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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Number conversion in LISP variants
Converts the value of a variant to another type when a LISP program asks for it.
- CadCraft
- 1 calculation
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 a PartCraft script file
Writes a part's dimensions, positions and parameters as text in a .pcscript file and reads them back.
- PartCraft
- 3 calculations
64-bit Open item -
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 edited PDF page content
How a number is written into the content stream of a PDF page that MarkupCraft edits.
- MarkupCraft
- 1 calculation
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 -
Numbers written into the VBA macro export
Turns a part's lengths, angles, points and check values into the numbers written in the exported .swb macro text, in meters and radians.
- PartCraft
- 11 calculations
64-bit Open item -
Numbers written to the saved PDF
Writes each markup into the PDF as an annotation: its position, its points, its drawn appearance, the sheet's scale and the measured text.
- MarkupCraft
- 13 calculations
64-bit Open item -
NURBS curves and surfaces: points, derivatives, normals and curvature
Evaluates a NURBS curve or surface at a parameter: its point, derivatives, tangent, normal and curvatures, and builds arcs and circles as exact rational curves.
- ModelCraft
- PartCraft
- 21 calculations in 5 files
64-bit Open item -
NURBS knot insertion and removal, degree change, split and join
Changes how a curve or surface is described without meaning to change its shape: adds or removes knots, raises or lowers the degree, splits, reverses, rescales the parameter and joins curves.
- ModelCraft
- PartCraft
- 15 calculations in 3 files
64-bit -
NURBS lengths, areas, closest points and tessellation
Measures a curve's length and a surface's area, finds the point of a curve or surface nearest a given point, and turns curves and surfaces into polylines and triangle grids within a tolerance.
- ModelCraft
- PartCraft
- 10 calculations in 3 files
64-bit Open item -
OBJ import and export
Reads and writes Wavefront OBJ files: points, faces, texture coordinates and normals as text, in meters with Y up.
- ModelCraft
- 6 calculations
64-bit Open item -
Objects on a tilted or flipped plane mapped to the plan
Maps circles, arcs, polylines, text, block references and hatches that a file stores in their own coordinate system onto the drawing's plan.
- CadCraft
- 6 calculations
64-bit -
Offcut stock after nesting
Works out the usable material left on a plate after a nest, keeps it as numbered remnants with their size and area, and nests the next job on remnants first.
- CadCraft
- PartCraft
- 13 calculations
64-bit -
Offset, extend, break and lengthen
Offsets an object by a distance, extends an end to a boundary, breaks an object between two points and lengthens or shortens it by an amount.
- CadCraft
- 5 calculations
64-bit Open item -
Open pit benches, haul ramp and pit surface
Works out the outline, area and perimeter of each bench, a haul ramp down the pit wall with its length and drop, and the pit cut into the ground with the volume dug.
- CivilCraft
- 6 calculations
64-bit -
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 -
Outline checks: inside, crossing, cut-outs
Decides whether a point is inside an outline, whether an outline crosses itself, and whether a cut-out sits fully inside its area and clear of the other cut-outs.
- TakeoffCraft
- 6 calculations
64-bit -
Outline minus holes: area and boundary lengths
Measures a closed outline with other shapes cut out of it: the remaining area, the length of outline left and the length of the cuts, as used for planted areas around paving, walls and steps.
- CivilCraft
- 5 calculations
64-bit Open item -
Overhead conductor sag and tension
Works out the load on a conductor in each load case, its tension by change of state on the ruling span, and the sag, length and support tensions of every span.
- CivilCraft
- 10 calculations in 2 files
64-bit -
Overhead line checks: clearances, support loads and sizing
Checks an overhead line span by span and support by support: clearance to the ground and to obstacles, phase spacing, insulator swing, the loads on each support, its size, foundation and fittings.
- CivilCraft
- 17 calculations in 4 files
64-bit Open item -
P&ID line geometry and connections
Works out where process and signal lines run, how long they are, and which symbols and lines they are joined to in a P&ID drawing.
- CadCraft
- 15 calculations in 4 files
64-bit Open item -
P&ID objects drawn from a built plant
Scales the P&ID symbols and lines of a plant built in millimeters to the drawing's units when they are drawn.
- CadCraft
- 1 calculation
64-bit -
P&ID placement, zones and values written to the drawing
Places P&ID symbols on process lines and connection points, cuts lines around inline symbols, draws hazard zones to scale, and writes imported stream values and relief sizes into the drawing.
- CadCraft
- 8 calculations
64-bit Open item -
Pad daylight lines and the graded surface
Finds where the cut and fill slopes around a pad meet the existing ground, and builds the proposed surface from the pad, its slopes and the ground outside them.
- CivilCraft
- 7 calculations
64-bit -
Pad side slopes and retaining walls
Reads a slope as typed, and works out the length, face area and heights of the retaining walls around a pad and the warnings for tall walls and steep slopes.
- CivilCraft
- 4 calculations
64-bit -
Paper sizes, drawing scales and viewport aim
Turns a scale 1:n and the drawing's units into a viewport scale, picks the standard scale at which a view fits, and sizes the space a new sheet leaves for views.
- CadCraft
- 10 calculations
64-bit -
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 -
Parameters and equations
Evaluates named parameters and the equations that drive dimensions, writes the results into the drawing or part, and solves backward for a parameter when a driven value is edited.
- CadCraft
- PartCraft
- 9 calculations
64-bit Open item -
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 -
Parcels: deed calls, closure, area and legal description
Reads bearings and distances, runs deed calls into corners, reports the misclosure and precision, and works out a parcel's courses, area, perimeter, labels and legal description.
- CivilCraft
- 13 calculations in 2 files
64-bit Open item -
Part and assembly mass in the bill of materials, measure panel and assistant
Mass, volume, area, center and inertia as the bill of materials, the measure panel and the assistant report them.
- PartCraft
- 5 calculations in 3 files
32-bit in part Open item -
Part and stock in machine coordinates
Turns the part into the machine's work frame for toolpaths: the stock block, the work origin, exact outlines of flat faces, hole positions and sizes, and the height of the part's top at any point.
- PartCraft
- 12 calculations
32-bit in part Open item -
Part export to STL, 3MF, DXF and STEP
Writes the part's mesh, a sketch, a face profile or a flat pattern to a file.
- PartCraft
- 9 calculations
64-bit Open item -
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 -
Pasted picture size
Sizes a pasted picture, or a copied area pasted at its true size, in drawing units.
- CadCraft
- 3 calculations
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 -
Pattern along a path
Places copies of a feature or body at stations along a path, optionally turned to follow it.
- PartCraft
- 5 calculations
64-bit -
Pattern outlines: curves, lengths and areas
Turns the points of a clothing pattern outline into a smooth curve, and measures lengths, areas and positions along it (Apparel add-on).
- CadCraft
- 10 calculations
64-bit -
Pattern piece lengths, seam walking and areas
Measures the sew line of a pattern piece: edge lengths, the distance round the outline between two points, seam walking against another piece, and the perimeter and area per size.
- CadCraft
- 4 calculations
64-bit -
Pattern pieces from drawing geometry
Makes a pattern piece from polylines, arcs, circles and ellipses of the drawing, places notches on it and moves its points by grips (Apparel add-on).
- CadCraft
- 9 calculations
64-bit 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
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.