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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Massing options placed on a lot
Reads alternative building footprints, places each inside the buildable envelope, and writes the envelope back as a file in millimeters.
- CivilCraft
- 6 calculations
64-bit Open item -
Massing window read-outs and typed height
The footprint and floor-area read-outs of a building mass, the zoning coverage field, and what happens to a typed height.
- CivilCraft
- 3 calculations
64-bit -
Matching and blending NURBS curves and surfaces
Moves the end of a curve or the edge of a surface so it meets another with position, tangent or curvature continuity, and builds blends between them.
- ModelCraft
- PartCraft
- 7 calculations
64-bit -
Material flow drawing and playback
Draws the layout in the 3D view and moves the loads and vehicles of a finished or running simulation.
- ModelCraft
- 4 calculations in 2 files
32-bit, display only -
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 -
Material flow simulation
Runs a discrete-event simulation of conveyors, stations, buffers, gates and automated vehicles and reports throughput, lead times, queue lengths and utilization.
- ModelCraft
- 18 calculations
64-bit Open item -
Material graphs baked to textures
Turns a node material, a decal or a texture bake (ambient occlusion, curvature, normals, lighting) into the pictures the renderers read.
- BimCraft
- ModelCraft
- 4 calculations in 4 files
32-bit, display only -
Material maps and statistics from a photo
Makes the color, roughness and normal maps of a tiling material from one photo, and reports how visible the tile's join is and how much relief the photo has.
- BimCraft
- ModelCraft
- 4 calculations
32-bit in part Open item -
Material packs: property curves by temperature
Returns a material property at a temperature from a pack's fitted curve, with its unit, valid range and fit error.
- PartCraft
- 3 calculations
64-bit -
Material units, gravity and custom material limits
The unit factor from density to the solver's mass unit, the gravity constant, and the limits on a custom material.
- PartCraft
- 3 calculations
64-bit Open item -
MaterialX files: numbers written and read
Writes a material's parameters, tile size and displacement to a MaterialX file, and reads them back from one.
- BimCraft
- ModelCraft
- 9 calculations in 2 files
32-bit in part Open item -
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 -
Measurements and typed values in the main window
The measured distances and areas, located points, typed lengths and quantity figures that BimCraft's main window shows or writes back to the file.
- BimCraft
- 9 calculations
32-bit in part Open item -
Measuring and mass properties in 3D
Reports lengths, radii, areas, distances and angles of picked points, edges, faces and bodies, and the mass, center of mass and inertia of a part or assembly.
- PartCraft
- 13 calculations in 2 files
32-bit in part Open item -
Measuring on the IFC view's mesh
Distances, face areas, room areas and volumes, and how far an element moved between two versions of a model, all measured on the triangle mesh the IFC view draws.
- BimCraft
- 10 calculations in 5 files
32-bit in part Open item -
Member axes and section properties
Works out each frame member's length and local axes, and the area, second moments and torsion constant of a section from its outline.
- CadCraft
- BimCraft
- DetailCraft
- 6 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 -
MEP clearances and openings through walls and slabs
How close a pipe or duct comes to a wall, slab, beam or column, and where a run passes through a wall or slab with the opening size it needs.
- BimCraft
- 6 calculations
32-bit in part Open item -
MEP equipment, ports and refrigerant line sets
Builds generic mechanical equipment from typed sizes, places its pipe and duct ports, sizes refrigerant line sets from a capacity table and routes them between units.
- BimCraft
- 12 calculations in 3 files
64-bit -
MEP openings and clearances shown and exported
Brings run points into the viewer frame and writes the opening sizes and positions to the screen list, the CSV and the BCF.
- 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 import, repair and storage
Reads STL, OBJ and 3MF meshes, welds and repairs them into a closed body, finds their flat faces and keeps the result in the part file.
- PartCraft
- 11 calculations
32-bit in part 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 -
Mode shapes returned by the simulation worker
The vibration mode shapes that the simulation worker returns for a modal study.
- PartCraft
- 1 calculation
32-bit in part Open item -
Model for rendering (glTF export)
Writes what the 3D view shows as a glTF 2.0 binary file for rendering programs: meshes, materials, lamps and the site's location.
- BimCraft
- 5 calculations
32-bit in part Open item -
Model points written to USD
Writes the vertices and edges of a model into USD meshes and curves.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 2 calculations
32-bit in part Open item -
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 -
Molar mass and group-contribution estimates
Works out a molecule's formula and molar mass from its structure and estimates boiling point, critical constants, formation energies and heat capacity by Joback's method.
- CadCraft
- BimCraft
- 4 calculations
64-bit -
Molecular dynamics
Simulates atoms under Lennard-Jones, bonded and Coulomb forces and reports temperature, pressure, energies, density, radial distribution and diffusion.
- CadCraft
- BimCraft
- 22 calculations in 3 files
64-bit Open item -
Motion study of an assembly
Drives one joint through its travel and records positions, speeds, accelerations, clashes and clearances at each step.
- PartCraft
- 6 calculations
32-bit in part 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 and mirror
Moves, rotates and mirrors selected members, footings and stairs, and keeps each section facing the right way.
- DetailCraft
- 10 calculations
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 -
Multigrid preconditioner for stress analysis
Builds and applies the smoothed-aggregation multigrid cycle that speeds up the conjugate-gradient solve of the tetrahedral stress model.
- PartCraft
- 8 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 -
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 -
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 -
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
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.