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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Sheet and path of a point on a schematic
Finds which numbered path column of a sheet frame a device or wire sits in, for the place printed in cross-references and lists.
- CadCraft
- 2 calculations
64-bit -
Sheet nesting
Lays parts out on sheets or a roll, reports the sheets used and the efficiency, checks the result, reads part outlines from DXF and writes the nest as DXF.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 19 calculations
64-bit Open item -
SHX font text: strokes and width
Turns the shapes of a loaded .shx font into strokes, and gives a text's width and the position of each stroke in the drawing.
- CadCraft
- 7 calculations in 2 files
64-bit -
Size of a copied area
Works out how big a copied area of a sheet is on paper and in the real world, the pixel size it is rendered at, and the scale and turn that fit it to two picked points.
- CadCraft
- BimCraft
- MarkupCraft
- DetailCraft
- 5 calculations
64-bit -
Sketch exchange macro and import
Writes the drawing as a .swb sketch macro with its coordinates in meters, and reads an exported sketch back as geometry, constraints and dimensions.
- CadCraft
- 8 calculations
64-bit Open item -
Sketch photo to drawing
Finds a sheet of paper in a photo, straightens it, and turns the pen lines on it into lines and arcs at a stated scale.
- CadCraft
- 6 calculations
64-bit Open item -
Smooth shading and texture placement
The normals that make faces joined by soft edges shade as one surface, and where an imported texture lies on a face.
- CadCraft
- ModelCraft
- 3 calculations
32-bit, display only -
Snap points picked in the 3D view
The 3D point a click gives when it snaps to a face, an edge, a midpoint, a face center, an axis direction or a locked direction. That point becomes model geometry.
- CadCraft
- ModelCraft
- 12 calculations
64-bit Open item -
Solvers shared by the process engine
The linear solve, Newton iteration, ODE integrator and bracketed root finder that the flowsheet, reactors and design specifications call.
- CadCraft
- BimCraft
- 4 calculations
64-bit Open item -
Solving an expression for one parameter
Finds the value of one parameter that makes an expression give a wanted result, the other parameters held.
- CadCraft
- BimCraft
- PartCraft
- 2 calculations
64-bit Open item -
Spending on a person's own AI model
Adds up what calls to a person's own AI model have cost today and this month, and stops a call that could pass the limits the person set.
Every app 64-bit, stated limit- 4 calculations
64-bit -
Spline through fit points
Works out the control points and knots of a cubic spline that a drawing stores only by its fit points and end tangents.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- 5 calculations
64-bit Open item -
Splines: curve points, fitting and editing
Evaluates a spline, builds one through fit points or from control points, turns it into points for drawing and measuring, and inserts control points without changing the curve.
- CadCraft
- 12 calculations in 2 files
64-bit Open item -
Spoken lengths, directions and extents
Works out the lengths, distances, directions and extents that CadCraft says when the drawing is described in words.
- CadCraft
- 9 calculations
64-bit Open item -
Spread between coarse and refined results
States how far a coarse live result is from the refined one, as a fraction.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 1 calculation
64-bit -
Stack plume rise and air dispersion screening
Works out the effective height of a stack plume, the worst-case and hour-by-hour ground concentrations at receptors, and the contours drawn on a plan.
- CadCraft
- BimCraft
- 10 calculations in 2 files
64-bit Open item -
Stage lighting plot: positions, fixtures and loads
Measures the pipes and trusses fixtures hang on, spreads fixtures evenly along them, finds which position a fixture belongs to and totals the wattage.
- CadCraft
- 11 calculations in 3 files
64-bit -
Standard parts and library items
Works out the dimensions, mass and drawing of standard bolts, nuts, washers, pins, keys, bearings and gears, and turns parts and steel sections into library items.
- CadCraft
- PartCraft
- 9 calculations in 2 files
64-bit -
Standard sections: member solids, mass and parts list
Builds a steel member as a solid from a standard section, shows a section's mass per meter, and totals the placed parts into a parts list.
- CadCraft
- 4 calculations
64-bit -
Steel member checks on a solved frame
Runs the steel code checks along every member for every strength combination, finds the governing ratio, checks the deflection limit, and finds what gives way first.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations in 2 files
64-bit -
Steel member resistance to EN 1993-1-1
The design resistances of a rolled I or H section: classification, tension, bending, shear, buckling, lateral-torsional buckling and the combined checks.
- CadCraft
- BimCraft
- DetailCraft
- 11 calculations
64-bit Open item -
Steel member strength to AISC 360-16
The design strengths of a rolled I-shape in tension, compression, bending and shear, and the combined bending and axial check.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations
64-bit Open item -
Steel section dimensions, areas and outlines
Gives the dimensions, published area and mass of every steel section in millimeters, the exact area from the dimensions, and the outline used to draw and sweep it.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 6 calculations
64-bit Open item -
Sun position for shadows
The sun's altitude and azimuth for a date, clock time, latitude, longitude and time zone, and the direction shadows are cast from.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- 5 calculations
64-bit -
Survey levels from text and the survey check
Reads spot levels written as text or block attributes into points with a height, and checks a surveyor's drawing for unit, origin, flat-contour, outlier and duplicate problems.
