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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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 text
Makes letters as flat faces or as solids of a given depth from the stroke font and a pen width.
- ModelCraft
- 2 calculations
32-bit in part Open item -
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 -
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 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 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 -
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 -
Alembic import
Reads meshes and their transforms from an Alembic cache and brings them in with Z up.
- ModelCraft
- 8 calculations
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 -
AR on site: lining the model up with the building
Fits the model to the real site from two reference points pointed at with a phone, and checks that fit on a later visit.
- BimCraft
- ModelCraft
- 4 calculations in 2 files
64-bit -
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 -
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 -
B-spline basis functions
The basis functions and derivatives under every NURBS curve and surface.
- ModelCraft
- PartCraft
- 3 calculations
64-bit -
Baked physics key times
The times of the keys written when rigid body physics is baked to the timeline.
- ModelCraft
- 1 calculation
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 -
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 -
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 -
Boolean modifier
Unites, subtracts or intersects the mesh with another object and returns the result as a new mesh.
- ModelCraft
- 2 calculations
32-bit in part 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 -
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 -
Camera exposure and white balance
The exposure value shown in the render dialog, the exposure in stops, and the color gains for a white-balance temperature.
- BimCraft
- ModelCraft
- 4 calculations
64-bit -
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 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 -
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 -
Control program host: placement position and turn
Lets a control program read and set the position, the turn about the vertical axis and the visibility of top-level placements.
- ModelCraft
- 2 calculations
64-bit -
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 -
Curve objects
Evaluates Bézier, NURBS and poly splines and makes the mesh a curve object shows: a tube, a ribbon, or a filled flat shape with thickness and a rounded edge.
- ModelCraft
- 14 calculations in 2 files
64-bit Open item -
Curves through points
Makes a curve that passes through every given point, with optional end directions.
- ModelCraft
- PartCraft
- 5 calculations in 2 files
64-bit -
Cut list sizes, areas and banding lengths
Works out each part's cut size from its finished size and edge banding, and totals pieces, areas, banding lengths and a rough sheet count.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 7 calculations
64-bit Open item -
Cutting profile pieces from stock bars
Packs the pieces of each profile onto stock bars and reports the bars to buy, where each piece is cut, the offcuts and the waste.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 5 calculations
64-bit Open item -
Decal placement and size
Works out where a clicked point lies on a face in the face's own coordinates, and the size a placed decal is stored with.
- ModelCraft
- 5 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.