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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Threaded solver kernels and conjugate gradients
Runs the matrix products, dot products and vector updates of the simulation solvers on several threads, and the conjugate-gradient solves built on them.
- PartCraft
- 12 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 -
Time of day, date and exposure from plain words
Works out the clock hour for a named time of day (dawn, noon, golden hour, dusk and so on), the date for a season, and the exposure for the weather.
- ModelCraft
- 3 calculations
64-bit -
Tolerance stack-ups
Adds up a chain of dimensions and their tolerances across an assembly: the nominal and mean gap, the worst-case and statistical spread, each link's share, and the share of assemblies expected outside the limits.
- PartCraft
- 10 calculations
64-bit Open item -
Traced sketch into model edges
Turns the lines, arcs and circles traced from a photo of a hand sketch into straight edges on the ground.
- ModelCraft
- 1 calculation
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 -
Transition curves and sampled alignment geometry
Evaluates the six kinds of transition curve (clothoid, cubic parabola, Bloss, Helmert, sine half-wave, sine), finds the nearest point on one, and cuts curves into straight pieces for linework.
- CivilCraft
- 12 calculations
64-bit -
Traverse closure and compass adjustment
Runs a survey traverse from field angles or bearings and distances, reports its angular and linear misclosure and precision, and adjusts the stations by the compass rule.
- CivilCraft
- 4 calculations
64-bit -
Trees, people and cars from numbers
Generates the mesh and plan symbol of each starter tree, shrub, rock, person and car from a size and a seed.
- ModelCraft
- 7 calculations
64-bit -
Triangle mesh built from IFC geometry
Holds every shape read from an IFC file as triangles, moves and joins them, and hands the result to the app.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 5 calculations
32-bit in part Open item -
Triangles inside a trimmed face
Adds points inside a triangulated face and keeps the triangles well shaped, for curved faces read from a .3dm file.
- ModelCraft
- PartCraft
- 6 calculations
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 -
Trim, extend and corner walls
Finds where two wall center lines meet and the new ends of a wall trimmed or extended to another.
- BimCraft
- 5 calculations
64-bit -
Trimmed surfaces: loops, cut tessellation and area
Keeps the part of a surface inside trim loops drawn in its (u, v) plane, cuts the tessellation along them and reports the area of the part shown.
- ModelCraft
- PartCraft
- 11 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 -
Turning a face mesh back into an extrusion
Recognizes a closed triangle mesh that is a straight prism and rewrites it in the IFC file as an outline pulled along a depth, so it stays editable.
- BimCraft
- 6 calculations
64-bit Open item -
Typed distances and coordinates while drawing
Places the next point of a run or outline from a typed distance, a distance and angle, or a pair of coordinates, and reads a typed spot elevation.
- TakeoffCraft
- 5 calculations in 2 files
64-bit -
Typed lengths and item units
Reads a typed length (feet-inches with fractions, decimal feet, inches, meters, centimeters, millimeters) into feet, and converts feet and square feet into an item's unit.
- TakeoffCraft
- 7 calculations
64-bit -
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 lengths, angles and pitches
Turns what a person types (feet and inches, fractions, metric, a point or a polar step, a roof pitch) into millimeters and degrees, and formats areas, angles and pitches for display.
- BimCraft
- 6 calculations
64-bit Open item -
Typed lengths, stations and unit text
Reads lengths and stations as typed, and writes stations, areas, volumes and bearings as text.
- CivilCraft
- 8 calculations
64-bit Open item -
Typed points and door or window positions
Turns a typed length, step, polar entry or distance into the next wall point, and places a door or window along a wall from the pointer or a typed distance.
- BimCraft
- 2 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 -
Typed scale factors and shrinkage allowance
Reads a scale factor a person types, and gives the pattern factor for a casting that shrinks as it cools.
- ModelCraft
- PartCraft
- 2 calculations
64-bit -
Underground cable routes: cover, crossings, joints and trench quantities
Works out a cable route's length, its cover under the surface, its vertical separation from pipes and other routes it crosses, the joints it needs and the trench quantities.
- CivilCraft
- 10 calculations
64-bit -
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 -
Units and tolerance read from a 3DM file
The size of one file unit in meters and the modeling tolerance of an opened 3DM file.
- ModelCraft
- PartCraft
- 2 calculations
64-bit -
Unsteady flow routing down a river
Routes a flood hydrograph down the cross-sections of a river model and reports water levels, flows, their peaks and a volume balance over time.
- CivilCraft
- 6 calculations
64-bit Open item -
USD export and render hand-off
Writes the open IFC models as an OpenUSD file and works out the transform that places the cameras, sun and lamps of a render hand-off in that file's world.
- BimCraft
- 6 calculations in 2 files
32-bit in part Open item -
USD export of a part or assembly
Writes the part's mesh, its placement in an assembly, and its volume and mass to an OpenUSD file in meters with Z up.
- PartCraft
- 3 calculations
64-bit -
USD export of the steel model
Writes each steel part as an extruded section in an OpenUSD file in meters, with its length and weight.
- DetailCraft
- 3 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 save, open and import
Opens ModelCraft's own USD files back to the exact model, takes in changes another program made, and imports any other USD scene in meters with Z up.
- ModelCraft
- 6 calculations
64-bit -
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 -
UV coordinates: unwrap result, projections, packing, stretch and editing
Writes texture coordinates for each face corner from an unwrap, a box, cylinder, sphere or view projection, packs UV islands into the unit square, measures stretch and moves UVs in the UV editor.
- ModelCraft
- 12 calculations in 3 files
32-bit in part Open item -
UV unwrap solvers
Flattens a piece of a mesh into the UV plane with as little distortion of angles as the method allows.
- ModelCraft
- 8 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 stored from picks in the workspace
Turns a picked flat face, a click on a drawing view or a new section into the plane, point or offset that is saved in the part or assembly.
- PartCraft
- 4 calculations
64-bit -
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 -
Values typed or picked in the main window
Takes what is typed in a property box or picked in the plan and profile views and stores it in the model: lengths, coordinates, profile points, pad elevations and default curve radii.
- CivilCraft
- 8 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.