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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Magnetic and electric field solvers
The field of wire segments, the mutual inductance of loops, and 2D finite-element magnetic and electric fields with energy, capacitance and force.
Every app 64-bit, stated limit- 12 calculations in 2 files
64-bit Open item -
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 -
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 -
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 -
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 -
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 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 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 -
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 -
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 -
OpenEXR and Radiance HDR picture files
Reads and writes rendered pictures and environment pictures as OpenEXR and Radiance HDR files.
- BimCraft
- ModelCraft
- 6 calculations in 2 files
64-bit -
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 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 -
Path tracer kernels
Follows light paths through the packed scene to work out each pixel of a high-quality render.
- BimCraft
- ModelCraft
- 4 calculations in 4 files
32-bit, display only -
Path tracer scene, light and sky buffers
Packs the model's triangles, materials, lamps, light profiles and sky into the 32-bit buffers the path-tracing kernels read to draw a picture.
- BimCraft
- ModelCraft
- 4 calculations in 3 files
32-bit, display only -
Path-traced picture sums and the saved file
Reads back the summed light of a path-traced picture from the graphics card and saves it as an EXR, a 16-bit PNG or a render file.
- BimCraft
- ModelCraft
- 7 calculations in 3 files
32-bit in part Open item -
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 -
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 -
Placing scene trees and people
Lists where trees and people can stand, scatters them over a region with a minimum spacing, and builds each one's placement matrix.
- ModelCraft
- 7 calculations in 2 files
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 -
Plant sizes, spacing and symbols
The height, spread, spacing and supplied sizes of each plant species, and the 2D symbol and library item made from them.
- BimCraft
- ModelCraft
- CivilCraft
- 10 calculations
64-bit -
PLY import and export
Reads and writes PLY meshes with their colors, in meters with Z up.
- ModelCraft
- 5 calculations
32-bit in part Open item -
Points picked for surfaces
Hands points picked in the model to the surfaces library, converting meters to millimeters.
- ModelCraft
- 1 calculation
64-bit -
Polygon mesh: attribute layers (UV, color, crease, weights)
The extra values a mesh keeps per vertex, corner, face or edge, such as texture coordinates, colors, edge crease and skin weights.
- CadCraft
- ModelCraft
- 4 calculations
32-bit in part Open item -
Polygon mesh: normals, areas, triangles and volume
The normal, area, center and flatness of a mesh face, the triangles the mesh is cut into, and the area and volume reported for a mesh.
- CadCraft
- ModelCraft
- 7 calculations
64-bit -
Polygon mesh: shading normals
The normal at each face corner that makes a mesh shade smooth or faceted on screen.
- CadCraft
- ModelCraft
- 1 calculation
32-bit, display only -
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 -
Print tool results back in the model
Collects a placement's triangles, runs the union or subtraction of solids, and turns the result into a solid group or a mesh in the model.
- ModelCraft
- 6 calculations
32-bit in part Open item -
Proportional editing weights and edge creases
Works out how far vertices near a selection follow a move, and stores the crease value of edges used by subdivision.
- ModelCraft
- 5 calculations in 2 files
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 -
Push/pull, move, stretch, follow me and intersect
The new positions of vertices when a face is pushed or pulled, geometry is moved or stretched, a face is swept along a path, or faces are cut where they cross.
- CadCraft
- ModelCraft
- 9 calculations
64-bit -
Random numbers and time distributions for material flow
Draws the arrival, service, breakdown and repair times of a material flow run from a seeded random number generator.
- ModelCraft
- 4 calculations
64-bit -
Ray casting for rendering and the render bench
Finds what a camera ray hits in the scene and shades a preview picture; used to draw and to time the renderers.
- BimCraft
- ModelCraft
- 4 calculations in 3 files
32-bit, display only -
Ray hits against 32-bit triangle records
Finds where a ray meets the triangles of a scene, used for walking through a model and for dropping scattered objects onto surfaces.
- BimCraft
- ModelCraft
- 6 calculations in 3 files
32-bit in part Open item -
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 -
Real-time view
Draws the live 3D view, its walk mode, its 360° panoramas and the standalone viewer file, with bounce light from baked probes.
- BimCraft
- ModelCraft
- 4 calculations in 4 files
32-bit, display only
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.