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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Connection plates, holes, bolts and cut-backs
Works out where each connection's plates, holes, bolts and welds go and how far the joined members are cut back, from the connection's parameters.
- DetailCraft
- 24 calculations
64-bit Open item -
Constructability checks
Warns about bolts a socket cannot reach, bolts too close for a socket, fillet welds outside size limits, welds a torch cannot reach, and tubes that hold water.
- DetailCraft
- 6 calculations
64-bit -
Contact between parts in stress analysis
Works out the gap between touching parts and the contact forces and stiffness that keep them from passing through each other.
- PartCraft
- 8 calculations
64-bit -
Continuity between curves and between surfaces
Measures the gap, the angle and the curvature difference where two curves join or two surfaces share an edge, and classes the join as G0, G1 or G2.
- ModelCraft
- PartCraft
- 5 calculations
64-bit Open item -
Coordinate reference systems
Converts project coordinates to and from a named map projection, longitude and latitude, and other systems, and reports grid scale factor, convergence and elevation factor at a point.
- CadCraft
- BimCraft
- CivilCraft
- 17 calculations in 2 files
64-bit -
Corner cabinet drilling positions
Works out where the shelf-pin, hinge-plate, fixing, pivot and shaft holes go on the parts of a corner cabinet.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 7 calculations
64-bit Open item -
Corner cabinets: parts and solids
Builds the cut list, door sizes, hardware counts and 3D solids of L-shaped, diagonal and lazy-susan corner cabinets (CabinetCraft add-on).
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 11 calculations
64-bit Open item -
Corridor cross sections and pavement quantities
Sweeps a road or track assembly along an alignment and profile: section stations, edge and shoulder points, targets, daylight points, and the area and volume of pavement courses.
- CivilCraft
- 6 calculations
64-bit -
Costs on the schedule
Prices each element from its quantities, adds the cost up per scheduled task, spreads it over the task's days and totals the cash flow.
- BimCraft
- 13 calculations
64-bit Open item -
CraftScript core math functions
The built-in math of the scripting language: elementary functions, rounding, the gamma function, sums and statistics, interpolation, polynomial fitting and number-to-text conversion.
- PartCraft
- 18 calculations
64-bit Open item -
CraftScript file readers and writers
Turns STL, OBJ, CSV, JSON, NPY and HDF5 files into script values and back, and writes a plot's data as CSV.
- PartCraft
- 14 calculations in 2 files
64-bit Open item -
CraftScript iterative solvers and sparse eigenvalues
Solves large sparse systems by iteration in a script and finds the smallest eigenvalues of a sparse problem.
- PartCraft
- 6 calculations
64-bit Open item -
CraftScript meshes and element kernels
Makes simple meshes in a script and gives scripts the app's own element matrices, voxel solver, stresses and lattice Boltzmann fields.
- PartCraft
- 10 calculations
64-bit -
Cubic equations of state
Works out compressibility, fugacity coefficients, enthalpy and entropy departures and vapor pressure from the Peng–Robinson and Soave–Redlich–Kwong equations.
- CadCraft
- BimCraft
- 8 calculations
64-bit Open item -
Culverts, bridges and junctions in a river model
Works out the headwater above a culvert, the water surface above a bridge, and the flows and water levels where river reaches join, for the steady water surface profile.
- CivilCraft
- 8 calculations
64-bit Open item -
Curve objects
Evaluates Bézier, NURBS and poly splines and makes the mesh a curve object shows: a tube, a ribbon, or a filled flat shape with thickness and a rounded edge.
- ModelCraft
- 14 calculations in 2 files
64-bit Open item -
Curved walls
Works out the circle, length and points of a wall whose center line is an arc, where doors and windows sit in it, and the curves it is saved with.
- BimCraft
- 11 calculations
64-bit -
Cut and fill map, spot levels, sloped pads and free sections
Works out the depth of cut or fill cell by cell with its volumes, spot levels on a grid, the elevations of a sloped pad or ramp, and a section cut along any line with its cut and fill areas.
- CivilCraft
- 8 calculations
64-bit -
Cut and fill volumes by the grid method
The cut, fill and net volume between two surfaces.
- CivilCraft
- 2 calculations
64-bit -
Cut list sizes, areas and banding lengths
Works out each part's cut size from its finished size and edge banding, and totals pieces, areas, banding lengths and a rough sheet count.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 7 calculations
64-bit Open item -
Cutting profile pieces from stock bars
Packs the pieces of each profile onto stock bars and reports the bars to buy, where each piece is cut, the offcuts and the waste.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 5 calculations
64-bit Open item -
Cutting speeds, feeds and tool profiles
Works out spindle speed and feed rates for a tool in a material, and the shape of each tool's tip used by the simulation and 3D finishing.
- PartCraft
- 3 calculations
64-bit -
Data collector files and polar reduction
Reads total-station field books (RW5, GSI, JobXML, CSV), reduces each shot to coordinates, and prepares directions and distances for the network adjustment.
- CivilCraft
- 6 calculations
64-bit Open item -
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 -
Design-it sizing and hand checks
Sizes a shelf bracket or a round shaft from a load and a material, and reports the stresses, deflection, bolt loads, volume and mass.
- PartCraft
- 9 calculations
64-bit Open item -
Detention pond hydrology and routing
Builds a runoff hydrograph, a stage and storage table and an outlet rating, routes the storm through the pond, sizes an orifice, and checks the result.
