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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Line sizing and pressure drop
Works out velocity, Reynolds number, friction factor and pressure drop of each line, picks pipe sizes, and fills the stream table that is drawn on the P&ID.
- CadCraft
- BimCraft
- 13 calculations in 3 files
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 -
Live feed values and times
Reads a value and a time from a message or poll answer of a live sensor feed.
- BimCraft
- 1 calculation
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 -
Luminaire files and point-by-point illuminance
Reads luminaire photometry files (IES LM-63 and EULUMDAT) and works out the direct illuminance on a grid of points, with its minimum, average, maximum, uniformity and power density.
- CadCraft
- BimCraft
- 17 calculations in 2 files
64-bit -
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 -
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 -
Manual roof planes
Works out the height of a hand-drawn roof plane at any point, its sloped slab, and its sloped and projected areas.
- BimCraft
- 4 calculations
64-bit Open item -
Map coordinate reprojection
Moves points, and a model's position on the map, between coordinate systems.
- BimCraft
- CivilCraft
- 3 calculations in 2 files
64-bit -
Map layers under the drawing
Draws map pictures and tiles under the drawing, warped from the map's coordinate system to the drawing's.
- CadCraft
- BimCraft
- 2 calculations
32-bit, display only -
Map layers: web Mercator, tile grids and world files
Converts longitude and latitude to web Mercator and back, lays out the tiles of a map service, reads a picture's world file, and writes the box of a map request.
- CadCraft
- BimCraft
- CivilCraft
- 10 calculations
64-bit Open item -
Map pictures warped onto the plan
Picks the tile level for the screen and cuts a map picture into pieces that are each drawn with one affine transform.
- CadCraft
- BimCraft
- CivilCraft
- 3 calculations
32-bit, display only -
Massing options from a room program
Adds up a room program, finds building shapes that hold it inside a buildable envelope, and reports each option's footprint, gross area, surplus and site coverage.
- BimCraft
- 7 calculations
64-bit -
Material graphs baked to textures
Turns a node material, a decal or a texture bake (ambient occlusion, curvature, normals, lighting) into the pictures the renderers read.
- BimCraft
- ModelCraft
- 4 calculations in 4 files
32-bit, display only -
Material maps and statistics from a photo
Makes the color, roughness and normal maps of a tiling material from one photo, and reports how visible the tile's join is and how much relief the photo has.
- BimCraft
- ModelCraft
- 4 calculations
32-bit in part Open item -
MaterialX files: numbers written and read
Writes a material's parameters, tile size and displacement to a MaterialX file, and reads them back from one.
- BimCraft
- ModelCraft
- 9 calculations in 2 files
32-bit in part Open item -
Measurements and typed values in the main window
The measured distances and areas, located points, typed lengths and quantity figures that BimCraft's main window shows or writes back to the file.
- BimCraft
- 9 calculations
32-bit in part Open item -
Measuring on the IFC view's mesh
Distances, face areas, room areas and volumes, and how far an element moved between two versions of a model, all measured on the triangle mesh the IFC view draws.
- BimCraft
- 10 calculations in 5 files
32-bit in part Open item -
Member axes and section properties
Works out each frame member's length and local axes, and the area, second moments and torsion constant of a section from its outline.
- CadCraft
- BimCraft
- DetailCraft
- 6 calculations
64-bit Open item -
MEP check messages: units and rounding
Turns pipe, duct, cable carrier and lighting results into the warnings a person reads, with the required and found values.
- BimCraft
- 4 calculations
64-bit -
MEP clearances and openings through walls and slabs
How close a pipe or duct comes to a wall, slab, beam or column, and where a run passes through a wall or slab with the opening size it needs.
- BimCraft
- 6 calculations
32-bit in part Open item -
MEP equipment, ports and refrigerant line sets
Builds generic mechanical equipment from typed sizes, places its pipe and duct ports, sizes refrigerant line sets from a capacity table and routes them between units.
- BimCraft
- 12 calculations in 3 files
64-bit -
MEP openings and clearances shown and exported
Brings run points into the viewer frame and writes the opening sizes and positions to the screen list, the CSV and the BCF.
- BimCraft
- 4 calculations
64-bit -
Meshing a slab or wall into plates
Cuts a slab or wall outline into four-node plates and places their nodes in the frame model.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations in 2 files
64-bit -
Model for rendering (glTF export)
Writes what the 3D view shows as a glTF 2.0 binary file for rendering programs: meshes, materials, lamps and the site's location.
- BimCraft
- 5 calculations
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 -
Molar mass and group-contribution estimates
Works out a molecule's formula and molar mass from its structure and estimates boiling point, critical constants, formation energies and heat capacity by Joback's method.
