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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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 -
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 -
Equipment list from drawing tags
Reads the equipment schedule hidden in a foodservice drawing's item tags: one row per item, its quantity and the sheets that show it.
- BimCraft
- 3 calculations
64-bit -
Erection movie player
Draws the erection sequence as a moving 3D picture in the exported movie page.
- DetailCraft
- 2 calculations
32-bit, display only -
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 -
Estimate and quantity exports (CSV and XLSX)
The numbers written to the estimate CSV, the XLSX workbook, the material list and the spot elevation point file.
- TakeoffCraft
- 11 calculations
64-bit Open item -
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 -
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 -
Factory layout checks
Checks equipment placed on a floor for overlaps, blocked access strips, narrow aisles, items outside the room and floor load, and measures the path between items.
- BimCraft
- 8 calculations
64-bit -
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 -
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 -
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 line grades, arcs, offsets and crossings
Works out a feature line's lengths, grades and arcs, sets elevations by grade, offsets the line, and finds where it crosses an alignment.
- CivilCraft
- 15 calculations in 2 files
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 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 layout points from the model
Works out the points a crew sets out from the model (column feet, wall axis ends, anchor bolts, sleeves, chosen elements) in model or survey coordinates, in meters, millimeters or feet.
- BimCraft
- 3 calculations
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 -
Figures shown in the residential panels and schedules
Works out the numbers the residential tools show in Properties and on schedules: a roof plane's area, the cut list, board feet, cut and fill, a new stair's direction and a building's width on an elevation.
- BimCraft
- 7 calculations
64-bit -
Fillet and chamfer
Rounds or cuts the corner between two objects, between two segments of one polyline, or at every corner of a polyline.
- CadCraft
- 9 calculations
64-bit -
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 -
Finding joints between members
Finds where a beam end meets a column, where two members meet end to end in line or at an angle, and where a brace lands on another member.
- DetailCraft
- 5 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 -
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 -
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 -
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: 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 -
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 -
Flowsheet variant metrics
Works out the heating, cooling and shaft power, the hourly operating cost and the hourly CO2 of one solved flowsheet variant, the numbers an optimization study ranks by.
- CadCraft
- BimCraft
- 1 calculation
64-bit -
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 -
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
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.