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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CraftScript array arithmetic
The elementwise operators, matrix product, backslash, ranges and sums that a script's own formulas run on.
- PartCraft
- 9 calculations
64-bit Open item -
CraftScript core math functions
The built-in math of the scripting language: elementary functions, rounding, the gamma function, sums and statistics, interpolation, polynomial fitting and number-to-text conversion.
- PartCraft
- 18 calculations
64-bit Open item -
CraftScript dense linear algebra
Solves dense systems and works out inverses, determinants, factorizations, eigenvalues, norms and condition numbers in a script.
- PartCraft
- 13 calculations
64-bit Open item -
CraftScript file readers and writers
Turns STL, OBJ, CSV, JSON, NPY and HDF5 files into script values and back, and writes a plot's data as CSV.
- PartCraft
- 14 calculations in 2 files
64-bit Open item -
CraftScript iterative solvers and sparse eigenvalues
Solves large sparse systems by iteration in a script and finds the smallest eigenvalues of a sparse problem.
- PartCraft
- 6 calculations
64-bit Open item -
CraftScript meshes and element kernels
Makes simple meshes in a script and gives scripts the app's own element matrices, voxel solver, stresses and lattice Boltzmann fields.
- PartCraft
- 10 calculations
64-bit -
CraftScript number type conversions
The script functions that convert values to single precision or to whole-number types.
- PartCraft
- 2 calculations
32-bit in part Open item -
CraftScript operators in the interpreter
Carries out the arithmetic a script writes: scalar operations, matrix division and powers, and the values of a counted loop.
- PartCraft
- 3 calculations
64-bit -
CraftScript sparse matrices and direct factorization
Builds sparse matrices in a script, adds and multiplies them, assembles element matrices, and factors a symmetric positive definite one.
- PartCraft
- 8 calculations
64-bit -
CraftScript values: storage, reading and number text
Holds the numbers a script works with, reads them back from a saved part, and writes the text shown when a statement echoes its result.
- PartCraft
- 5 calculations
64-bit -
Curves through points
Makes a curve that passes through every given point, with optional end directions.
- ModelCraft
- PartCraft
- 5 calculations in 2 files
64-bit -
Cut list sizes, areas and banding lengths
Works out each part's cut size from its finished size and edge banding, and totals pieces, areas, banding lengths and a rough sheet count.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 7 calculations
64-bit Open item -
Cutting profile pieces from stock bars
Packs the pieces of each profile onto stock bars and reports the bars to buy, where each piece is cut, the offcuts and the waste.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 5 calculations
64-bit Open item -
Cutting speeds, feeds and tool profiles
Works out spindle speed and feed rates for a tool in a material, and the shape of each tool's tip used by the simulation and 3D finishing.
- PartCraft
- 3 calculations
64-bit -
Depth and angle set by dragging a handle
Works out the new extrude depth or revolve angle when the handle of a selected feature is dragged.
- PartCraft
- 3 calculations
64-bit -
Design study variants and ranking
Makes the list of variants a design study runs, checks each result against its limits, finds the trade-off front and ranks the variants.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 6 calculations
64-bit Open item -
Design-it sizing and hand checks
Sizes a shelf bracket or a round shaft from a load and a material, and reports the stresses, deflection, bolt loads, volume and mass.
- PartCraft
- 9 calculations
64-bit Open item -
Deterministic sine, cosine, exp, log and power
Works out sin, cos, exp, log, powers and inverse trigonometric functions from + − × ÷ and √ only, so every browser gives the same bits.
- PartCraft
- 21 calculations
64-bit Open item -
Device number check
The check on the accuracy page that reports how many bits this device's numbers carry, how many processor threads and how much memory the browser shows, and what it says about the graphics processor.
Every app 64-bit, direct- 2 calculations
64-bit -
Distance grid: baking, sampling and volume
Stores a shape as signed distances on a sparse voxel lattice, built from a formula or from a closed triangle mesh, and reads values, gradients and the enclosed volume back from it.
- PartCraft
- 14 calculations in 4 files
32-bit in part Open item -
Draft and curvature analysis
Works out the draft angle of each face corner against a pull direction, the areas that pass or need draft, and the curvature limit shown with the curvature colors.
- PartCraft
- 3 calculations
32-bit in part Open item -
Drawing annotations: tolerance frames, datums and surface finish
Lays out feature control frames, datum symbols and surface texture symbols on a drawing sheet and writes their tolerance and roughness values.
- PartCraft
- 3 calculations
64-bit -
Drawing NURBS curves and surfaces
Turns tessellated curves and surfaces into the buffers the 3D view draws, with zebra stripes and curvature colors.
- ModelCraft
- PartCraft
- 2 calculations
32-bit, display only -
Drawing section view of a faceted part
Cuts the faceted solid with the section plane and draws what is behind it, with the cut outline.
- PartCraft
- 1 calculation
32-bit in part Open item -
Drawing sheet views, dimensions and PDF
Projects the part into front, top, right and isometric views, finds hidden lines, places overall dimensions and the hole table, and writes the sheet as a PDF.
