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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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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
PDF page vectors and snapping to them
Reads the lines, curves and text of a PDF page into page points, and finds the end, middle, crossing or nearest point of those lines for snapping.
- CadCraft
- BimCraft
- 8 calculations in 2 files
32-bit in part Open item -
PDF underlay placement and PDF import
Places a PDF page at its true size in the drawing's units, and turns a page's lines, arcs, circles, fills and text into drawing objects.
- CadCraft
- 13 calculations in 2 files
32-bit in part Open item -
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 -
Point cloud positions and read-in values
Turns the points of a scan file into the kept cloud (positions, intensities, size) that the apps measure, slice and snap to.
- CadCraft
- BimCraft
- 6 calculations
32-bit in part Open item -
Points and faces picked for 3D measuring
Finds the corner, edge point or face under the pointer for the 3D Measure tool, the area of that face, and the bounding box of each element.
- BimCraft
- 3 calculations
32-bit in part Open item -
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 -
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 -
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 -
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 -
Radio coverage over the terrain
Works out the received power from a transmitter at every cell of a grid over the terrain and the share of cells that are covered.
- CivilCraft
- 2 calculations
32-bit in part Open item -
Rain on the ground: overland flow, ponding and outflow
Runs rain over a grid of the graded ground and reports where water ponds, how deep it gets, what overtops, and the volumes that fall, soak in, drain and leave.
- CivilCraft
- 14 calculations
32-bit in part Open item -
Rainfall run read-outs: deepest water and depth scale
The deepest-water figure, the depth scale of the picture, and the unit factors in the rainfall run window.
- CivilCraft
- 3 calculations
32-bit in part Open item -
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 -
Rebar congestion map of a footing
Shows how tight the openings between reinforcing bars are for concrete to pass, and reports the tightest place.
- DetailCraft
- 6 calculations
32-bit in part Open item -
Registered scans written as LAS and E57
Moves every point of the registered scans by its scan's matrix and writes the result as a LAS 1.2 or an E57 file.
- CadCraft
- BimCraft
- 6 calculations
32-bit in part Open item -
Rendered picture: mixing, post and color
The pixel values of a high-quality render as shown and as saved to an 8-bit or 16-bit picture, after light mixing, denoising, exposure, bloom, the view transform and the sRGB curve.
- BimCraft
- ModelCraft
- 14 calculations in 5 files
32-bit in part Open item -
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 -
Room acoustic measures from an impulse response
Reads a recorded or computed impulse response and works out reverberation times, early decay time, clarity, definition and center time.
- BimCraft
- 4 calculations
32-bit in part Open item -
Room impulse response and listening
Builds a room's impulse response from its reverberation times, and the sound of a clap, speech or music heard through it, to play or save.
- BimCraft
- 9 calculations
32-bit in part Open item -
Room modes and low-frequency wave solver
Lists the standing-wave frequencies of a box-shaped room, the frequency below which the room behaves as separate modes, and runs a small wave simulation to find the resonances at a listener.
- BimCraft
- 5 calculations
32-bit in part Open item -
Samples per pixel reported after a render
Works out the average and the largest number of samples a pixel received in an adaptive path-traced render, shown on the finish line.
- BimCraft
- ModelCraft
- 1 calculation
32-bit in part Open item -
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 compared with the model
Compares a point cloud with each model element's box and reports whether the element is built, partly built or missing, how far the scanned surface is from it, and the percent complete.
- BimCraft
- 5 calculations
32-bit in part Open item -
Scan registration
Finds the rigid move (rotation and shift) that lines one scan up with others, from picked point pairs or by iterative closest point, and reports the remaining error.
- CadCraft
- BimCraft
- 15 calculations
32-bit in part Open item -
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 -
Sculpt brushes
Moves the vertices under a round brush: draw, clay, smooth, grab, inflate, crease, pinch and flatten, with a mask that protects vertices.
- ModelCraft
- 10 calculations in 2 files
32-bit in part Open item -
Shape keys: offsets, editing and blending
The vertex offsets stored for each shape key, the way a key is made from an edit or from imported positions, and the blended points of a mesh.
- ModelCraft
- 5 calculations in 2 files
32-bit in part Open item -
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 -
Skin weights and skinning
Works out how much each bone moves each vertex, and moves the mesh's points with the bones.
- ModelCraft
- 9 calculations in 3 files
32-bit in part Open item -
Solar arrays on the model
Reads the roof planes from the model, plans an array on a roof or the ground, stores it in the file, and combines shading over the modules for the yield.
- BimCraft
- 7 calculations
32-bit in part 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 -
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 -
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 -
STL import and export
Reads and writes STL triangles, with a unit on import and millimeters on export.
- ModelCraft
- 6 calculations
32-bit in part Open item -
Stress analysis
Linear static stress and displacement of a part on a voxel grid.
- PartCraft
- 3 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.