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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Export of the 3D model to DXF and DWG
The coordinates, block placements and rotation angles written when the 3D model is exported to DXF R12 or handed to the DWG writer.
- CadCraft
- ModelCraft
- 6 calculations
64-bit Open item -
Export to glTF and STL
The vertex coordinates and placement matrices written when a model is exported as a binary glTF (.glb) or a binary STL file.
- CadCraft
- ModelCraft
- 4 calculations
32-bit in part Open item -
Export to IFC
The points, directions, placements and level elevations written when a model is exported as an IFC4 file.
- CadCraft
- ModelCraft
- 6 calculations
64-bit Open item -
Export to OBJ and Collada
The coordinates, normals and placement matrices written when a model is exported as an OBJ or a Collada (.dae) text file.
- CadCraft
- ModelCraft
- 8 calculations
64-bit Open item -
Face planes, areas, triangles and solid volume
The plane and area of a drawn face, the triangles it is split into, and the surface area and volume of a closed shape.
- CadCraft
- ModelCraft
- 4 calculations
64-bit Open item -
Fault trees and reliability block diagrams
The probability of a top event, minimal cut sets, importance measures, system reliability and mean time to failure.
Every app 64-bit, stated limit- 10 calculations
64-bit Open item -
Fermentation (Monod kinetics)
Biomass, substrate, product and volume over time in a batch or fed-batch vessel.
- CadCraft
- BimCraft
- 1 calculation
64-bit -
Fillet and chamfer
Rounds or cuts the corner between two objects, between two segments of one polyline, or at every corner of a polyline.
- CadCraft
- 9 calculations
64-bit -
Fitting losses summed from a pack
Adds up the loss coefficients K of the fittings on a pipe link and turns K into a head loss.
- CadCraft
- BimCraft
- 2 calculations
64-bit -
Flat views of 3D solids
Projects the 3D model onto a view plane, splits its edges into visible and hidden parts, and places the result as 2D lines at a drawing scale.
- CadCraft
- 10 calculations
64-bit Open item -
Floats read from USD files
Reads numbers from .usda and .usdc files, in the type each value is stored as.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 5 calculations in 2 files
32-bit in part Open item -
Flow simulation (discrete events)
Queues, servers, conveyors, vehicles and resources simulated event by event: utilization, waiting times, throughput and their confidence ranges.
Every app 64-bit, stated limit- 15 calculations in 2 files
64-bit Open item -
Flowsheet solver and unit operations
Runs the units of a flowsheet in order, converges recycle loops and design specifications, and works out each unit's outlet streams, heat and work.
- CadCraft
- BimCraft
- 15 calculations in 2 files
64-bit -
Flowsheet variant metrics
Works out the heating, cooling and shaft power, the hourly operating cost and the hourly CO2 of one solved flowsheet variant, the numbers an optimization study ranks by.
- CadCraft
- BimCraft
- 1 calculation
64-bit -
Forces and deflection along a member
The axial force, shears, torque, bending moments and deflected shape along each member, and the largest values the report and the design checks read.
- CadCraft
- BimCraft
- DetailCraft
- 4 calculations
64-bit Open item -
Frame analysis with slabs, walls and rigid floors
Solves a frame that has plates and rigid floor diaphragms, and works out plate results at nodes and the drift of each story.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations
64-bit Open item -
Frame analysis: loads, releases, end forces and reactions
Turns loads into nodal forces, takes released ends out of each member, and works out member end forces, support reactions and the load and reaction totals of a solved frame.
- CadCraft
- BimCraft
- DetailCraft
- 13 calculations
64-bit -
G-code dry run and hole check
Reads a generated G-code file and reports its extent, cutting and rapid lengths, depths and cutting time, and checks that every drilled hole lies on its panel.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 10 calculations
64-bit Open item -
Gaussian plume concentration and contours
Works out the concentration downwind of a continuous release, how far a concentration level reaches, and the outline of that level on a site plan.
- CadCraft
- BimCraft
- 7 calculations
64-bit Open item -
GDSII layout read and placement
Reads an IC layout stream file and places every cell reference and array so the layout can be viewed and measured as drawing objects.
- CadCraft
- 3 calculations
64-bit -
GDSII layout: reals, flattening, areas and checks
Reading and writing chip layout streams, flattening cell hierarchies, layer areas and the basic width, spacing and area checks.
Every app 64-bit, stated limit- 12 calculations
64-bit Open item -
Gerber and drill file numbers
The coordinates and sizes written to Gerber layers, drill files and the job file, and read back from them.
Every app 64-bit, stated limit- 7 calculations
64-bit Open item -
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 -
Groups, placements and the model file
How coordinates are carried when geometry is grouped, placed, exploded or turned into a mesh, and which numbers the model file holds.
- CadCraft
- ModelCraft
- 10 calculations
64-bit -
Half floats in USD
Converts between 16-bit half floats and 32-bit floats for USD half types.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 2 calculations
32-bit in part 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 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 -
Heat-exchanger network design
Proposes the matches, heaters and coolers of a heat-exchanger network from stream data by the pinch design method, with the duty and end temperatures of each.
- CadCraft
- BimCraft
- 5 calculations
64-bit -
I/O channel counts with spare allowance
Counts the control system channels of each type on a P&ID and adds the spare allowance.
- CadCraft
- BimCraft
- 1 calculation
64-bit Open item -
IFC measures in SI for USD
Converts IFC lengths, areas and volumes to meters, square meters and cubic meters when properties are written to USD.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 1 calculation
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 -
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 -
Installation loads and cable lengths
Adds up the load on each electrical circuit of a building plan, works out its current, and measures each circuit's cable along the drawn routes.
- CadCraft
- 10 calculations
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 -
Join and stretch
Joins lines, arcs and polylines that line up or meet end to end into one object, and stretches the parts of objects inside a window.
- CadCraft
- 3 calculations
64-bit -
Lab results to stream composition
Turns lab results in mass, mole, ppm or mg/L terms into a proposed stream composition in mole fractions, and writes calculated compositions back in the lab's terms.
- CadCraft
- BimCraft
- 2 calculations
64-bit -
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 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 -
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 -
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
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.