- PartCraft
- 12 calculations
64-bit -
Drawing views of the exact solid
Produces the visible and hidden lines of the front, top, right, isometric and section views as 2D segments in model millimeters.
- PartCraft
- 5 calculations
64-bit Open item -
DWG object values written and read
Carries the coordinates, angles, widths and scales of drawing objects between the drawing and the DWG file's object records.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 15 calculations in 3 files
64-bit Open item -
Engineering units: factors, dimensions and conversion
Reads a unit text such as W/(m^2 K), checks it is the right kind of quantity and converts values to and from SI.
- PartCraft
- 9 calculations
64-bit -
Environment: gravity, ambient pressure and temperature
Sets the gravity, ambient pressure and ambient temperature the solvers use, and converts them to the solvers' units.
- PartCraft
- 7 calculations
64-bit -
Exact solid: mesh, volume, area and tables
Produces the triangle mesh of the exact solid used for the view, STL and 3MF export and assembly checks, and reads its volume, surface area, face areas and edge lengths from the kernel.
- PartCraft
- 9 calculations
32-bit in part Open item -
Exact surface records for meshing
Reads each curved face's true surface (sphere, cone, torus, revolution, extrusion, spline) out of the kernel as plain numbers for the analysis mesher, and verifies it.
- PartCraft
- 3 calculations
64-bit -
Exact surfaces for the tetrahedral mesher
Evaluates the exact curved faces of a part (spheres, cones, tori, surfaces of revolution and extrusion, B-spline surfaces) and finds the point on a face closest to a given point, so that mesh nodes can be put on the true surface.
- PartCraft
- 11 calculations
64-bit -
Exact-kernel feature dimensions
Works out the lengths, angles and positions handed to the solid kernel for extrudes, revolves, holes, patterns, shells and chamfers.
- PartCraft
- 11 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 -
Feature tool dimensions on the mesh kernel
Works out the depth, position, axis and angles of the solid each extrude, revolve, hole and pattern adds to or cuts from the part.
- PartCraft
- 9 calculations
64-bit -
Field builtins for scripts
Lets a script build implicit shapes, sample them, turn them into a body, measure its volume and check it for manufacturing.
- PartCraft
- 6 calculations
32-bit in part Open item -
Field shapes: signed distance functions
Turns a shape description (spheres, boxes, beams, revolved profiles, lattices, booleans, offsets, shells) into a signed distance at any point.
- PartCraft
- 17 calculations
64-bit Open item -
Fillet, chamfer, draft, thread and mesh bodies on the mesh kernel
Builds rounds, bevels, drafted faces, threads and imported mesh bodies from the body as it is at that point in the history.
- PartCraft
- 9 calculations
32-bit in part Open item -
Fitted curves and surfaces: sweeps, networks, Coons patches, offsets, rebuilds and extensions
Builds curves and surfaces that follow a target within a tolerance: least-squares fits, sweeps along one or two rails, surfaces through a network of curves, offsets, rebuilds and extensions.
- ModelCraft
- PartCraft
- 17 calculations in 2 files
64-bit -
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 -
Flow study: 32-bit steps in the mesh and the result fields
The largest speed, the pressure range, the values under the result probe and the surface pressure of a flow study, and the mesh the study is built from.
- PartCraft
- 5 calculations in 3 files
32-bit in part Open item -
Flow study: fluid cells, openings and wall distances
Finds which grid cells are fluid, closes the openings, measures each opening's area, and cuts every wall link against the part for its wall distance.
- PartCraft
- 8 calculations in 2 files
64-bit -
Flow study: lattice Boltzmann solver
Steps the fluid's velocity and density on a grid of cells to a steady state and sums the mass through openings and the force on walls.
- PartCraft
- 10 calculations
64-bit -
Flow study: results in physical units
Sets inlet speeds from the given velocity or flow rate, and turns the lattice result into mass flow, pressure drop, force, drag and lift coefficients and Reynolds number.
- PartCraft
- 8 calculations in 2 files
64-bit -
Flow study: turbulence model and wall functions
Adds an eddy viscosity to the flow solver and sets the wall shear from a wall law, for turbulent runs marked experimental.
- PartCraft
- 10 calculations
32-bit in part Open item -
Form cage to exact solid: sewing and volume
The tolerances and the volume used when a Form cage is converted to exact B-rep geometry.
- PartCraft
- 2 calculations
64-bit -
Freeform bodies: display mesh
Makes the triangles the Form workspace draws for the smooth surface.
- PartCraft
- 1 calculation
32-bit, display only -
Freeform bodies: subdivision surface and cage edits
Refines a control cage into a smooth surface, converts it to Bézier patches for the solid model, and moves, mirrors, extrudes and flattens cage vertices.
- PartCraft
- 19 calculations
64-bit -
Freeform cage edits from the workspace
Turns gizmo drags, clicks on the ground plane and edge extrusions in the Form workspace into new positions of the control cage that defines a freeform shape.
- PartCraft
- 4 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.