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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Decimate modifier
Reduces the number of triangles of a mesh to a ratio of the original while keeping its shape as closely as the method allows.
- ModelCraft
- 4 calculations
64-bit -
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 -
Dimensions and typed sizes in 3D
The length, radius, diameter or angle a 3D dimension shows, and how the model is resized when a new value is typed into a dimension, an edge length or a group size.
- CadCraft
- ModelCraft
- 13 calculations in 2 files
64-bit Open item -
Drawing an edge: welding, splitting and re-facing
What happens to the model when a line is drawn: which points become one vertex, where edges are split, and which closed loops become faces.
- CadCraft
- ModelCraft
- 11 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 -
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 -
Edits and settings from the main window
Places the mirror plane for a flipped copy, turns a drawn curve into a curve object, bakes node meshes into the model, guesses storey heights, reads the sun settings, and hands a room to add-ons.
- ModelCraft
- 7 calculations
64-bit -
Entity info: volume, size, angle and area
Shows the volume and size of a selected group, component or mesh as it is placed, an arc's angle, the total area of selected faces, and the print check's size and volume.
- ModelCraft
- 5 calculations
64-bit -
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 -
Fast render lights and texture placement
Sets lamp strength, soft sun shadows and where a material's texture falls on a surface for the fast render and the 3D views.
- BimCraft
- ModelCraft
- 3 calculations in 2 files
32-bit, display only -
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 import: axes, units and transforms
Turns an FBX file's axes and unit into Z up and meters, and builds each object's matrix from its translation, pivots, rotations and scaling.
- ModelCraft
- 7 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 -
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 -
Focus distance picked in the view
The focus distance set by clicking a point in the live rendered view.
- BimCraft
- ModelCraft
- 1 calculation
32-bit in part Open item -
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 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 -
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 -
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 -
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 -
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 -
Hollowing a body to a wall thickness
Makes the inside surface that leaves a wall of the asked thickness, reports the volume taken out, and builds drain holes through the wall.
- ModelCraft
- 8 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 -
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 -
Imported material parameters
Turns a glTF or FBX material's numbers (roughness, index of refraction, film thickness, emission strength) into the renderer's parameters and back.
- ModelCraft
- 4 calculations
64-bit Open item -
Inset, bevel and moves along normals
Places the new vertices of an inset or a bevel at the stated thickness or width from the old edges, and moves vertices along their normals.
- ModelCraft
- 7 calculations
64-bit -
Inverse kinematics and constraints
Moves a bone or a placement so it reaches a target, looks at it, copies it, stays within limits, hangs from it or sits on a path.
- ModelCraft
- 11 calculations in 2 files
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 -
Issue viewpoints in BCF files
Converts cameras and section planes between the viewer and the model's own coordinates, and writes and reads them in BCF issue files.
- BimCraft
- ModelCraft
- 8 calculations
64-bit Open item -
Keys dragged in the graph editor
Turns a drag on the curve editor's canvas into a key's new time and value, or a handle's new offset.
- ModelCraft
- 3 calculations
64-bit -
Knot vectors
Builds and checks the knot vectors that NURBS curves and surfaces are defined on.
- ModelCraft
- PartCraft
- 6 calculations
64-bit -
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 -
Lineweights in a DWG file
Converts a lineweight between its value in hundredths of a millimeter and the index a DWG file stores.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- 2 calculations
Exact -
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 -
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
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.