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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Calculator results and export
Turns what a process calculator works out into the lines of its results table, its CSV export and the one figure it gives the status bar.
- CadCraft
- BimCraft
- 7 calculations in 2 files
64-bit Open item -
Carried, stamped and pasted markup geometry
Where markups land when they are carried onto a revised sheet, where a stamp or a picture is placed, and where copied page content is pasted.
- MarkupCraft
- 6 calculations in 3 files
64-bit Open item -
Check report values
The required and found values written in the Problems panel and in the check report exported as CSV.
Every app 64-bit, direct- 1 calculation
64-bit Open item -
Clipping block references to a boundary
Cuts the lines, arcs and fills of a clipped block reference or linked drawing at the clip polygon, and converts the clip between drawing and block coordinates.
- CadCraft
- 10 calculations
64-bit Open item -
COBie export: sizes, areas and durations
Writes floor elevations and heights, room heights and areas, warranty durations and expected life into the COBie workbook, and reads service life and warranty back from one.
- BimCraft
- 6 calculations
64-bit -
Columns: height and quantities
Works out a column's height from its levels and the length, cross-section area and volume written with it.
- BimCraft
- 4 calculations
64-bit -
Constraint values and signs
Measures what a dimensional constraint holds (distance, radius, diameter, angle), records which side or direction a constraint applies to, and decides what an edit moved.
- CadCraft
- 13 calculations
64-bit Open item -
Constraints kept through mirror and trim
Works out again the sense of an angle constraint on mirrored geometry and decides which piece of a trimmed object keeps each constraint.
- CadCraft
- 2 calculations
64-bit -
Control program host: placement position and turn
Lets a control program read and set the position, the turn about the vertical axis and the visibility of top-level placements.
- ModelCraft
- 2 calculations
64-bit -
Controller standard functions and integer types
Timers, counters, arithmetic functions and type conversions of the soft controller.
Every app 64-bit, direct- 6 calculations
64-bit Open item -
Coordinate readouts and survey point
Says where a point is: its distance from the project origin, the level it is on, its height above that level and its map grid coordinates.
- BimCraft
- 8 calculations
64-bit -
Coordinate system helpers
Finds the coordinate systems a project's coordinates fit, reads and writes latitude and longitude text, applies a local grid fit, and converts a project's coordinates to another system.
- CivilCraft
- 7 calculations
64-bit -
Cores of a cable on a schematic
Finds which wires a cable marker's slash crosses, in order, for the cable list.
- CadCraft
- 2 calculations
64-bit Open item -
Countertop outline and quantities
Finds the run of cabinets a countertop covers, pushes the front edges out by the overhang, and writes the countertop's shape, area, perimeter and front edge length.
- BimCraft
- 4 calculations
64-bit -
Counting blocks, shapes and texts in a CAD drawing
Finds every block reference, shape and text of a DWG or DXF drawing with its place, and counts the ones that match.
- TakeoffCraft
- 5 calculations in 2 files
64-bit -
CraftScript array arithmetic
The elementwise operators, matrix product, backslash, ranges and sums that a script's own formulas run on.
- PartCraft
- 9 calculations
64-bit Open item -
CraftScript dense linear algebra
Solves dense systems and works out inverses, determinants, factorizations, eigenvalues, norms and condition numbers in a script.
- PartCraft
- 13 calculations
64-bit Open item -
CraftScript operators in the interpreter
Carries out the arithmetic a script writes: scalar operations, matrix division and powers, and the values of a counted loop.
- PartCraft
- 3 calculations
64-bit -
CraftScript sparse matrices and direct factorization
Builds sparse matrices in a script, adds and multiplies them, assembles element matrices, and factors a symmetric positive definite one.
- PartCraft
- 8 calculations
64-bit -
CraftScript values: storage, reading and number text
Holds the numbers a script works with, reads them back from a saved part, and writes the text shown when a statement echoes its result.
- PartCraft
- 5 calculations
64-bit -
Cross sections and end-area volumes along an alignment
Cuts the ground and the design along sample lines square to an alignment, works out cut and fill areas at each section and the volumes between sections.
- CivilCraft
- 10 calculations
64-bit Open item -
Cursor point and status readouts
Works out the point a click stands for when ortho is on, and the coordinates, distance and angle shown in the status line and beside the cursor.
- CadCraft
- 6 calculations
64-bit -
Curves through points
Makes a curve that passes through every given point, with optional end directions.
- ModelCraft
- PartCraft
- 5 calculations in 2 files
64-bit -
Cut-list nesting of bars
Nests the linear parts of a model on stock bars and reports the bars to buy, the length bought and used, the drop of each bar and the waste.
- BimCraft
- DetailCraft
- 3 calculations
64-bit -
Decal placement and size
Works out where a clicked point lies on a face in the face's own coordinates, and the size a placed decal is stored with.
- ModelCraft
- 5 calculations
64-bit Open item -
Depth and angle set by dragging a handle
Works out the new extrude depth or revolve angle when the handle of a selected feature is dragged.
- PartCraft
- 3 calculations
64-bit -
Design study variants and ranking
Makes the list of variants a design study runs, checks each result against its limits, finds the trade-off front and ranks the variants.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 6 calculations
64-bit Open item -
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 -
Dimension measurement and geometry
Measures what a dimension spans from its defining points and works out its extension lines, dimension line, arrowheads and text position.
- CadCraft
- 8 calculations
64-bit -
Dimension text: units, rounding and tolerances
Writes the number a dimension shows: measurement scale, round-off, decimal places, degrees-minutes-seconds, alternate units and tolerance limits.
- CadCraft
- 11 calculations
64-bit Open item -
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 -
Distance, area, angle and point inquiries
Works out what DIST, AREA, MEASUREGEOM, ID and LIST print: distances, Δx and Δy, angles, areas, perimeters, running area totals and coordinates; and the unit factor EXPORTPOINTS applies to the points it writes.
- CadCraft
- 8 calculations
64-bit -
Doors and windows in walls
Works out where a door or window sits along its wall, whether it fits, the box that cuts the wall, and the sizes and area written with it.
- BimCraft
- 9 calculations
64-bit -
Dormer geometry
Works out a gable or shed dormer on a roof face: its roof planes, front and cheek walls, where it meets the main roof, and the hole cut in the roof.
- BimCraft
- 5 calculations
64-bit -
Drafting lines and hatch regions
Keeps the drafting lines and hatch regions drawn in a view, checks them, moves them and works out the strokes of each hatch pattern inside its region.
- BimCraft
- 11 calculations in 2 files
64-bit -
Drainage structure types and their library items
Works out the inside and outside size of a manhole, inlet or junction type, and writes the type as a library item in millimeters and reads it back.
- CivilCraft
- 6 calculations
64-bit -
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 annotations: tolerance frames, datums and surface finish
Lays out feature control frames, datum symbols and surface texture symbols on a drawing sheet and writes their tolerance and roughness values.
- PartCraft
- 3 calculations
64-bit -
Drawing audit: zero-size and duplicate objects
Finds lines of zero length, circles and arcs of zero radius, and objects that are exact copies of another, so they can be listed and erased.
- CadCraft
- 2 calculations
64-bit -
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 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 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 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 -
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 -
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 -
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
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.