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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Line sizing and pressure drop
Works out velocity, Reynolds number, friction factor and pressure drop of each line, picks pipe sizes, and fills the stream table that is drawn on the P&ID.
- CadCraft
- BimCraft
- 13 calculations in 3 files
64-bit -
Line, arc and circle intersections
Where two drawn objects cross: the basis of snaps, trim and extend.
- CadCraft
- 4 calculations
64-bit Open item -
Linetype dashes
Cuts lines and arcs into the dashes, gaps and dots of their linetype for the screen and for plots.
- CadCraft
- 2 calculations
64-bit -
Lineweights in a DWG file
Converts a lineweight between its value in hundredths of a millimeter and the index a DWG file stores.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- 2 calculations
Exact -
LISP arithmetic, conversions and geometry
The numbers a LISP routine gets from the built-in arithmetic, number and angle formatting, unit conversion and point geometry functions.
- CadCraft
- 12 calculations
64-bit Open item -
Load flow and short-circuit currents
Bus voltages, branch flows and losses of an AC network, and fault currents by symmetrical components.
Every app 64-bit, stated limit- 12 calculations in 3 files
64-bit Open item -
Load reserve and escape route checks
Finds the load factor at which a design first reaches its limit, and the narrowest door on the best way out of every room.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 3 calculations
64-bit Open item -
Luminaire files and point-by-point illuminance
Reads luminaire photometry files (IES LM-63 and EULUMDAT) and works out the direct illuminance on a grid of points, with its minimum, average, maximum, uniformity and power density.
- CadCraft
- BimCraft
- 17 calculations in 2 files
64-bit -
Lumped system models
Operating point and response over time of electrical, thermal, hydraulic and mechanical networks built from lumped elements.
Every app 64-bit, stated limit- 12 calculations in 3 files
64-bit Open item -
Magnetic and electric field solvers
The field of wire segments, the mutual inductance of loops, and 2D finite-element magnetic and electric fields with energy, capacitance and force.
Every app 64-bit, stated limit- 12 calculations in 2 files
64-bit Open item -
Map layers under the drawing
Draws map pictures and tiles under the drawing, warped from the map's coordinate system to the drawing's.
- CadCraft
- BimCraft
- 2 calculations
32-bit, display only -
Map layers: web Mercator, tile grids and world files
Converts longitude and latitude to web Mercator and back, lays out the tiles of a map service, reads a picture's world file, and writes the box of a map request.
- CadCraft
- BimCraft
- CivilCraft
- 10 calculations
64-bit Open item -
Map pictures warped onto the plan
Picks the tile level for the screen and cuts a map picture into pieces that are each drawn with one affine transform.
- CadCraft
- BimCraft
- CivilCraft
- 3 calculations
32-bit, display only -
Markers: pieces laid on fabric
Keeps the pieces of a marker on the fabric, checks grain direction and overlaps, and works out the marker's length and fabric use (Apparel add-on).
- CadCraft
- 9 calculations
64-bit Open item -
Member axes and section properties
Works out each frame member's length and local axes, and the area, second moments and torsion constant of a section from its outline.
- CadCraft
- BimCraft
- DetailCraft
- 6 calculations
64-bit Open item -
Meshing a slab or wall into plates
Cuts a slab or wall outline into four-node plates and places their nodes in the frame model.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations in 2 files
64-bit -
Model points written to USD
Writes the vertices and edges of a model into USD meshes and curves.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 2 calculations
32-bit in part Open item -
Molar mass and group-contribution estimates
Works out a molecule's formula and molar mass from its structure and estimates boiling point, critical constants, formation energies and heat capacity by Joback's method.
- CadCraft
- BimCraft
- 4 calculations
64-bit -
Molecular dynamics
Simulates atoms under Lennard-Jones, bonded and Coulomb forces and reports temperature, pressure, energies, density, radial distribution and diffusion.
- CadCraft
- BimCraft
- 22 calculations in 3 files
64-bit Open item -
Move, rotate, scale and mirror
Applies a move, rotation, scale or mirror to drawing objects, and places block references and viewports.
- CadCraft
- 8 calculations
64-bit Open item -
Move, rotate, scale, mirror, array, stretch and lengthen
Builds the transform or the length change for the modify commands from the picked points and typed values.
- CadCraft
- 10 calculations
64-bit -
Moving a grid line with what hangs on it
Moves a grid line sideways by a distance and carries the walls, columns, bubbles, tags and dimension points that sit on it.
- CadCraft
- 2 calculations
64-bit -
Multileader geometry
Works out what a multileader draws: its line with the landing, the arrowhead and where the text starts.
- CadCraft
- 2 calculations
64-bit -
Nesting add-on: outlines in, placed copies out
Reads closed outlines and their holes from the drawing as parts for the nesting engine, and writes the placed copies and sheet rectangles back.
- CadCraft
- 5 calculations
64-bit -
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 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 -
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 -
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 -
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 -
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 -
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 -
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 -
PDF underlay in a plot
Plots the lines, curves, fills and text of a PDF underlay at its place in the drawing.
- CadCraft
- 1 calculation
64-bit Open item -
PDF underlay placement and PDF import
Places a PDF page at its true size in the drawing's units, and turns a page's lines, arcs, circles, fills and text into drawing objects.
- CadCraft
- 13 calculations in 2 files
32-bit in part Open item -
Pen sketch cleanup
Decides what a freehand stroke was meant to be (a line, circle, arc, rectangle or polyline) and makes that exact shape, then joins nearby ends.
- CadCraft
- MarkupCraft
- 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.