Resources
Numerical accuracy
The calculations in our apps: the policy each one is under, the precision it runs at, and the code itself.
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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2.5-axis toolpaths
Generates the tool moves for facing, pockets, contours, drilling and chamfering: depth levels, entry helixes and ramps, lead arcs, tabs and hole depths.
- PartCraft
- 17 calculations
64-bit -
2D curve offsets for toolpaths
Offsets outlines made of lines and arcs by the tool radius, intersects and trims them, and measures their lengths, areas and distances.
- PartCraft
- 18 calculations
64-bit -
3D check view: walls, slabs and their quantities
Stands the takeoff up in 3D (walls from runs with a height, slabs from areas with a depth) and reports each object's length, wall area, net area and volume.
- TakeoffCraft
- 6 calculations
64-bit -
3D drawing and editing tools
Turns clicks and typed values into the arcs, rectangles, offsets, moves, rotations, scales, guides and dimensions that are stored in the 3D model.
- CadCraft
- ModelCraft
- 18 calculations
64-bit -
3D frame analysis
Member forces, reactions and deflections of a 3D frame by the direct stiffness method.
- CadCraft
- BimCraft
- DetailCraft
- 4 calculations
64-bit -
3D vectors, planes and transforms
The vector, plane, ray and 4×4 matrix helpers that the 3D modeling kernel uses for every point it stores.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- 12 calculations
64-bit Open item -
3D-print mesh repair
Fixes a mesh for printing: removes tiny loose pieces, closes holes and turns inside-out pieces, and reports what it changed.
- ModelCraft
- 4 calculations
64-bit -
3DM curves and surfaces: points on them
Works out points on the lines, arcs, NURBS curves, planes, NURBS surfaces, surfaces of revolution and sum surfaces a .3dm file stores.
- ModelCraft
- PartCraft
- 9 calculations
64-bit -
3DM mesh import: placement and units
Brings the meshes of a .3dm file, including block placements, into one triangle list in the part's units.
- PartCraft
- 2 calculations
64-bit -
Activity coefficients and Henry's law
Works out liquid activity coefficients by NRTL, Wilson and UNIQUAC and Henry's constants for dissolved gases.
- CadCraft
- BimCraft
- 6 calculations
64-bit -
Add-on solids placed on the 3D tab
Converts the faces an add-on hands over from drawing units into the 3D model's units and places them.
- CadCraft
- 1 calculation
64-bit -
Advanced simulation add-on: result summary and color bands
Lists the headline numbers of a nonlinear or contact result and cuts the deformed plot mesh into color bands with a legend.
- PartCraft
- 3 calculations
64-bit -
Align and distribute
Works out the move, turn and scale that carry picked source points onto destination points, and the moves that line objects up or space them evenly.
- CadCraft
- 5 calculations
64-bit -
Alignment lines and circular curves
Works out a horizontal alignment from its points of intersection: tangents, circular curves, curve facts, stations, and the station and offset of any point.
- CivilCraft
- 7 calculations
64-bit -
Anchor points of manual annotations
Turns a point picked on a part in the Illustrate workspace into the anchor that labels, arrows and measurements of a manual are attached to.
- PartCraft
- 1 calculation
64-bit -
Arc through three points and angle measurement
Works out the arc markup's circle from its three points, its length, and the angle between two legs shown by the angle measurement.
- MarkupCraft
- 5 calculations
64-bit Open item -
Arcs from bulges and three points
Works out the circle behind each arc segment of a run or an outline, the arc through three picked points, and the numbers shown while a mark is being drawn.
- TakeoffCraft
- 9 calculations in 2 files
64-bit Open item -
Area markup with cut-outs, and clipboard placement
The area and perimeter of an area markup less its cut-outs, whether cut-outs fit, and where pasted markups land.
- MarkupCraft
- 6 calculations in 2 files
64-bit -
Area, perimeter and length
Works out the area and perimeter of circles, polylines and hatches and the length of lines, arcs, polylines and splines.
- CadCraft
- 5 calculations
64-bit Open item -
Areas of flat upward faces by color
Adds up the area of the level, upward-facing faces on screen for each color, in square meters, for the wet-surface look.
- ModelCraft
- 1 calculation
64-bit Open item -
Arithmetic on typed lengths
Works out a length typed as an expression, such as 4+7/16 or 2*450mm, wherever a length is asked for.
- CadCraft
- ModelCraft
- MarkupCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 4 calculations
64-bit -
As-built points compared with the drawing
Brings the drawing's design points and surveyed as-built points to the same units, compares them against a tolerance, and marks and reports the differences.
- CadCraft
- 3 calculations
64-bit -
Assembly joints and part placement
Works out where each part of an assembly sits from its joints: mate frames on faces, the motion each joint allows, and the chain of transforms from the grounded part.
- PartCraft
- 7 calculations
64-bit Open item -
Asset service life and maintenance due dates
Stores an asset's service life in the IFC file and reads it back in years, and marks maintenance as overdue or due soon from its next date.
- BimCraft
- 4 calculations
64-bit -
Assistant answers: fire ratings and room areas
Answers two questions a connected assistant asks of the open model: which walls have a given fire rating, and which rooms are under or over a given area.
