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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Line and arc primitives
Breaks every drawing object into straight segments and arcs and works out points, parameters, lengths, bounds, tangent points and snap points on them.
- CadCraft
- 12 calculations
64-bit -
Line, arc and circle intersections
Where two drawn objects cross: the basis of snaps, trim and extend.
- CadCraft
- 4 calculations
64-bit Open item -
Linetype dashes
Cuts lines and arcs into the dashes, gaps and dots of their linetype for the screen and for plots.
- CadCraft
- 2 calculations
64-bit -
Linework checks for linked landscape objects
Checks a line or outline taken from other linework before a landscape object uses it, and detects when that source has moved.
- CivilCraft
- 3 calculations
64-bit -
LISP arithmetic, conversions and geometry
The numbers a LISP routine gets from the built-in arithmetic, number and angle formatting, unit conversion and point geometry functions.
- CadCraft
- 12 calculations
64-bit Open item -
Live feed values and times
Reads a value and a time from a message or poll answer of a live sensor feed.
- BimCraft
- 1 calculation
64-bit -
Machining picks and readouts
Decides which faces and edges a machining operation accepts, matches stored picks to the part, and formats the numbers shown in the Manufacture panel.
- PartCraft
- 3 calculations
64-bit -
Magnetics add-on: readouts in the panel
Formats the flux density, forces and flux per line that the magnet study shows, and states the size of the air box.
- PartCraft
- 2 calculations
64-bit -
Magnetics add-on: template shapes and hand formulas
Builds ready-made magnet study cross-sections and the textbook value each result is compared with.
- PartCraft
- 7 calculations
64-bit -
Manual annotations: measured lengths, angles and radii
Works out the value a measurement annotation shows in a manual: a distance, an angle or a radius through three points.
- PartCraft
- 3 calculations
64-bit -
Manual parts list: quantities and mass
Builds the parts list of an illustrated manual: the quantity, volume and mass of each part, and the CSV export.
- PartCraft
- 3 calculations
64-bit -
Manual roof planes
Works out the height of a hand-drawn roof plane at any point, its sloped slab, and its sloped and projected areas.
- BimCraft
- 4 calculations
64-bit Open item -
Map layers: web Mercator, tile grids and world files
Converts longitude and latitude to web Mercator and back, lays out the tiles of a map service, reads a picture's world file, and writes the box of a map request.
- CadCraft
- BimCraft
- CivilCraft
- 10 calculations
64-bit Open item -
Markup geometry while drawing and editing
Works out the points and boxes that are stored when a markup is drawn, snapped, typed to scale, resized, moved, simplified or lined up.
- MarkupCraft
- 12 calculations in 4 files
64-bit -
Markup outlines and measurement labels
Builds what each markup draws, on screen and in the saved PDF: its outline as lines and Bézier curves, and the label text of a length, area, angle or count.
- MarkupCraft
- 9 calculations
64-bit -
Material flow layout geometry
Places conveyors, stations and vehicle paths, finds which ports touch, and turns the layout into the lengths, speeds and times the simulation runs on.
- ModelCraft
- 9 calculations in 2 files
64-bit -
Measure tool
The lengths, bearings, grades, total length, ground length and area of what the person measures in plan, and the difference between two points on a profile.
- CivilCraft
- 2 calculations
64-bit Open item -
Member frames and local coordinates
Turns a member's start point, end point and rotation into its own axes, and moves points between the model and a member's own coordinates.
- DetailCraft
- 5 calculations
64-bit -
MEP check messages: units and rounding
Turns pipe, duct, cable carrier and lighting results into the warnings a person reads, with the required and found values.
- BimCraft
- 4 calculations
64-bit -
Merge, spin, bridge, slide and smooth
Merges vertices at their center or within a distance, spins a region round an axis, pairs two loops for a bridge, slides vertices along edges and smooths them.
- ModelCraft
- 7 calculations
64-bit -
Mesh edit moves: grab, rotate, scale, extrude, spin, knife, bisect
Works out where the selected vertices of a mesh go when they are moved, turned, scaled, extruded or spun, and where a knife or bisect cut lies.
- ModelCraft
- 8 calculations
64-bit Open item -
Mesh primitives
Builds the starting meshes: plane, grid, cube, circle, cylinder, cone, UV sphere, ico sphere and torus, at the sizes asked for.
