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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Drawing autocomplete
Finds a repeat, a stair or a nearly closed figure in the newest objects and offers the next copy, the next steps or the closing sides as geometry that is added to the drawing when accepted.
- CadCraft
- 7 calculations
64-bit Open item -
Drawing compare
Decides which objects are unchanged, moved, changed, added or removed between two versions of a drawing.
- CadCraft
- 4 calculations
64-bit -
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 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 -
Drawing placed on a map grid
Describes where the drawing's own coordinates sit on a projected map system: scale, rotation and one matching pair of points.
- CadCraft
- BimCraft
- 1 calculation
64-bit -
Drawing section view of a faceted part
Cuts the faceted solid with the section plane and draws what is behind it, with the cut outline.
- PartCraft
- 1 calculation
32-bit in part 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 sheets to scale and the PDF
Picks the scale of each plan, elevation and section, places it on its sheet, and writes the sheet's lines, fills and text into the PDF.
- BimCraft
- 14 calculations in 2 files
64-bit Open item -
Drawing the 3D check view and CAD sheets on screen
Draws the 3D check view with three.js and a DWG or DXF sheet on the canvas.
- TakeoffCraft
- 2 calculations in 2 files
32-bit, display only -
Drawing to laser paths
Turns the drawing's lines, arcs, polylines, curves and hatches into paths in millimeters for the laser panel.
- CadCraft
- 4 calculations
64-bit -
Drawing values handed to and from LISP routines
The numbers that pass between a LISP routine and the drawing: answers typed for a command, object data lists, object properties, system variables and coordinate transforms.
- CadCraft
- 18 calculations in 3 files
64-bit Open item -
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 -
Drawn points: angle, length and wall-face paths
Decides the plan point a click becomes when it follows an angle step, a length step or a wall, and offsets a path drawn on a wall face to the wall's center line.
- BimCraft
- 4 calculations
64-bit -
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 and DXF views on screen
Draws a compiled drawing in the 2D view and in the 3D view.
- BimCraft
- 3 calculations in 2 files
32-bit, display only -
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 -
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 -
DWG save: objects to the file's model
Turns drawing objects into the entities a DWG file holds: dimensions with their defining points, hatches with pattern lines, text, viewports, sheets, lineweights and extents.
- CadCraft
- 13 calculations
64-bit Open item -
DXF reading into the shared drawing model
Reads an ASCII DXF file into the same model the DWG reader gives, for the apps that list, convert or draw DXF content.
- CadCraft
- BimCraft
- TakeoffCraft
- CivilCraft
- 4 calculations
64-bit -
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 input: points from typed distance, angle, X and Y
Works out the point a command receives when a distance, an angle, or X and Y are typed into the fields by the crosshair.
- CadCraft
- 4 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 -
Earthwork balance and haul plan
Finds the pad level, and the tilt if allowed, at which cut fills the fill, and plans which cut goes to which fill and how far.
- CivilCraft
- 9 calculations
64-bit -
Earthwork progress from repeat surveys
Compares dated surveys with the original ground and the design to give volumes done and remaining, percent complete, over-cut and over-fill, stockpiles, and a forecast finish date.
- CivilCraft
- 3 calculations
64-bit -
Earthwork, route and pond tools: values stored and exported
Carries the results of the earthwork balancer, the route finder and the pond tools into the project, into CSV files and into the answers given to assistants.
- CivilCraft
- 14 calculations in 2 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 -
Edits to a page's own content
Moves, scales, turns, reshapes and rewords the drawing's own lines, pictures and text in the PDF (the Page content tool), and writes the result back into the file.
- MarkupCraft
- 16 calculations in 2 files
64-bit Open item -
Electrical devices: positions, loads and circuit amps
Places sockets, switches and lights on wall faces or ceilings, keeps them on their wall when it moves, and totals the load and current of each circuit.
- BimCraft
- 7 calculations
64-bit Open item -
Element outlines in the IFC view
Finds the edge lines drawn on each element in the IFC view.
- BimCraft
- 2 calculations
32-bit, display only -
Element quantities for carbon and cost
Reads each element's volume, area and length and splits the volume between its materials, as the embodied carbon and cost calculations use them.
- BimCraft
- 5 calculations
64-bit Open item -
Element triangles for analysis
Hands the placed triangles of an IFC element, in the file's coordinates and length unit, to the daylight, solar, embodied-carbon, library and placement code.
- BimCraft
- 1 calculation
32-bit in part Open item -
Elevation grids into survey points and a grid surface
Places the cells of an elevation raster in the project's coordinates, converts heights between meters and feet, and makes survey points or a triangulated surface from the grid.
- CadCraft
- BimCraft
- CivilCraft
- 7 calculations
64-bit -
Elevation grids read from GeoTIFF and ASCII files
Reads a terrain grid's position, cell size and elevations from a GeoTIFF or an ESRI ASCII grid, with its scale, offset and no-data value.
- BimCraft
- CivilCraft
- 8 calculations
64-bit -
Ellipses and curves as short segments
Turns ellipses, sheared arcs, splines and outlines into runs of short straight segments, and measures ellipses.
- CadCraft
- 7 calculations
64-bit Open item -
Embodied carbon from quantities
Multiplies each item's quantity, with waste, by a carbon factor to give kilograms of CO2 equivalent.
- TakeoffCraft
- 4 calculations
64-bit Open item -
Energy model input file (IDF) and its results
Writes the rooms of a model as an IDF input file for an outside energy simulation engine, and reads back the design loads and yearly energy that engine reports.
- BimCraft
- 14 calculations
64-bit -
Engineering units: factors, dimensions and conversion
Reads a unit text such as W/(m^2 K), checks it is the right kind of quantity and converts values to and from SI.
- PartCraft
- 9 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.