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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Named faces and edges from the body mesh
Matches each triangle of the built body to the surface that made it and reports each face's area and each edge's length, ends and circle.
- PartCraft
- 7 calculations
32-bit in part Open item -
Nested sheets from DXF to toolpaths
Reads nested sheets and parts from a DXF file, converts them to millimeters and to lines and arcs, and hands them to the contour toolpath.
- PartCraft
- 4 calculations
64-bit Open item -
Node graph functions
Works out the value of each node in a node graph or script: arithmetic, lists, points and vectors, transforms and arrays of geometry.
- ModelCraft
- PartCraft
- 12 calculations
64-bit -
Non-uniform scale of an exact body
Scales a solid by different factors along different axes while keeping it an exact boundary model.
- PartCraft
- 10 calculations
64-bit Open item -
Nonlinear and contact stress study
Solves an elastic–plastic stress study in load steps, with contact between pieces when asked, and reports the peak stress, plastic strain, displacement, safety factor and reactions.
- PartCraft
- 11 calculations in 2 files
32-bit in part Open item -
Nonlinear study fields and thermal stress history
The defaults and checks of a nonlinear or contact study, and the time steps and loads of a thermal stress history.
- PartCraft
- 4 calculations in 2 files
64-bit -
Number text in USD files
Writes numbers into .usda text and decides which attribute types are 32-bit and which are 64-bit.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 3 calculations in 2 files
32-bit in part Open item -
Numbers in a DWG file, read and written bit for bit
Reads and writes the number codes of a DWG file: full and compressed 64-bit values, whole numbers of several sizes and object handles.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 16 calculations in 2 files
64-bit -
Numbers in a PartCraft script file
Writes a part's dimensions, positions and parameters as text in a .pcscript file and reads them back.
- PartCraft
- 3 calculations
64-bit Open item -
Numbers sent between people editing together
How a number in an edit is written into a Studio Live message and read back on the other side.
Every app 64-bit, direct- 5 calculations
64-bit -
Numbers typed into the property grid
Turns what a person types or drags in a Properties row into the number handed to the app.
Every app 64-bit, direct- 3 calculations
64-bit -
Numbers written into the VBA macro export
Turns a part's lengths, angles, points and check values into the numbers written in the exported .swb macro text, in meters and radians.
- PartCraft
- 11 calculations
64-bit Open item -
NURBS curves and surfaces: points, derivatives, normals and curvature
Evaluates a NURBS curve or surface at a parameter: its point, derivatives, tangent, normal and curvatures, and builds arcs and circles as exact rational curves.
- ModelCraft
- PartCraft
- 21 calculations in 5 files
64-bit Open item -
NURBS knot insertion and removal, degree change, split and join
Changes how a curve or surface is described without meaning to change its shape: adds or removes knots, raises or lowers the degree, splits, reverses, rescales the parameter and joins curves.
- ModelCraft
- PartCraft
- 15 calculations in 3 files
64-bit -
NURBS lengths, areas, closest points and tessellation
Measures a curve's length and a surface's area, finds the point of a curve or surface nearest a given point, and turns curves and surfaces into polylines and triangle grids within a tolerance.
- ModelCraft
- PartCraft
- 10 calculations in 3 files
64-bit Open item -
Offcut stock after nesting
Works out the usable material left on a plate after a nest, keeps it as numbered remnants with their size and area, and nests the next job on remnants first.
- CadCraft
- PartCraft
- 13 calculations
64-bit -
Parameter expressions
Evaluates the formulas typed for parameters and dimensions: arithmetic, units, trigonometry in degrees, rounding functions and comparisons.
- CadCraft
- BimCraft
- PartCraft
- 11 calculations
64-bit -
Parameters and equations
Evaluates named parameters and the equations that drive dimensions, writes the results into the drawing or part, and solves backward for a parameter when a driven value is edited.
- CadCraft
- PartCraft
- 9 calculations
64-bit Open item -
Parametric PCB footprints
Pad positions, pad sizes and the courtyard of standard-style footprints, worked out from pitch, row spacing and pin count.
Every app 64-bit, stated limit- 7 calculations
64-bit -
Part and assembly mass in the bill of materials, measure panel and assistant
Mass, volume, area, center and inertia as the bill of materials, the measure panel and the assistant report them.
- PartCraft
- 5 calculations in 3 files
32-bit in part Open item -
Part and stock in machine coordinates
Turns the part into the machine's work frame for toolpaths: the stock block, the work origin, exact outlines of flat faces, hole positions and sizes, and the height of the part's top at any point.
- PartCraft
- 12 calculations
32-bit in part Open item -
Part export to STL, 3MF, DXF and STEP
Writes the part's mesh, a sketch, a face profile or a flat pattern to a file.
- PartCraft
- 9 calculations
64-bit Open item -
Part labels on label sheets
Places a label for every piece on a printable label sheet and sizes its bar code.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 2 calculations
64-bit -
Pattern along a path
Places copies of a feature or body at stations along a path, optionally turned to follow it.
- PartCraft
- 5 calculations
64-bit -
People flow and evacuation time
How fast people pass doors, corridors and stairs, which way each room empties, and how long it takes everyone to reach an exit.