- ModelCraft
- 6 calculations
64-bit -
Mesh volume, area and watertightness checks
Works out a triangle mesh's volume and area and checks that it is closed and manifold.
- PartCraft
- 3 calculations
64-bit Open item -
Meshing a slab or wall into plates
Cuts a slab or wall outline into four-node plates and places their nodes in the frame model.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations in 2 files
64-bit -
Modifier references and lattice cages
Places the objects, curves and cages a mesh's modifiers refer to into that mesh's own space.
- ModelCraft
- 3 calculations
64-bit -
Modifier stack: scale, mirror, array, solidify, displace, lattice, curve, shrinkwrap
Builds the mesh that shows, exports, prints and renders by applying each modifier in turn to a copy of the mesh.
- ModelCraft
- 11 calculations
64-bit Open item -
Move, align and distribute
Works out how far each wall, floor, column or placed item moves to line up with the others or to be spaced evenly, and where an item turned about a point ends up.
- BimCraft
- 7 calculations in 3 files
64-bit -
Move, rotate, scale and mirror
Applies a move, rotation, scale or mirror to drawing objects, and places block references and viewports.
- CadCraft
- 8 calculations
64-bit Open item -
Move, rotate, scale, mirror, array, stretch and lengthen
Builds the transform or the length change for the modify commands from the picked points and typed values.
- CadCraft
- 10 calculations
64-bit -
Moving a grid line with what hangs on it
Moves a grid line sideways by a distance and carries the walls, columns, bubbles, tags and dimension points that sit on it.
- CadCraft
- 2 calculations
64-bit -
Multileader geometry
Works out what a multileader draws: its line with the landing, the arrowhead and where the text starts.
- CadCraft
- 2 calculations
64-bit -
Narration cue times
Places the spoken lines of a walkthrough narration in time, keeps their start times and writes them as subtitles.
- BimCraft
- 3 calculations
64-bit -
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 -
Nesting add-on: outlines in, placed copies out
Reads closed outlines and their holes from the drawing as parts for the nesting engine, and writes the placed copies and sheet rectangles back.
- CadCraft
- 5 calculations
64-bit -
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 -
Number conversion in LISP variants
Converts the value of a variant to another type when a LISP program asks for it.
- CadCraft
- 1 calculation
64-bit -
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 the frame analysis report
The values printed in the analysis and design report tables, which are also what the CSV and PDF downloads contain.
- CadCraft
- BimCraft
- DetailCraft
- 10 calculations in 5 files
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 -
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 -
OBJ import and export
Reads and writes Wavefront OBJ files: points, faces, texture coordinates and normals as text, in meters with Y up.
- ModelCraft
- 6 calculations
64-bit Open item -
Objects on a tilted or flipped plane mapped to the plan
Maps circles, arcs, polylines, text, block references and hatches that a file stores in their own coordinate system onto the drawing's plan.
- CadCraft
- 6 calculations
64-bit -
Offset, extend, break and lengthen
Offsets an object by a distance, extends an end to a boundary, breaks an object between two points and lengthens or shortens it by an amount.
- CadCraft
- 5 calculations
64-bit Open item -
Outline checks: inside, crossing, cut-outs
Decides whether a point is inside an outline, whether an outline crosses itself, and whether a cut-out sits fully inside its area and clear of the other cut-outs.
- TakeoffCraft
- 6 calculations
64-bit -
Outline minus holes: area and boundary lengths
Measures a closed outline with other shapes cut out of it: the remaining area, the length of outline left and the length of the cuts, as used for planted areas around paving, walls and steps.
- CivilCraft
- 5 calculations
64-bit Open item -
P&ID line geometry and connections
Works out where process and signal lines run, how long they are, and which symbols and lines they are joined to in a P&ID drawing.
- CadCraft
- 15 calculations in 4 files
64-bit Open item -
P&ID objects drawn from a built plant
Scales the P&ID symbols and lines of a plant built in millimeters to the drawing's units when they are drawn.
- CadCraft
- 1 calculation
64-bit -
Pad side slopes and retaining walls
Reads a slope as typed, and works out the length, face area and heights of the retaining walls around a pad and the warnings for tall walls and steep slopes.
- CivilCraft
- 4 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.