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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2D constraint solver
Moves lines, circles, arcs, points and polyline vertices so that the geometric and dimensional constraints placed on them are met.
- CadCraft
- 9 calculations
64-bit Open item -
2D drawing on screen
Draws the drawing, the grid and the cursor aids on the two canvases of the 2D view.
- CadCraft
- 4 calculations
32-bit, display only -
2D flow solver (finite volume)
Computes laminar flow in a rectangular region and the mixing of a tracer in it: velocities, pressure, concentration and a mixing time.
- CadCraft
- 14 calculations
64-bit Open item -
2D mixing solver (lattice Boltzmann)
Computes laminar flow and tracer mixing in tanks and flow-through boxes on a lattice, with a mixing time and a residence time distribution.
- CadCraft
- 10 calculations
64-bit Open item -
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 solid commands: sizes, paths and reported volume
Turns the heights, angles, outlines and paths typed or picked for EXTRUDE, SWEEP and REVOLVE into the numbers the solid is built from, and works out the volume the command line prints.
- CadCraft
- 5 calculations
64-bit -
3D solids, faces and units in a drawing
Builds boxes, cylinders, wedges and extrusions from 2D outlines, reports their volume, and carries the 3D model between drawing units and meters.
- CadCraft
- 9 calculations
64-bit -
3D tab drawing of the 2D lines and kept solids
Sends the 2D drawing's lines and the solids kept from DWG files to the graphics card for the 3D tab.
- CadCraft
- 2 calculations
32-bit, display only -
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 view drawing
Builds the meshes, edges, lights and overlay lines that draw the 3D model on screen.
- CadCraft
- ModelCraft
- 3 calculations
32-bit, display only -
ACIS solids turned into triangles
Turns the 3D solids stored in DWG and DXF files (ACIS data) into triangle meshes: shown on CadCraft's 3D tab, and brought into ModelCraft as groups when such a file is imported.
- CadCraft
- ModelCraft
- 26 calculations in 2 files
64-bit Open item -
Activated sludge plant steady state (ASM1)
Works out the steady concentrations in a chain of treatment tanks with recycles and a clarifier, the effluent and waste sludge, the sludge age and the mass balances.
- CadCraft
- BimCraft
- 8 calculations
64-bit Open item -
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 -
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 -
Analysis results drawn on the model
The deflected shape, force diagrams and colored plate contours shown on the 3D view.
- CadCraft
- BimCraft
- DetailCraft
- 3 calculations in 2 files
32-bit, display only -
Apparel commands: piece table, marks and marker output
The Apparel add-on's commands that put numbers into the drawing or a file: the piece table, grain lines and buttonholes, automatic nesting on a marker and the marker's PDF.
- CadCraft
- 11 calculations
64-bit Open item -
Arcs, circles, smooth curves, divide and offset
The corner points of arcs, circles, polygons and smooth curves, what is reported about a curve, equal division, and the offset of a face outline or a chain of edges.
- CadCraft
- ModelCraft
- 11 calculations
64-bit Open item -
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 -
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 -
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 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 -
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 -
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 -
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 -
Board placement and routing
Where parts are placed and where tracks and vias run on a board, with the wire length reported.
Every app 64-bit, stated limit- 8 calculations in 2 files
64-bit Open item -
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 -
Burn levels of an engraved picture
Resamples a gray picture to the engraving grid and turns each cell into a burn level.
- CadCraft
- PartCraft
- 2 calculations
32-bit in part Open item -
Cabinet job cost estimate
Prices a cabinet job from its sheets, edge banding, frame stock, hardware, countertops, labor and machine time, with markup and tax.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 10 calculations
64-bit Open item -
Cabinet job edits that change sizes
Works out the sizes an edit puts into a cabinet job: the job in the other unit, a filler for a leftover, a gap at a door or window, and the notch of a new L or U room.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 4 calculations
64-bit Open item -
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 material sizes, grooves and drill files
Holds the thicknesses of the sheet materials and edge bands, derives the groove and sheet size from the picks, and writes the drill and G-code files.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 5 calculations in 2 files
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 -
Cabinet run layout and countertops
Places every cabinet, filler and end panel along its wall or island, works out how runs meet at corners, and sizes the countertops.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 19 calculations in 2 files
64-bit Open item -
Cabinet shop drawings as drawing objects
Turns the cabinet plan, elevations, sections, schedule, cut list and nested sheets into lines, polylines, texts, hatches and dimensions of the open drawing (CabinetCraft add-on).
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 6 calculations
64-bit Open item -
CabinetCraft in a drawing: units, room outline and solids
Reads a room from a closed polyline of the drawing in millimeters, converts cabinet shop drawings and 3D solids to the drawing's unit, and decides where the sheets are drawn (CabinetCraft add-on in CadCraft).
- CadCraft
- 7 calculations
64-bit Open item -
CabinetCraft parts, fronts and face frames
Works out the cut-list parts of a cabinet job: face-frame stiles and rails, overlay doors and drawer fronts, drawer boxes, blind panels, fillers and end panels.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 11 calculations
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 -
Cabinets as 3D viewport bodies
Turns the cabinet job into boxes and meshes for the 3D viewport: every panel, the floor and the walls with their openings (CabinetCraft add-on).
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 2 calculations
32-bit, display only -
Cabinets on angled and curved walls
The geometry of cabinets on walls that are not at right angles or are curved: arc walls from radius, sweep or three points, cabinets stepped round an arc, and the corner cabinet at any angle (CabinetCraft add-on).
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 16 calculations
64-bit Open item -
Cable routes in trays and conduits on the installation plan
Turns the routes drawn on the plan and the circuits into cables with a route, and into the fill rows of each tray and conduit.
- CadCraft
- 3 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 -
Calculator results and export
Turns what a process calculator works out into the lines of its results table, its CSV export and the one figure it gives the status bar.
- CadCraft
- BimCraft
- 7 calculations in 2 files
64-bit Open item -
Capital and operating cost
Estimates the purchased and installed cost of process equipment and the yearly cost of its energy.
- CadCraft
- BimCraft
- 5 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.