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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glTF import: reading numbers
Reads the positions, normals, weights, matrices and other numbers a glTF file stores, and each node's transform.
- ModelCraft
- 4 calculations
64-bit -
Grade rule library
Keeps named grade rules (how far a pattern point moves for each size), converts them between millimeters and inches, and reads and writes them as RUL files.
- CadCraft
- 4 calculations
64-bit Open item -
Grading a pattern across sizes
Moves the points of a pattern piece by its grade rules to draw the piece in each size (Apparel add-on).
- CadCraft
- 8 calculations
64-bit Open item -
Gravity pipe network: slopes, cover and automatic inverts
Works out each pipe's length, slope and least cover, each structure's rim and sump, and sets inverts that keep the minimum slope, cover and drop.
- CivilCraft
- 3 calculations
64-bit -
Ground modifiers: cut and fill, overlaps, level labels and junction checks
Reports the cut and fill each landscape object makes in the ground, where two of them overlap, the levels and gradients read off the surface, and where walls, steps and planted areas do not meet the levels beside them.
- CivilCraft
- 8 calculations in 2 files
64-bit -
Ground points from an unclassified point cloud
Finds which points of a drone or scanner cloud are ground, so a surface can be built from them.
- CivilCraft
- 5 calculations
64-bit -
Ground surface from contour lines and points
Checks contour lines, gives them elevations, and builds a ground surface from them, filling in the flat triangles that contours leave on ridges, valleys and hilltops.
- CivilCraft
- 8 calculations
64-bit -
Ground-mounted solar arrays on terrain
Places solar tables on the ground inside a region, spaces each row so the row in front does not shade it at the winter sun, and reports table positions, pile heights, ground slope, row pitch and installed power.
- CivilCraft
- 7 calculations
64-bit Open item -
Hardscape: paving, paths, walls, ramps and steps
Sets out paving, paths, walls, curbs, ramps and steps on the ground, checks grades, risers and goings, and totals their quantities.
- CivilCraft
- 9 calculations
64-bit Open item -
Hatch boundaries and pattern lines
Finds the closed area round a picked point to hatch, with its islands, and lays the pattern's lines inside it.
- CadCraft
- 9 calculations
64-bit Open item -
Hazardous area extents and zone geometry
Works out how far a flammable zone extends from a release source, the zone shapes in plan, section and 3D, and the files that carry them to a site plan.
- CadCraft
- BimCraft
- 10 calculations in 2 files
64-bit Open item -
Heat conduction, steady and transient
Solves the temperature field of a part with fixed temperatures, heat flux, power, convection and radiation, and reports temperatures, heat flux and the heat balance.
- PartCraft
- 20 calculations
64-bit -
Heat exchanger rating
Works out the duty, outlet temperatures, film coefficients, required area, pressure drops and tube count of a shell-and-tube, plate or air-cooled exchanger, and screens tubes for vibration.
- CadCraft
- BimCraft
- 18 calculations in 2 files
64-bit Open item -
Heating and cooling loads per room
Works out what bounds each room, the U-value of each bounding element, and from them the design heating load, a degree-day year and a cooling peak.
- BimCraft
- 11 calculations
64-bit -
Hull lines: fairness measures and fairing
Measures how fair a hull curve is (inflections, curvature jumps, roughness) and rebuilds it with fewer control points within a tolerance.
- PartCraft
- 5 calculations
64-bit -
Hull surfaces to a closed solid and its volume
Joins NURBS patches into one closed triangle mesh, mirrors and caps it, and works out its volume.
- PartCraft
- 5 calculations
64-bit -
IFC 4.3 infrastructure quantities and files
Reads the quantities, stations and alignment lengths of roads, railways, bridges and other infrastructure from an IFC file, totals them per class, and writes a new IFC 4.3 file.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 9 calculations
64-bit Open item -
IFC alignment curves and stations
Reads the alignment curves of an IFC 4.3 file as sampled 3D polylines, finds the point at a station, places elements along them and builds solids swept between cross sections.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 7 calculations
64-bit Open item -
IFC curves and profiles as point lists
Turns the curves and cross-section profiles of an IFC file into polylines: arcs, circles, ellipses, trimmed curves, B-splines, offsets, and the standard steel shapes with their fillets.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 10 calculations in 2 files
64-bit Open item -
IFC export
Writes the steel parts, holes, copes, mitre cuts, bolts, footings, bars and grids of the model as an IFC4 file.
- DetailCraft
- 10 calculations
64-bit Open item -
IFC export: geometry and quantities gathered from the project
Turns the project's alignments, corridors, pads, walls, track, pipes and parcels into the meshes, lengths, areas and volumes that the IFC export writes.
- CivilCraft
- 15 calculations
64-bit Open item -
IFC export: numbers written to the file
Writes the whole project as an IFC file: coordinates, alignment parameters, lengths, areas, volumes and unit factors as text.
- CivilCraft
- 25 calculations
64-bit Open item -
IFC faces on curved surfaces
Tessellates faces that lie on cylinders, cones, spheres, tori, swept surfaces and B-spline surfaces into triangles.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 11 calculations
64-bit -
IFC import
Turns the steel members, plates, holes, copes, bolts, grids and levels of an IFC file into a DetailCraft model.