Every app 64-bit, stated limit- 6 calculations
64-bit -
Photo to sketch: outline fitting and scale
Turns the outline of a flat part in a photo, or the lines of a pen drawing, into sketch lines, arcs and circles in millimeters.
- PartCraft
- 9 calculations
64-bit Open item -
Pipe, duct and gas networks
Heads, pressures, flows and velocities in a steady network of pipes, pumps and fittings.
Every app 64-bit, stated limit- 9 calculations in 2 files
64-bit Open item -
Planar faces of a mesh
Groups a mesh's triangles into flat faces and traces each face's outline, for face picking, face profiles in DXF and merged faces in STEP.
- PartCraft
- 5 calculations
64-bit -
Planar linkages (closed loops)
The pose of four-bars, slider-cranks and other planar linkages, their sweep, velocity ratios, mobility and Grashof class.
Every app 64-bit, stated limit- 9 calculations
64-bit Open item -
Polygon triangulation (ear clipping)
Splits a flat polygon with holes into triangles, for caps of extruded sections and faces with holes.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 9 calculations
64-bit -
Print check: weld, volume, area and intersections
Checks whether a mesh is ready for a 3D printer and reports its size, volume, surface area, overhang area and problems.
- ModelCraft
- PartCraft
- 8 calculations
64-bit -
Printability checks on a voxel solid
Finds walls that are too thin, gaps that are too narrow, loose pieces, sealed cavities and overhangs before a part goes to a printer.
- PartCraft
- 8 calculations
32-bit in part Open item -
Protection curves and grading
Relay and fuse operating times, grading margins between devices, and the cable damage time.
Every app 64-bit, stated limit- 6 calculations
64-bit Open item -
Quadratic tetrahedron element matrices
Works out the stiffness, mass, heat and load matrices of each 10-node tetrahedron used by the stress, vibration, heat and buckling studies on a tetrahedral mesh.
- PartCraft
- 18 calculations in 2 files
64-bit -
Rays and distances on a printer mesh
Finds the nearest face a ray meets and the distance from a point to the nearest face, for the supports preview, the wall-thickness check, hollowing and splitting.
- ModelCraft
- PartCraft
- 5 calculations
64-bit -
Reference geometry, sweep paths and extrude extents
Finds points on edges for reference planes, axes and points, chains curves into a sweep path, and works out how far an extrude runs when it stops at a face, a vertex or the next face.
- PartCraft
- 9 calculations
64-bit -
Reference planes, axes and points
Works out a reference plane, axis or point from the faces, edges, planes and points it is defined by.
- PartCraft
- 9 calculations
64-bit -
Result fields sent to the plot, legend and probe
Copies the solved temperature, heat flux, stress, strain and displacement values onto the plot mesh that the result view colors, labels and probes.
- PartCraft
- 8 calculations in 2 files
32-bit in part Open item -
Rib feature
Builds the region a rib fills from an open sketch line: the line extended past the body, swept to one side, and trimmed by the body.
- PartCraft
- 2 calculations
64-bit -
Rigid-body dynamics of a mechanism
Joint torques for a given motion, the mass matrix, joint accelerations for given torques, energy, and a simulated motion over time.
Every app 64-bit, stated limit- 6 calculations
64-bit -
Roof faces, ridges and areas from an outline
Works out the roof over a building outline: the plan of every roof face, the ridge, hip and valley lines with their heights, the eave and fascia lines, and the roof's area and line lengths.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 23 calculations in 2 files
64-bit -
Room outline, walls and openings
Builds the room a cabinet job sits in: its corners, the frame of each wall, inside tests, distances to walls, and the doors and windows along the walls.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 19 calculations in 2 files
64-bit Open item -
Rooms and building outline from walls
Finds the closed rooms and the outer outline that a set of wall outlines encloses, with each room's area, perimeter and centroid.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 11 calculations
64-bit -
Rotations, transforms and small linear algebra (motion)
Rotation matrices, roll-pitch-yaw angles, rotation vectors, rigid transforms and the dense solve used by the robot and linkage calculations.
Every app 64-bit, direct- 7 calculations
64-bit Open item -
Scale feature for printing
Scales a body by a factor per axis about a chosen point, including a shrinkage allowance given as a percent.
- PartCraft
- 3 calculations
64-bit -
Scaled mesh for printing
Scales the part's mesh for shrinkage or by typed factors and writes it as STL or 3MF.
- PartCraft
- 3 calculations
32-bit in part Open item -
Scan clean-up and JPEG decoding
Reads a scanned image, turns it into black and white, finds how far the sheet is rotated and turns it straight.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- PartCraft
- 6 calculations in 2 files
64-bit Open item -
Schedule risk (Monte Carlo)
The finish at P10, P50, P80 and P90, how often each task is critical, and which durations drive the finish.
Every app 64-bit, stated limit- 3 calculations
64-bit -
Script result fields and meshes shown in the window
The scalar a script's field plot colors by, its range, and the outer surface of a result mesh.
- PartCraft
- 4 calculations
32-bit, display only -
Script workspace: the part handed to scripts and picked values
Hands the open part's mesh to scripts, and reports the point, node and field values under a click on what a script showed.
- PartCraft
- 4 calculations
32-bit in part 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.