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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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 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 -
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 -
Framing panels and cut lists
Lays out the studs, plates, headers, joists and rafters of a framing panel, lists the pieces to cut, and places them in the model as members.
- BimCraft
- DetailCraft
- 12 calculations
64-bit Open item -
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 -
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 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 -
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 -
Geometric room acoustics
Works out how sound energy arrives at a listener over time in a room, by image sources or by ray tracing, and from that the reverberation and clarity measures per octave band.
- BimCraft
- 6 calculations
32-bit in part Open item -
Georeference written to the IFC file
Writes a model's place on the map into the file: the map conversion numbers, the coordinate reference system and its length unit.
- BimCraft
- 5 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 -
GIS feature geometry
Works out ring areas and winding, tests whether a point is inside a ring, sorts rings into polygons and holes, and moves layers between coordinate systems.
- CivilCraft
- 8 calculations in 2 files
64-bit Open item -
GIS import: reprojection and elevation units
Places the features of shapefiles, GeoJSON, KML and GeoPackage files in the project's coordinate system and converts their elevations to the project's unit.
- CivilCraft
- 4 calculations
64-bit -
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 -
glTF import: meshes, skins and placements
Turns a read glTF scene into mesh definitions and placements with Z up: welds vertices, applies skins and morph weights, drops empty triangles and marks sharp edges.
- ModelCraft
- 9 calculations
32-bit in part Open item -
glTF import: reading numbers
Reads the positions, normals, weights, matrices and other numbers a glTF file stores, and each node's transform.
- ModelCraft
- 4 calculations
64-bit -
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 -
Gravity pipe network: slopes, cover and automatic inverts
Works out each pipe's length, slope and least cover, each structure's rim and sump, and sets inverts that keep the minimum slope, cover and drop.
- CivilCraft
- 3 calculations
64-bit -
Grid lines
Lays out grid lines by spacing and angle, finds where they cross for snapping, and decides which lines an elevation sees end on.
- BimCraft
- 6 calculations
64-bit -
Ground modifiers: cut and fill, overlaps, level labels and junction checks
Reports the cut and fill each landscape object makes in the ground, where two of them overlap, the levels and gradients read off the surface, and where walls, steps and planted areas do not meet the levels beside them.
- CivilCraft
- 8 calculations in 2 files
64-bit -
Ground points from an unclassified point cloud
Finds which points of a drone or scanner cloud are ground, so a surface can be built from them.
- CivilCraft
- 5 calculations
64-bit -
Ground read from a survey file
Reads ground points from a points file, drawing contours, a LAS or LAZ cloud, an elevation grid or LandXML, and sets their unit, offset and datum before they become the site's ground.
- BimCraft
- 4 calculations
32-bit in part Open item -
Ground surface from contour lines and points
Checks contour lines, gives them elevations, and builds a ground surface from them, filling in the flat triangles that contours leave on ridges, valleys and hilltops.
- CivilCraft
- 8 calculations
64-bit -
Ground surface triangulation and contours
Builds the triangulated ground surface from points, breaklines and a boundary, and works out its contours, elevation bands and outline.
- BimCraft
- CivilCraft
- 17 calculations
64-bit -
Ground-mounted solar arrays on terrain
Places solar tables on the ground inside a region, spaces each row so the row in front does not shade it at the winter sun, and reports table positions, pile heights, ground slope, row pitch and installed power.
- CivilCraft
- 7 calculations
64-bit Open item -
Group modifiers: scale and array placements
Works out where each copy of a group or component sits when it has Scale and Array modifiers.
- ModelCraft
- 2 calculations
64-bit -
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 EXR
Converts between 16-bit half floats and 32-bit floats for EXR channels.
- BimCraft
- ModelCraft
- 2 calculations
32-bit in part 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 -
Hardscape: paving, paths, walls, ramps and steps
Sets out paving, paths, walls, curbs, ramps and steps on the ground, checks grades, risers and goings, and totals their quantities.
- CivilCraft
- 9 calculations
64-bit 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 -
Headset review: measuring, section cuts and issue cameras
Works out the distance between two points picked in a headset, the plane of a section cut made there, and the camera and place saved with an issue.
- BimCraft
- ModelCraft
- 9 calculations in 2 files
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 -
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
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.