady flow routing down a river
Routes a flood hydrograph down the cross-sections of a river model and reports water levels, flows, their peaks and a volume balance over time.
- CivilCraft
- 6 calculations
64-bit Open item -
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 -
Values changed when a DWG is written
The few places where the DWG writer changes a number on its way into the file: lineweights, ellipse axes, ray directions, the drawing extents and the defaults of a light.
- CadCraft
- ModelCraft
- CivilCraft
- DetailCraft
- PartCraft
- 5 calculations in 2 files
64-bit Open item -
Values typed or picked in the main window
Takes what is typed in a property box or picked in the plan and profile views and stores it in the model: lengths, coordinates, profile points, pad elevations and default curve radii.
- CivilCraft
- 8 calculations
64-bit Open item -
Vehicle swept paths
Drives a vehicle with up to three trailers along a path, forward or reversing, and reports its wheel paths, steering and articulation angles and the area its bodies sweep.
- CivilCraft
- 8 calculations
64-bit -
Vertical profile: grades and parabolic curves
Works out the design elevation and grade at any station from the PVIs and their vertical curves, and samples the existing ground along the alignment.
- CivilCraft
- 4 calculations
64-bit -
Water mains as objects: depths, fittings and take-off
Places each water main at the ground less the cover, derives the bends, tees, reducers and caps the layout implies, and lists pipe lengths and fitting counts.
- CivilCraft
- 5 calculations in 2 files
64-bit Open item -
Water mains network: heads, flows and pressures
Solves a looped water network for the head and pressure at every node and the flow, velocity and head loss in every pipe, then runs fire-flow and extended-period cases on it.
- CivilCraft
- 12 calculations
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 -
Why a curve does not fit, and the radius or length that would
When an alignment's curves or a profile's vertical curves overlap, works out by how much and offers the largest radius or curve length that fits.
- CivilCraft
- 5 calculations
64-bit -
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 -
Worksheets: formulas, column rounding and totals
Works out each worksheet cell from an object's fields with a small formula language, rounds it to the column's decimals, and adds sums, counts, averages and extremes.
- CivilCraft
- 5 calculations
64-bit Open item -
Zoning envelope and limit checks
Works out the buildable area of a lot from its setbacks, the height a sky-exposure plane allows, and the coverage and floor area ratio of the masses on the lot against the limits the person typed.
- CivilCraft
- 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.