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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Earthwork balance and haul plan
Finds the pad level, and the tilt if allowed, at which cut fills the fill, and plans which cut goes to which fill and how far.
- CivilCraft
- 9 calculations
64-bit -
Earthwork progress from repeat surveys
Compares dated surveys with the original ground and the design to give volumes done and remaining, percent complete, over-cut and over-fill, stockpiles, and a forecast finish date.
- CivilCraft
- 3 calculations
64-bit -
Earthwork, route and pond tools: values stored and exported
Carries the results of the earthwork balancer, the route finder and the pond tools into the project, into CSV files and into the answers given to assistants.
- CivilCraft
- 14 calculations in 2 files
64-bit Open item -
Edits to a page's own content
Moves, scales, turns, reshapes and rewords the drawing's own lines, pictures and text in the PDF (the Page content tool), and writes the result back into the file.
- MarkupCraft
- 16 calculations in 2 files
64-bit Open item -
Electrical devices: positions, loads and circuit amps
Places sockets, switches and lights on wall faces or ceilings, keeps them on their wall when it moves, and totals the load and current of each circuit.
- BimCraft
- 7 calculations
64-bit Open item -
Elevation grids into survey points and a grid surface
Places the cells of an elevation raster in the project's coordinates, converts heights between meters and feet, and makes survey points or a triangulated surface from the grid.
- CadCraft
- BimCraft
- CivilCraft
- 7 calculations
64-bit -
Elevation grids read from GeoTIFF and ASCII files
Reads a terrain grid's position, cell size and elevations from a GeoTIFF or an ESRI ASCII grid, with its scale, offset and no-data value.
- BimCraft
- CivilCraft
- 8 calculations
64-bit -
Ellipses and curves as short segments
Turns ellipses, sheared arcs, splines and outlines into runs of short straight segments, and measures ellipses.
- CadCraft
- 7 calculations
64-bit Open item -
Embodied carbon from quantities
Multiplies each item's quantity, with waste, by a carbon factor to give kilograms of CO2 equivalent.
- TakeoffCraft
- 4 calculations
64-bit Open item -
Energy model input file (IDF) and its results
Writes the rooms of a model as an IDF input file for an outside energy simulation engine, and reads back the design loads and yearly energy that engine reports.
- BimCraft
- 14 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 -
Erection plan: picks, crane loads and times
Works out what the crane lifts, each pick's weight, radius, share of the load chart, hook height and time.
- DetailCraft
- 10 calculations
64-bit Open item -
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 -
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 -
Family editor: sketch points, handles and solved sizes
Changes a family's recipe when a point is moved or a handle is dragged, solving for the parameter that puts a face or a hotspot where it was dragged.
- BimCraft
- 13 calculations in 2 files
64-bit Open item -
Family geometry from parameters
Works out a family's solids, plan symbol and connectors from its parameters and formulas, and writes them to the IFC file.
- BimCraft
- 21 calculations in 3 files
64-bit -
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 -
FBX reader: number types as stored
Reads the numbers of an FBX file, binary or text, into the node tree the importer uses.
- ModelCraft
- 3 calculations
64-bit -
Feature line arcs as straight pieces
Cuts the arcs of a feature line into straight pieces for surfaces, grading, linework and DWG or DXF, and follows a line along an alignment for profile views.
- CivilCraft
- 7 calculations
64-bit -
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 -
Fermentation (Monod kinetics)
Biomass, substrate, product and volume over time in a batch or fed-batch vessel.
- CadCraft
- BimCraft
- 1 calculation
64-bit -
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 -
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 -
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 -
Flood depth and wind load playback
Works out how deep each room floods over time from a water-level record, the water's push on a wall, and the wind force, shear and overturning moment on each story.
- BimCraft
- 4 calculations
64-bit Open item -
Flood extent on the ground surface
Lays the computed river water surface over the ground and gives the flooded area, the waterline and the greatest depth.
- CivilCraft
- 5 calculations
64-bit 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: 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 -
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 -
Footing design checks
Checks a footing for bearing, sliding, overturning, bending, shear, punching, bar development and depth from the column loads and the soil you describe.
- DetailCraft
- 18 calculations
64-bit Open item -
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 -
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 -
Foundation parts and quantities
Sizes footings from a default table, builds the slab, stem wall and footing shapes under the building outline, steps them to the ground, and writes their lengths, widths and volumes.
- BimCraft
- 8 calculations
64-bit Open item -
Foundation settlement
Works out the stress under a loaded rectangle, immediate and consolidation settlement of a layered soil, and how settlement develops with time.
- CivilCraft
- 10 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 model from a building model
Turns the model's beams, columns, braces and concrete slabs and walls into the lines, sections, joints, supports and loads the frame analysis solves.
- BimCraft
- 17 calculations
64-bit Open item -
Freeform mesh objects: quantities and placement on the ground
Reads a mesh from an STL or OBJ file, works out its volume, surface area, footprint and height, and sets it on or into the terrain.
- CivilCraft
- 5 calculations
64-bit -
Furniture layout of a room
Places a room's furniture by rule: against the walls or in the middle, clear of doors, windows and each other.
- BimCraft
- ModelCraft
- 9 calculations
64-bit -
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 -
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: 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 -
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 -
glTF export
Writes the model as a binary glTF file: each definition's triangles, each placement's matrix, lamps and saved views.
- ModelCraft
- 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.