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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G-code and toolpath exports
Writes a program's moves as G-code, CSV or JSON.
- PartCraft
- 4 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 -
G-code written by text post definitions
Writes the coordinates, feeds and arc offsets of a machining program as G-code words, using a post definition a person can edit.
- PartCraft
- 6 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 -
Generated part exports: data sheet, VTK, 3MF and OpenVDB
Writes a generated part's field and surface to VTK, 3MF and OpenVDB files and its values to a data sheet.
- PartCraft
- 8 calculations in 2 files
32-bit in part Open item -
Generative design by topology optimization
Finds which part of a design space to keep for the stiffest shape at a given volume, turns the result into a solid design and a surface mesh, and checks its mass, stress and displacement.
- PartCraft
- 15 calculations
32-bit in part Open item -
Geometric multigrid for the voxel stress model
Builds and applies the multigrid cycle that speeds up the conjugate-gradient solve of the voxel stress analysis.
- PartCraft
- 6 calculations
64-bit -
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 -
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 -
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 -
Hull hydrostatics and righting arms
Works out a floating part's displaced volume, displacement, centers of buoyancy and flotation, metacentric heights and the righting-arm curve at a given draft.
- PartCraft
- 5 calculations
32-bit in part Open item -
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 export of parts, assemblies and library items
Writes the mesh, placements, quantities and parameter values of a part, an assembly or a library item into an IFC4 file.
- PartCraft
- 6 calculations
32-bit in part 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 -
IGES files of NURBS curves and surfaces
Writes B-spline curves and surfaces to an IGES file in millimeters and reads them back, converting the file's unit.
- ModelCraft
- PartCraft
- 5 calculations
64-bit Open item -
Illustrate: projection, hidden lines and vector pictures
Projects a manual view onto the picture, removes hidden lines and writes the result as line art and PDF pages.
- PartCraft
- 4 calculations in 4 files
32-bit, display only -
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 a parametric export file
Rebuilds a part feature by feature from a cadcraft-sw-export file: sketches moved into the part's planes, edges and faces found from their positions, parameters and equations carried over, and the volume compared with the one in the file.
- PartCraft
- 11 calculations
32-bit in part Open item -
Interference between assembly parts
Finds pairs of placed parts that overlap, with the overlapping volume, and steps a joint through a range to check for clashes along the way.
- PartCraft
- 3 calculations
32-bit in part Open item -
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 -
Knot vectors
Builds and checks the knot vectors that NURBS curves and surfaces are defined on.
- ModelCraft
- PartCraft
- 6 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 -
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 -
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 -
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 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 -
Matching and blending NURBS curves and surfaces
Moves the end of a curve or the edge of a surface so it meets another with position, tangent or curvature continuity, and builds blends between them.
- ModelCraft
- PartCraft
- 7 calculations
64-bit -
Material packs: property curves by temperature
Returns a material property at a temperature from a pack's fitted curve, with its unit, valid range and fit error.
- PartCraft
- 3 calculations
64-bit -
Material units, gravity and custom material limits
The unit factor from density to the solver's mass unit, the gravity constant, and the limits on a custom material.
- PartCraft
- 3 calculations
64-bit Open item -
Measuring and mass properties in 3D
Reports lengths, radii, areas, distances and angles of picked points, edges, faces and bodies, and the mass, center of mass and inertia of a part or assembly.
- PartCraft
- 13 calculations in 2 files
32-bit in part Open item -
Mesh import, repair and storage
Reads STL, OBJ and 3MF meshes, welds and repairs them into a closed body, finds their flat faces and keeps the result in the part file.
- PartCraft
- 11 calculations
32-bit in part Open item -
Mesh volume, area and watertightness checks
Works out a triangle mesh's volume and area and checks that it is closed and manifold.
- PartCraft
- 3 calculations
64-bit Open item -
Mode shapes returned by the simulation worker
The vibration mode shapes that the simulation worker returns for a modal study.
- PartCraft
- 1 calculation
32-bit in part Open item -
Model points written to USD
Writes the vertices and edges of a model into USD meshes and curves.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 2 calculations
32-bit in part Open item -
Motion study of an assembly
Drives one joint through its travel and records positions, speeds, accelerations, clashes and clearances at each step.
- PartCraft
- 6 calculations
32-bit in part Open item -
Multigrid preconditioner for stress analysis
Builds and applies the smoothed-aggregation multigrid cycle that speeds up the conjugate-gradient solve of the tetrahedral stress model.
- PartCraft
- 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.