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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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 -
Length tags and tag schedules
Keeps a length tag on an element as an IFC property and lists tag values in schedules, in millimeters.
- BimCraft
- 3 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 -
Lengths and units for Library items
Reads lengths written as text (30", 2'-6 1/2", 762 mm) into millimeters and writes sizes back as short labels.
- CadCraft
- BimCraft
- 5 calculations
64-bit Open item -
Lengths as text: formats and typed lengths
Writes lengths and areas in the drawing's format (decimal, engineering, architectural, fractional, scientific) and reads lengths typed at the command line.
- CadCraft
- 9 calculations
64-bit Open item -
Lengths, areas and volumes as text
Turns a length in millimeters, an area or a volume into text in the display unit a person picked.
- BimCraft
- 9 calculations
64-bit -
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 -
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 -
Library item placed as a block
Turns a Library item's plan into a block in the drawing's units and counts the Library items a drawing uses.
- CadCraft
- 4 calculations
64-bit Open item -
Library items from IFC types
Turns an IFC type or element into a library item: its body mesh, its width, depth and height, its plan outline and its sizes from properties, in millimeters.
- BimCraft
- 4 calculations
32-bit in part Open item -
Line and arc primitives
Breaks every drawing object into straight segments and arcs and works out points, parameters, lengths, bounds, tangent points and snap points on them.
- CadCraft
- 12 calculations
64-bit -
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 -
Line, arc and circle intersections
Where two drawn objects cross: the basis of snaps, trim and extend.
- CadCraft
- 4 calculations
64-bit Open item -
Linetype dashes
Cuts lines and arcs into the dashes, gaps and dots of their linetype for the screen and for plots.
- CadCraft
- 2 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 -
Linework checks for linked landscape objects
Checks a line or outline taken from other linework before a landscape object uses it, and detects when that source has moved.
- CivilCraft
- 3 calculations
64-bit -
LISP arithmetic, conversions and geometry
The numbers a LISP routine gets from the built-in arithmetic, number and angle formatting, unit conversion and point geometry functions.
- CadCraft
- 12 calculations
64-bit Open item -
Live feed values and times
Reads a value and a time from a message or poll answer of a live sensor feed.
- BimCraft
- 1 calculation
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 -
Luminaire files and point-by-point illuminance
Reads luminaire photometry files (IES LM-63 and EULUMDAT) and works out the direct illuminance on a grid of points, with its minimum, average, maximum, uniformity and power density.
- CadCraft
- BimCraft
- 17 calculations in 2 files
64-bit -
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 -
Machining picks and readouts
Decides which faces and edges a machining operation accepts, matches stored picks to the part, and formats the numbers shown in the Manufacture panel.
- PartCraft
- 3 calculations
64-bit -
Magnet study: 2D field, force and torque
Solves the magnetic field of a sketch's profiles (air, iron, magnets, coils) and reports the peak flux density and the force and torque on chosen bodies.
- PartCraft
- 18 calculations in 3 files
64-bit -
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 -
Magnetics add-on: field readout, flux lines and exports
Works out each body's area and mean and peak flux density, compares the result with a hand formula, traces flux lines and writes CSV and VTK files.
- PartCraft
- 9 calculations
32-bit in part Open item -
Magnetics add-on: readouts in the panel
Formats the flux density, forces and flux per line that the magnet study shows, and states the size of the air box.
- PartCraft
- 2 calculations
64-bit -
Magnetics add-on: template shapes and hand formulas
Builds ready-made magnet study cross-sections and the textbook value each result is compared with.
- PartCraft
- 7 calculations
64-bit -
Magnetics add-on: the result drawn as display bodies
Draws a magnet study's field bands, flux lines, bodies and force arrows in the part's view.
- PartCraft
- 3 calculations
32-bit, display only -
Manual annotations: measured lengths, angles and radii
Works out the value a measurement annotation shows in a manual: a distance, an angle or a radius through three points.
- PartCraft
- 3 calculations
64-bit -
Manual parts list: quantities and mass
Builds the parts list of an illustrated manual: the quantity, volume and mass of each part, and the CSV export.
- PartCraft
- 3 calculations
64-bit -
Manual roof planes
Works out the height of a hand-drawn roof plane at any point, its sloped slab, and its sloped and projected areas.
- BimCraft
- 4 calculations
64-bit Open item -
Manual scene in the 3D view
Draws the parts of an illustrated manual, their edges and the filled cut faces in the 3D view.
- PartCraft
- 2 calculations
32-bit, display only -
Manual: imported product meshes, copies and part volume
Reads a product from glTF, OBJ, STL or 3MF into a manual, scales it to millimeters, recognizes copies of one part and works out each part's volume and area.
- PartCraft
- 13 calculations in 2 files
32-bit in part Open item -
Manufacturing cost estimate
Estimates what a part costs to machine or print from its volume, bounding box, material price and shop rates.
- PartCraft
- 5 calculations
64-bit -
Map coordinate reprojection
Moves points, and a model's position on the map, between coordinate systems.
- BimCraft
- CivilCraft
- 3 calculations in 2 files
64-bit -
Map layers under the drawing
Draws map pictures and tiles under the drawing, warped from the map's coordinate system to the drawing's.
- CadCraft
- BimCraft
- 2 calculations
32-bit, display only -
Map layers: web Mercator, tile grids and world files
Converts longitude and latitude to web Mercator and back, lays out the tiles of a map service, reads a picture's world file, and writes the box of a map request.
- CadCraft
- BimCraft
- CivilCraft
- 10 calculations
64-bit Open item -
Map pictures warped onto the plan
Picks the tile level for the screen and cuts a map picture into pieces that are each drawn with one affine transform.
- CadCraft
- BimCraft
- CivilCraft
- 3 calculations
32-bit, display only -
Markers: pieces laid on fabric
Keeps the pieces of a marker on the fabric, checks grain direction and overlaps, and works out the marker's length and fabric use (Apparel add-on).
- CadCraft
- 9 calculations
64-bit Open item -
Marks and sheets written to PDF
Draws the takeoff's marks into a copy of the PDF, with a legend of quantities, and writes a DWG or DXF sheet as a vector PDF page.
- TakeoffCraft
- 4 calculations in 3 files
64-bit -
Markup geometry while drawing and editing
Works out the points and boxes that are stored when a markup is drawn, snapped, typed to scale, resized, moved, simplified or lined up.
- MarkupCraft
- 12 calculations in 4 files
64-bit -
Markup outlines and measurement labels
Builds what each markup draws, on screen and in the saved PDF: its outline as lines and Bézier curves, and the label text of a length, area, angle or count.
- MarkupCraft
- 9 calculations
64-bit -
Mass-haul diagram
Works out the mass ordinate at each section, the balance points, the volume moved in each balanced stretch and its average haul distance.
- CivilCraft
- 5 calculations
64-bit -
Massing options from a room program
Adds up a room program, finds building shapes that hold it inside a buildable envelope, and reports each option's footprint, gross area, surplus and site coverage.
- BimCraft
- 7 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.