- DetailCraft
- 14 calculations
64-bit Open item -
IFC import: alignments, surfaces and units
Reads alignments, terrain surfaces and reference geometry from an IFC file into project coordinates and units.
- CivilCraft
- 13 calculations
64-bit -
IFC swept solids, primitives and faceted shapes
Builds the meshes of extruded, revolved and swept solids, swept disks such as rebar and pipes, the basic primitives, and faceted boundary shapes.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 10 calculations in 2 files
64-bit -
Illuminance values written on the lighting plot
Places the fixtures of a plot in millimeters for the photometric engine and writes the computed lux at each grid point as text in the drawing.
- CadCraft
- 2 calculations
64-bit -
Illustrate: vector, matrix and rigid-fit math
Places points with 4 × 4 matrices, inverts them, and finds the rigid move that best maps one set of points onto another.
- PartCraft
- 8 calculations
64-bit -
Import of DXF and DWG drawings into the 3D model
The edges and faces made when a DXF or DWG drawing is brought into the 3D model as a site plan: unit scaling, block placement, and arcs, circles, ellipses and splines turned into straight segments.
- CadCraft
- ModelCraft
- 15 calculations
64-bit Open item -
Import of OBJ, glTF and Collada models
The vertex positions and placements read from an OBJ, glTF or Collada file, turned to the model's Z-up meters.
- CadCraft
- ModelCraft
- 8 calculations
64-bit -
Imported carbon factors, prices and climate data
Reads a person's own carbon-factor file, cost book or climate answer into the tables the carbon, cost and solar panes calculate from.
- BimCraft
- 5 calculations
64-bit Open item -
Inverse kinematics and constraints
Moves a bone or a placement so it reaches a target, looks at it, copies it, stays within limits, hangs from it or sits on a path.
- ModelCraft
- 11 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 -
Irrigation zones: flow, pressure and coverage
Adds up the flow of each irrigation zone, works out the pressure it needs at the valve and at the supply, the precipitation rate and run time, and checks head coverage.
- CivilCraft
- 20 calculations in 2 files
64-bit Open item -
Joist depth from a span table the person loads
Picks the smallest joist depth whose listed clear span reaches the span asked for, from a table the person loads.
- BimCraft
- 6 calculations
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 -
Landscape grading: platforms, swales, slope classes and ponding
Shapes the proposed ground from platforms, berms, swales and free grading areas, and reads the surface for slope classes and ponds.
- CivilCraft
- 6 calculations
64-bit Open item -
Landscape IFC export
Writes plants, beds, hedges, planted areas, hardscape and freeform objects to an IFC file in meters.
- CivilCraft
- 7 calculations
64-bit Open item -
Landscape sections and detail drawings
Cuts a section line through the ground, walls, paving, planted areas, steps and plants and lays the result out to scale on a sheet, and draws wall, paving and step details from their numbers.
- CivilCraft
- 11 calculations in 3 files
64-bit -
LandXML export and import
Writes points, surfaces, alignments, profiles, pipe networks and feature lines as LandXML, and reads them back.
- CivilCraft
- 16 calculations
64-bit Open item -
LAS and LAZ point coordinates
Reads a LiDAR file's header and turns each stored point into x, y, z in the file's coordinates.
- CadCraft
- BimCraft
- CivilCraft
- 4 calculations
64-bit -
Laser job paths, fill lines and run estimate
Turns the drawing's shapes into the paths a laser follows: arcs as chords, fill lines across closed shapes, the moves in machine coordinates, and the length and time of the job.
- CadCraft
- PartCraft
- 10 calculations in 2 files
64-bit Open item -
Layer of protection and SIL arithmetic
Works out the mitigated frequency of a hazard scenario, the risk reduction still needed, and the average probability of failure on demand of a safety function with its SIL band.
- CadCraft
- BimCraft
- 7 calculations
64-bit Open item -
Layout point files and as-built comparison
Writes points for a total station as a text file, reads such a file back, and compares as-built points with the design.
- CadCraft
- BimCraft
- 6 calculations
64-bit -
Lengths and areas taken from CAD objects
Turns the lines, arcs, circles, polylines, hatches, ellipses and splines of a DWG or DXF sheet into runs and outlines that can be measured.
- TakeoffCraft
- 6 calculations in 2 files
64-bit -
Library item geometry from blocks, meshes and tables
Builds a Library item's plan and 3D body in millimeters from a drawing block, a mesh file (glTF, OBJ, STL) or a table of sizes.
- CadCraft
- BimCraft
- 18 calculations
64-bit Open item -
Line sizing and pressure drop
Works out velocity, Reynolds number, friction factor and pressure drop of each line, picks pipe sizes, and fills the stream table that is drawn on the P&ID.
- CadCraft
- BimCraft
- 13 calculations in 3 files
64-bit -
Line study file (.DON) export and import
Writes an overhead line study as a .DON XML file in meters and decanewtons for another line program, and reads such a file back into a line.
- CivilCraft
- 7 calculations
64-bit -
Lineweights in a DWG file
Converts a lineweight between its value in hundredths of a millimeter and the index a DWG file stores.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- 2 calculations
Exact -
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
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.