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 finishing toolpaths
Finds the height of the tool tip over the part for parallel and scallop finishing, and the spacing of passes for a given cusp height.
- PartCraft
- 14 calculations
32-bit in part Open item -
3D view of the part
Draws the part, its edges, highlights and result colors in the 3D view, and finds what is under the pointer.
- PartCraft
- 3 calculations
32-bit, display only -
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 import: units, placements and mesh points
Brings the meshes, curves and block placements of a .3dm file into the model in meters.
- ModelCraft
- PartCraft
- 5 calculations in 2 files
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 -
3DM surfaces into triangles
Turns the trimmed surfaces and extrusions of a .3dm file into triangle meshes, or uses the render mesh the file saved.
- ModelCraft
- PartCraft
- 10 calculations in 2 files
64-bit -
Adaptive clearing passes
Plans roughing passes that keep the cutter's sideways engagement near a set width, and re-checks the engagement they give.
- PartCraft
- 9 calculations
64-bit -
Add-on display bodies: stored coordinates and placement
Checks the boxes and meshes an add-on places in the view, stores them in the part file, and places them in the world.
- PartCraft
- 4 calculations
64-bit Open item -
Advanced simulation add-on: finding contact pairs
Finds flat faces of two separate pieces that face each other within a gap, as candidate contact pairs.
- PartCraft
- 2 calculations
32-bit in part Open item -
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 -
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 -
Animation keys, curves and poses
Where the camera and every moving object are at a given time of an animation, and the value of every animated property.
- BimCraft
- ModelCraft
- PartCraft
- 23 calculations
64-bit -
Assembly drawing sheet and mesh exports
Lays out the assembly drawing (view scale, positions on the sheet, bill of materials masses) and writes the placed assembly as one mesh for STL or as a 3MF file.
- PartCraft
- 5 calculations
32-bit in part Open item -
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 -
Automatic mesh refinement of tetrahedral studies
Decides which elements to refine after a solve, how small to make them, refines the mesh and stops when the estimated error meets the target.
- PartCraft
- 5 calculations
64-bit -
B-spline basis functions
The basis functions and derivatives under every NURBS curve and surface.
- ModelCraft
- PartCraft
- 3 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 -
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 -
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 -
Buckling load factors and thermal stress setup
Finds the lowest load factors at which a part buckles and their shapes, and sets up thermal loads for a stress study on the voxel model.
- PartCraft
- 7 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 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 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 -
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 -
CalculiX deck export and result import
Writes a nonlinear study as a text input deck for the separate CalculiX program and reads its text result file back.
- PartCraft
- 6 calculations
64-bit Open item -
Check report values
The required and found values written in the Problems panel and in the check report exported as CSV.
Every app 64-bit, direct- 1 calculation
64-bit Open item -
Circuit board outline, holes and part boxes
Reads a KiCad board file into a part: the board outline, its drilled holes and one box per component.
- PartCraft
- 5 calculations
64-bit -
Circuit solver
Operating point, DC sweep, AC response and transient of a circuit of resistors, capacitors, inductors, sources, diodes, transistors and switches.
Every app 64-bit, stated limit- 18 calculations in 2 files
64-bit Open item -
Closed-loop joint solver
Finds joint values that make every closed chain of joints in an assembly meet, and reports how many values remain free.
- PartCraft
- 6 calculations
64-bit -
Contact and magnet study results
Gathers the results of a contact study between parts and of a 2-D magnet study: maximum stress, displacement and flux density, contact force, and the per-vertex and per-element fields.
- PartCraft
- 10 calculations
32-bit in part Open item -
Contact between parts in stress analysis
Works out the gap between touching parts and the contact forces and stiffness that keep them from passing through each other.
- PartCraft
- 8 calculations
64-bit -
Continuity between curves and between surfaces
Measures the gap, the angle and the curvature difference where two curves join or two surfaces share an edge, and classes the join as G0, G1 or G2.
- ModelCraft
- PartCraft
- 5 calculations
64-bit Open item -
Controller standard functions and integer types
Timers, counters, arithmetic functions and type conversions of the soft controller.
Every app 64-bit, direct- 6 calculations
64-bit Open item -
Corner cabinet drilling positions
Works out where the shelf-pin, hinge-plate, fixing, pivot and shaft holes go on the parts of a corner cabinet.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 7 calculations
64-bit Open item -
Corner cabinets: parts and solids
Builds the cut list, door sizes, hardware counts and 3D solids of L-shaped, diagonal and lazy-susan corner cabinets (CabinetCraft add-on).
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 11 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.