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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Section view plane
The cutting plane of the live section view: its normal and position, and the range of its slider.
- PartCraft
- 2 calculations
32-bit, display only -
Sheet metal base and edge flanges
Builds the cross-section of a sheet metal flange (bend arcs, leg, tip) and its bend reliefs from thickness, bend radius, angle and length.
- PartCraft
- 4 calculations
64-bit -
Sheet metal bends and flat pattern
Works out the bent profile of a sheet metal base, the bend allowance of every bend, and the flat pattern with its bend lines, size and area.
- PartCraft
- 13 calculations in 2 files
64-bit Open item -
Sheet nesting
Lays parts out on sheets or a roll, reports the sheets used and the efficiency, checks the result, reads part outlines from DXF and writes the nest as DXF.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 19 calculations
64-bit Open item -
Simulation and flow result plots
Draws the colored cut plane, the surface colors and the streamlines of a result, and makes the finer mesh the colors are drawn on.
- PartCraft
- 4 calculations in 3 files
32-bit, display only -
Simulation numbers shown as text
How the simulation window rounds the numbers it prints and puts into input boxes.
- PartCraft
- 2 calculations
64-bit -
Simulation workspace: plot values and the hover probe
Prepares the values a result plot colors by and reads the result under the pointer.
- PartCraft
- 8 calculations
32-bit in part Open item -
Sketch editor drawing
Draws the sketch, its dimensions and their labels on the canvas over the 3-D view.
- PartCraft
- 2 calculations
32-bit, display only -
Sketch editor: typed sizes and dimension values
Takes the numbers a person types in the sketch editor (a dimension's value, the sizes of a shape being drawn) and turns them into stored values and point coordinates.
- PartCraft
- 8 calculations
64-bit Open item -
Sketch geometry and measured values
Works out radii, arc angles, the current value of a dimension, sketch fillets and the size of a sketch.
- PartCraft
- 9 calculations
64-bit -
Sketch intersections of lines, arcs and circles
Finds where sketch lines, arcs and circles cross each other; trim, extend and offset use the points.
- PartCraft
- 7 calculations
64-bit -
Sketch intersections with splines
Finds where a sketch spline crosses a line, an arc, a circle or another spline.
- PartCraft
- 3 calculations
64-bit -
Sketch profiles as closed polygons
Turns the lines, arcs, circles and splines of a sketch into closed polygon loops, tests whether a point is inside them, and gives a loop's area.
- PartCraft
- 5 calculations
64-bit -
Sketch profiles for exact solids
Turns a sketch's lines, arcs, circles and splines into closed loops, decides which loops are holes, and hands the exact curves to the solid kernel.
- PartCraft
- 6 calculations
64-bit Open item -
Sketch solver
Moves the points and radii of a sketch until every relation and dimension is met, and reports how many degrees of freedom are left and which relations conflict or repeat.
- PartCraft
- 11 calculations in 2 files
64-bit Open item -
Sketch splines: evaluation, fitting and exact pieces
Evaluates sketch splines and their derivatives, fits a spline through points, cuts an exact piece out of one, and gives the area a closed spline encloses.
- PartCraft
- 13 calculations
64-bit -
Sketch splines: length, nearest point, polyline and offset
The length of a sketch spline, the point on it nearest a given point, its points within a chord tolerance, and its offset curve.
- PartCraft
- 4 calculations
64-bit -
Sketch tools: trim, extend, offset, mirror, pattern, polygon, slot, project
Changes sketch geometry with the editing tools: new end points for trimmed and extended curves, offset copies, mirrored and patterned copies, polygons, slots and projected model edges.
- PartCraft
- 11 calculations
64-bit Open item -
Solid modeling
Rebuilds a part from its feature history: extrudes, cuts, patterns and boolean operations.
- PartCraft
- 2 calculations
32-bit in part Open item -
Solving an expression for one parameter
Finds the value of one parameter that makes an expression give a wanted result, the other parameters held.
- CadCraft
- BimCraft
- PartCraft
- 2 calculations
64-bit Open item -
Spending on a person's own AI model
Adds up what calls to a person's own AI model have cost today and this month, and stops a call that could pass the limits the person set.
Every app 64-bit, stated limit- 4 calculations
64-bit -
Splitting a model into printable pieces
Cuts a model too big for the printer into pieces that fit the bed, places connectors and part numbers on the cut faces, and lists the pieces.
- ModelCraft
- PartCraft
- 23 calculations in 2 files
32-bit in part Open item -
Spread between coarse and refined results
States how far a coarse live result is from the refined one, as a fraction.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 1 calculation
64-bit -
Standard part templates
Builds a parametric part for a standard bolt, nut, washer, pin, bearing or key at a size from the standards tables.
- PartCraft
- 4 calculations
64-bit Open item -
Standard parts and library items
Works out the dimensions, mass and drawing of standard bolts, nuts, washers, pins, keys, bearings and gears, and turns parts and steel sections into library items.
- CadCraft
- PartCraft
- 9 calculations in 2 files
64-bit -
Steel section dimensions, areas and outlines
Gives the dimensions, published area and mass of every steel section in millimeters, the exact area from the dimensions, and the outline used to draw and sweep it.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 6 calculations
64-bit Open item -
STEP curves and surfaces: parameters from points
Finds where a 3D point of an edge lies on a free-form curve or surface, so the face it bounds can be laid out flat and triangulated.