- CadCraft
- BimCraft
- CivilCraft
- 6 calculations
64-bit -
Symbols imported from another drawing
Turns a block of a DWG or DXF drawing into an electrical symbol in millimeters, with its connection points.
- CadCraft
- 4 calculations
64-bit -
Tapered, revolved and swept solids
Builds a solid from a 2D outline: an extrusion with tapered sides, a revolution about an axis, or a sweep along a path.
- CadCraft
- 6 calculations
64-bit -
Text from drawings as stroked edges
The line segments that draw the text of an imported drawing in the 3D model, and the width of a string.
- CadCraft
- ModelCraft
- PartCraft
- 3 calculations
64-bit -
Three-phase flash
Splits a mixture into a vapor and two liquids at a temperature and pressure with an activity-coefficient model.
- CadCraft
- BimCraft
- 4 calculations
64-bit -
TIFF scan resolution
Reads the resolution of a scanned drawing from a TIFF file as dots per inch.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- PartCraft
- 2 calculations
64-bit -
Tracing a scan into lines and arcs
Turns the black-and-white pixels of a scanned drawing into lines and arcs, cleans them up, and offers their ends, middles, centers and crossings as snap points.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- PartCraft
- 10 calculations in 2 files
64-bit Open item -
Triangulation of faces with holes
Splits a flat face, with any holes, into triangles.
- CadCraft
- ModelCraft
- TakeoffCraft
- 9 calculations
64-bit -
Triangulation of solid faces
Splits a face of an imported 3D solid, with its holes, into triangles; the triangles are what the solid's mesh is built from.
- CadCraft
- ModelCraft
- 6 calculations
64-bit -
Trim
Cuts a line, arc, circle, polyline or construction line at the objects that cross it and keeps or removes the pieces.
- CadCraft
- 4 calculations
64-bit Open item -
Truss geometry, cut list and shop outputs
Builds the centerline frame of a truss from its type or from the roof's section, and produces the cut list, joint schedule, jig drawing, stock plan, 3D members and CAD drawings.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 26 calculations in 7 files
64-bit Open item -
Truss layout 3D picture
Draws the truss layout as a wireframe picture seen from an angle.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 3 calculations
32-bit, display only -
Truss layout over a roof
Sets out the trusses along a roof: where each one stands, its span, and which trusses share a design, including hip-end girders and jacks and valley sets.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 9 calculations in 2 files
64-bit Open item -
Truss member forces and timber checks
Works out the force in every member of a roof truss for each load case and combination, checks each member in tension or compression with bending, picks sizes, and estimates deflection and bearing reactions.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 20 calculations in 3 files
64-bit Open item -
Typed lengths and length readouts in 3D
Reads a length typed in feet, inches, fractions or metric units into meters, and writes lengths, areas and volumes in the model's unit.
- CadCraft
- ModelCraft
- 8 calculations
64-bit -
Typed points, distances and angles
Turns what is typed or clicked at a prompt (x,y, @dx,dy, distance<angle, a distance along the cursor direction, an angle in degrees) into the point, length or angle a command uses.
- CadCraft
- 5 calculations
64-bit Open item -
Unit conversion
Converts lengths, areas, volumes, angles and slopes between 57 units.
Every app Exact values- 4 calculations
64-bit -
Unit table: reading and writing values
Holds every unit's size as an exact fraction, reads typed values such as 12'6 1/2", 45°30'15" or 3:1, and writes values as feet and inches, degrees-minutes-seconds or decimals.
Every app Exact values- 8 calculations
64-bit -
USD mesh coordinates in saved and exported files
Writes the points of every mesh into a USD file and reads them back when a USD file is opened.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 7 calculations in 3 files
32-bit in part Open item -
USD transforms and placement
Works out where every object of a USD scene sits: each object's own transform, its place in the world, the change to meters with Z up, and the placement of instanced copies.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 11 calculations in 3 files
64-bit Open item -
User coordinate system set by command
Works out the origin and angle of the user coordinate system that UCS and the quarter-turn commands set, and what they print.
- CadCraft
- 4 calculations
64-bit Open item -
User coordinate systems
Converts points, directions and angles between a user coordinate system and world coordinates, and sets a coordinate system from points or from an object.
- CadCraft
- 5 calculations
64-bit -
Values changed when a DWG is written
The few places where the DWG writer changes a number on its way into the file: lineweights, ellipse axes, ray directions, the drawing extents and the defaults of a light.
- CadCraft
- ModelCraft
- CivilCraft
- DetailCraft
- PartCraft
- 5 calculations in 2 files
64-bit Open item -
Values given to assistants and scripts
Rounds and reports the coordinates, lengths, areas and sheet sizes that an assistant or a script reads from a drawing, and writes a plot as SVG.
- CadCraft
- 12 calculations
64-bit Open item -
Values typed in the Properties panel
Reads what is typed into a number field: plain numbers, lengths with units, angles, and expressions such as =3'6"/2.
- CadCraft
- 6 calculations
64-bit Open item -
Vessel outline and inside volume
Works out the revolved outline of a vessel with its two heads, its height and inside volume, and where a nozzle sits on it.
- CadCraft
- BimCraft
- 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.