- CivilCraft
- 12 calculations
64-bit -
Deterministic sine, cosine, exp, log and power
Works out sin, cos, exp, log, powers and inverse trigonometric functions from + − × ÷ and √ only, so every browser gives the same bits.
- PartCraft
- 21 calculations
64-bit Open item -
DEXPI and PCF plant exchange files
Reads and writes plant models as DEXPI XML and piping component files (PCF), converting positions, sizes and angles between the file's units and the drawing.
- CadCraft
- BimCraft
- 15 calculations in 3 files
64-bit Open item -
Diagram layout into drawing objects
Places the blocks, connectors, arrowheads and labels of a diagram written as text, and turns them into lines, polylines, hatches and text in the drawing.
- CadCraft
- 7 calculations
64-bit -
Dimensions and views on drawing sheets
Lays out plans, elevations, assembly drawings and anchor plans, and works out the dimension figures, scales and hidden lines printed on them.
- DetailCraft
- 13 calculations
64-bit Open item -
Distillation and absorption columns
Sizes a column by shortcut methods and solves stage-by-stage columns, absorbers and strippers for flows, temperatures, compositions and duties.
- CadCraft
- BimCraft
- 18 calculations in 2 files
64-bit Open item -
Drawing comparison by vector paths
Compares two revisions of a sheet by their drawn lines: which lines were taken out or put in, how much, where, and whether the drawing inside a task's region changed.
- MarkupCraft
- 16 calculations in 4 files
64-bit Open item -
Drawing location written to DWG and DXF
Writes where the drawing sits on its map grid (design point, reference point, north direction) into the file's GEODATA object, and reads another program's back.
- CadCraft
- 3 calculations
64-bit Open item -
Drawing sheet views, dimensions and PDF
Projects the part into front, top, right and isometric views, finds hidden lines, places overall dimensions and the hole table, and writes the sheet as a PDF.
- PartCraft
- 12 calculations
64-bit -
Drawing sheets as DWG and DXF
Writes a drawing sheet's lines, circles, fills and text into a DWG model or a DXF R12 file at 1 unit = 1 mm on paper.
- DetailCraft
- 6 calculations
64-bit -
Drawing views of the exact solid
Produces the visible and hidden lines of the front, top, right, isometric and section views as 2D segments in model millimeters.
- PartCraft
- 5 calculations
64-bit Open item -
Drawn floors: outline, openings and quantities
Checks a floor outline drawn by hand, cuts openings in it, and works out its perimeter, area and volume.
- BimCraft
- 7 calculations
64-bit Open item -
DSTV NC files
Writes one NC file per part mark for the shop's machines: the header, the outer contours and the holes.
- DetailCraft
- 8 calculations
64-bit -
Duct network pressure: drawing adapter
Turns drawn duct runs into the network the pressure engine analyzes: runs in millimeters, the fan point, the terminals and their airflows, and the result rows.
- CadCraft
- 8 calculations
64-bit Open item -
Duct runs, fittings and schedule
Works out the elbows, transitions and branch fittings of drawn duct runs, the straight lengths between them, and the schedule of lengths and sheet-metal areas.
- CadCraft
- 15 calculations in 2 files
64-bit Open item -
DWG and DXF drawings compiled for the plan view
Turns the entities of a DWG or DXF drawing into the lines, fills and text of each space, in the drawing's own coordinates.
- BimCraft
- TakeoffCraft
- 20 calculations in 2 files
64-bit -
DWG and DXF drawings in 3D
Turns a drawing's model space into 3D lines, faces and text, with every block insert, elevation, thickness and extrusion direction applied.
- BimCraft
- 12 calculations in 2 files
64-bit -
DWG and DXF linework into project units
Turns the lines, arcs, polylines, splines, ellipses and block references of a drawing into linework, feature lines and survey points in the project's units.
- CivilCraft
- 15 calculations in 2 files
64-bit -
DWG import: objects from the file's model
Turns the entities read from a DWG file into drawing objects: dimensions, hatch boundaries, block arrays, pictures, viewports, text angles and lineweights.
- CadCraft
- 13 calculations
64-bit Open item -
DXF reading: objects from the file's text
Reads the numbers of an ASCII DXF file into drawing objects: coordinates, angles, hatch boundaries and pattern lines, block arrays, dimensions, viewports, lineweights and sheet sizes.
- CadCraft
- 15 calculations
64-bit Open item -
DXF writing: numbers as text
Writes a drawing's coordinates, sizes and angles as decimal text in a DXF file, in the R12 and 2000 formats.
- CadCraft
- 21 calculations in 2 files
64-bit Open item -
DXF-AAMA and ASTM pattern files
Writes pattern pieces and their grade rules to DXF-AAMA or ASTM D6673 files with a RUL rule file, and reads such files back (Apparel add-on).
- CadCraft
- 14 calculations
64-bit Open item -
Dynamic simulation and controller tuning
Simulates tanks, reactors, gas vessels, valves and PID controllers over time and suggests controller settings from a step test.
- CadCraft
- BimCraft
- 12 calculations
64-bit -
E57 point cloud reading
Reads the points of an E57 scan file into absolute coordinates in meters, with each scan's pose applied, and the bounds of every point read.
- CadCraft
- BimCraft
- 8 calculations
64-bit -
Earthquake time-history of a building
Shakes a building of one mass per floor through a ground acceleration record and reports periods, mode shapes, story drifts, floor accelerations and base shear; the floor stiffness can come from the frame model.
- BimCraft
- 12 calculations in 2 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.