- CadCraft
- BimCraft
- 4 calculations
64-bit -
Molecular dynamics
Simulates atoms under Lennard-Jones, bonded and Coulomb forces and reports temperature, pressure, energies, density, radial distribution and diffusion.
- CadCraft
- BimCraft
- 22 calculations in 3 files
64-bit Open item -
Move, align and distribute
Works out how far each wall, floor, column or placed item moves to line up with the others or to be spaced evenly, and where an item turned about a point ends up.
- BimCraft
- 7 calculations in 3 files
64-bit -
Narration cue times
Places the spoken lines of a walkthrough narration in time, keeps their start times and writes them as subtitles.
- BimCraft
- 3 calculations
64-bit -
Number text in USD files
Writes numbers into .usda text and decides which attribute types are 32-bit and which are 64-bit.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 3 calculations in 2 files
32-bit in part Open item -
Numbers in a DWG file, read and written bit for bit
Reads and writes the number codes of a DWG file: full and compressed 64-bit values, whole numbers of several sizes and object handles.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 16 calculations in 2 files
64-bit -
Numbers in the frame analysis report
The values printed in the analysis and design report tables, which are also what the CSV and PDF downloads contain.
- CadCraft
- BimCraft
- DetailCraft
- 10 calculations in 5 files
64-bit Open item -
Numbers sent between people editing together
How a number in an edit is written into a Studio Live message and read back on the other side.
Every app 64-bit, direct- 5 calculations
64-bit -
Numbers typed into the property grid
Turns what a person types or drags in a Properties row into the number handed to the app.
Every app 64-bit, direct- 3 calculations
64-bit -
Numbers written into the IFC model
Turns the millimeter values the building tools work in into the coordinates, directions, extrusion depths and quantities stored in the IFC file.
- BimCraft
- 8 calculations
64-bit Open item -
OpenEXR and Radiance HDR picture files
Reads and writes rendered pictures and environment pictures as OpenEXR and Radiance HDR files.
- BimCraft
- ModelCraft
- 6 calculations in 2 files
64-bit -
Orthogonal pipe router
Finds a pipe route between two nozzles that runs only along X, Y and Z, keeps clear of obstacles and has few bends, and reports its length.
- BimCraft
- 6 calculations
64-bit Open item -
Parameter expressions
Evaluates the formulas typed for parameters and dimensions: arithmetic, units, trigonometry in degrees, rounding functions and comparisons.
- CadCraft
- BimCraft
- PartCraft
- 11 calculations
64-bit -
Parametric PCB footprints
Pad positions, pad sizes and the courtyard of standard-style footprints, worked out from pitch, row spacing and pin count.
Every app 64-bit, stated limit- 7 calculations
64-bit -
Part labels on label sheets
Places a label for every piece on a printable label sheet and sizes its bar code.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 2 calculations
64-bit -
Pass or fail against a regulation limit
Decides whether a found value meets the minimum, maximum or range of a regulation rule.
- CadCraft
- BimCraft
- CivilCraft
- DetailCraft
- 1 calculation
64-bit -
Path tracer kernels
Follows light paths through the packed scene to work out each pixel of a high-quality render.
- BimCraft
- ModelCraft
- 4 calculations in 4 files
32-bit, display only -
Path tracer scene, light and sky buffers
Packs the model's triangles, materials, lamps, light profiles and sky into the 32-bit buffers the path-tracing kernels read to draw a picture.
- BimCraft
- ModelCraft
- 4 calculations in 3 files
32-bit, display only -
Path-traced picture sums and the saved file
Reads back the summed light of a path-traced picture from the graphics card and saves it as an EXR, a 16-bit PNG or a render file.
- BimCraft
- ModelCraft
- 7 calculations in 3 files
32-bit in part Open item -
PCF piping files from and to pipe runs
Writes BimCraft's pipe runs as piping components with end points, bores, bend angles and corner points, and turns the components of a piping file back into runs.
- BimCraft
- 5 calculations
64-bit -
PDF page vectors and snapping to them
Reads the lines, curves and text of a PDF page into page points, and finds the end, middle, crossing or nearest point of those lines for snapping.
- CadCraft
- BimCraft
- 8 calculations in 2 files
32-bit in part Open item -
People flow and evacuation time
How fast people pass doors, corridors and stairs, which way each room empties, and how long it takes everyone to reach an exit.
Every app 64-bit, stated limit- 6 calculations
64-bit -
People movement and travel distance
Works out how far the farthest point of each room is from an exit and simulates people walking out of or into the building, with times, queues and walked distances.
- BimCraft
- 12 calculations in 2 files
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.