- BimCraft
- ModelCraft
- PartCraft
- 5 calculations
64-bit -
STEP curves and surfaces: points from parameters
Works out the 3D point at a parameter on each kind of curve and surface a STEP file can hold, which is where the triangles of an imported solid get their corners.
- BimCraft
- ModelCraft
- PartCraft
- 14 calculations
64-bit -
STEP files of NURBS curves and surfaces
Writes B-spline curves and surfaces, with their trims, to a STEP file in millimeters and reads such files back.
- ModelCraft
- PartCraft
- 7 calculations
64-bit -
STEP import: triangles for curved faces
Turns each face of an imported STEP solid into triangles that stay within a chord tolerance of the true surface and share their edge points with the neighboring faces.
- BimCraft
- ModelCraft
- PartCraft
- 14 calculations
64-bit -
STEP import: units, points and assembly placement
Turns the numbers of a STEP file into millimeters and radians and puts every solid where the file's assembly structure places it.
- BimCraft
- ModelCraft
- PartCraft
- 10 calculations
64-bit -
STL and 3MF files for the printer
Writes the checked mesh as a binary STL or a 3MF file.
- ModelCraft
- PartCraft
- 3 calculations
32-bit in part Open item -
Stock simulation and machining time
Simulates the stock being cut by every tool move, reports material removed, stock left and gouges, and estimates the machining time.
- PartCraft
- 8 calculations
64-bit -
Stress analysis
Linear static stress and displacement of a part on a voxel grid.
- PartCraft
- 3 calculations
32-bit in part Open item -
Stress, displacement and error results on tetrahedra
Turns the solved displacements into stresses, principal stresses, strain, reactions, the reported maxima, the safety factor and the estimated error of the mesh.
- PartCraft
- 11 calculations in 2 files
32-bit in part Open item -
Structural members and their cut list
Places steel sections along sketch lines, works out the miter, butt and fitted cuts where members meet, and lists each piece's length and end angles in the cut list.
- PartCraft
- 10 calculations
32-bit in part Open item -
Study set-up: element size and the mesh handed to the solver
Prepares a simulation or generative study for solving: the automatic element size, the estimated element count, the design box, and the copy of the body's mesh the solver works on.
- PartCraft
- 4 calculations
32-bit in part Open item -
Surface display meshes, curvature map and zebra stripes
Makes the triangles that draw a surface body and colors a mesh by curvature or by zebra stripes.
- PartCraft
- 3 calculations
32-bit, display only -
Surface features built with the kernel
Makes freeform surface bodies and turns them into solids: patches, lofts, network surfaces, offsets, thickened and stitched surfaces.
- PartCraft
- 8 calculations
64-bit -
Surface mesh from a distance grid (dual contouring)
Turns a distance grid into a closed triangle mesh, one vertex per surface cell.
- PartCraft
- 5 calculations
32-bit in part Open item -
Surface through a network of curves
Builds one B-spline surface that passes through a grid of profile curves and guide curves, and reports how far it strays from them.
- PartCraft
- 19 calculations
64-bit -
Surfaces from curves: extrude, ruled, revolve and loft
Builds a surface by pulling a curve along a direction, spanning two curves, turning a profile about an axis or passing through a set of sections.
- ModelCraft
- PartCraft
- 7 calculations
64-bit Open item -
Tetrahedral mesh of a part
Builds the tetrahedral analysis mesh of a solid from its surface triangles: element sizes, inside and outside, cut points on the surface, boundary vertices on the true faces, and the mesh quality and volume that are reported.
- PartCraft
- 20 calculations
64-bit -
Tetrahedral stress, vibration and buckling solve
Assembles the stiffness of the tetrahedral model, applies supports and loads, and solves for displacements, natural frequencies and the pre-stress of a buckling study.
- PartCraft
- 12 calculations in 2 files
64-bit -
Text from drawings as stroked edges
The line segments that draw the text of an imported drawing in the 3D model, and the width of a string.
- CadCraft
- ModelCraft
- PartCraft
- 3 calculations
64-bit -
Thermal window temperature range and balance read-outs
The temperature range of a thermal plot, the probed temperature and the heat balance figures.
- PartCraft
- 3 calculations
32-bit in part Open item -
Thread dimensions and modeled threads
Works out a thread's diameters and profile from its size, picks the size that fits a round face, and builds the helical solid of a modeled thread.
- PartCraft
- 8 calculations
64-bit Open item -
Threaded solver kernels and conjugate gradients
Runs the matrix products, dot products and vector updates of the simulation solvers on several threads, and the conjugate-gradient solves built on them.
- PartCraft
- 12 calculations
64-bit -
TIFF scan resolution
Reads the resolution of a scanned drawing from a TIFF file as dots per inch.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- PartCraft
- 2 calculations
64-bit -
Tolerance stack-ups
Adds up a chain of dimensions and their tolerances across an assembly: the nominal and mean gap, the worst-case and statistical spread, each link's share, and the share of assemblies expected outside the limits.
- PartCraft
- 10 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.