- BimCraft
- 3 calculations
64-bit -
Automatic constraints and dimension conversion
Finds ends that meet and lines that are level or upright and constrains them, and turns a plain dimension into a constraint on the objects it measures.
- CadCraft
- 2 calculations
64-bit -
Automatic dimensions
Chooses what to dimension from the level and plumb edges, openings, circles and grid lines of a drawing and places chains, overall dimensions and diameters.
- CadCraft
- 6 calculations
64-bit Open item -
Automatic plan dimensions
Chooses the points an automatic row of dimensions measures between: the building's overall size and the stops along each outside edge.
- BimCraft
- 6 calculations
64-bit Open item -
Automatic sheet layout
Splits a drawing into parts, picks a paper size and standard scale, and places a viewport for every part on the sheet.
- CadCraft
- 7 calculations
64-bit -
B-spline basis functions
The basis functions and derivatives under every NURBS curve and surface.
- ModelCraft
- PartCraft
- 3 calculations
64-bit -
Batch schedule and batch inventory
Places a recipe's steps on the plant's vessels for a number of batches and reports start and finish hours, utilization, cycle time and batches per day; keeps a mole inventory of charges, transfers, reactions and discharges.
- CadCraft
- BimCraft
- 4 calculations
64-bit -
BCF viewpoint of a markup
The camera position and view scale written to a BCF file for each markup, in meters of paper.
- MarkupCraft
- 1 calculation
64-bit -
Bearings and degrees-minutes-seconds
Reads typed quadrant bearings and degrees-minutes-seconds angles, and writes angles in decimal degrees, degrees-minutes-seconds, grads, radians or surveyor's bearings.
- CadCraft
- 6 calculations
64-bit -
Beginner shapes, align and drop to ground
Builds the 20 mm starter shapes (box, cylinder, cone, sphere, roof) and moves placements so their boxes line up or stand on the ground.
- ModelCraft
- 6 calculations
64-bit -
Bid packages and leveling
Our own cost of each bid package, each subcontractor's bid leveled with plugs for the scope it leaves out, the low bid, and the base bid with the chosen bids in it.
- TakeoffCraft
- 5 calculations
64-bit -
Blank pages: paper sizes and grid
The size of a new blank page in PDF points and the positions of its grid lines or dots.
- MarkupCraft
- 2 calculations
64-bit -
Board geometry and clearances
Distances between tracks, pads and zones, point-in-shape tests, areas and pad positions on a printed circuit board.
Every app 64-bit, direct- 10 calculations in 2 files
64-bit Open item -
Bodies: volume, move and scale
Lists each body with its volume and box, and moves, copies or scales bodies.
- PartCraft
- 4 calculations
64-bit -
Body move, scale and path pattern arithmetic
Builds the matrices that move, rotate and scale bodies, and the positions of pattern copies along a path.
- PartCraft
- 5 calculations
64-bit -
Bone frames and pose matrices
Works out each bone's rest frame from its head, tail and roll, and the matrices that carry the mesh from rest to a pose.
- ModelCraft
- 6 calculations in 2 files
64-bit -
Boring logs and the soil profile between borings
Cleans boring logs, corrects blow counts, places borings along a section line and joins their layers into a soil profile.
- CivilCraft
- 6 calculations
64-bit -
Box tree for picking and collisions
Finds which items have a box that a point range or a ray touches, for picking, snapping and collision checks.
- CadCraft
- ModelCraft
- PartCraft
- 2 calculations
64-bit -
Building data for flood, wind and earthquake checks
Takes room floor heights, opening sills, storey heights, areas, widths and masses from the model for the hazard checks.
- BimCraft
- 3 calculations
64-bit -
Cabinet job totals: linear stock and sheet count
Adds up the hardwood to buy by length and counts the sheets a nested job uses.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 2 calculations
64-bit -
Cabinet parts from a box and construction rules
Turns a cabinet's width, height and depth and the shop's construction rules into the parts to cut: sides, bottom, top or rails, back, shelves, doors, drawer fronts and drawer boxes.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 6 calculations
64-bit -
Cabinet plan, elevation, section and 3D boxes
Builds the drawing geometry of a cabinet job: each cabinet in plan, front view and section, the dimensioned shop drawings, and the boxes of the 3D view.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 13 calculations in 3 files
64-bit Open item -
CabinetCraft room picking and dry-run units
Snaps picked room corners to a grid, decides which way round the picked outline runs, and converts sheet sizes between the job's units and a G-code program's units for the dry run.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 4 calculations
64-bit Open item -
Cabinets along a wall line
Places cabinets one after another along a wall line picked in the plan, finds which cabinets belong to a front view, and prints areas and lengths of the cut list (Cabinet add-on).
- CadCraft
- 6 calculations
64-bit -
Calc sheet units, functions and driven parameters
The unit factors, powers, functions and conversions of a calc sheet, and the values a sheet writes into the app's parameters.
Every app 64-bit, direct- 13 calculations
64-bit Open item -
Calc sheets
Unit-aware formulas saved with the file: spans, loads, moments, pass or fail checks.
Every app 64-bit, direct- 3 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.