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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Points and heights picked in the 3D view
Turns a click in the 3D tab into a point or a height in drawing units, and lays the 2D drawing on the ground as edges the 3D snaps use.
- CadCraft
- 5 calculations
64-bit -
Points picked for surfaces
Hands points picked in the model to the surfaces library, converting meters to millimeters.
- ModelCraft
- 1 calculation
64-bit -
Polar and object snap tracking
Pulls the pointer onto a ray at a set angle from a base point, or onto the crossing of two such rays, and returns that point for the drawing.
- CadCraft
- 3 calculations
64-bit 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 -
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 -
Polygon triangulation by ear clipping
Splits a flat polygon with holes into triangles for IFC shapes.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 5 calculations
64-bit -
Power line tables, quantities and GIS export
Turns a line study into stringing tables, a support table, material quantities and GIS features in the project's units.
- CivilCraft
- 7 calculations
64-bit Open item -
Power network: load current and voltage drop
Joins lines, cable routes and equipment into a network and works out the current in every span and cable and the voltage drop at every node from each source.
- CivilCraft
- 5 calculations
64-bit -
Pressure vessel thickness and support formulas
Works out required shell, head and cone thickness, allowable pressures, nozzle reinforcement areas, saddle and skirt stresses and wind and seismic loads on a vessel.
- CadCraft
- BimCraft
- 19 calculations in 2 files
64-bit Open item -
Priced estimate
Each row's quantity with waste, its material and labor amounts, crew hours, and the totals of the estimate, of each bid area and of each alternate.
- TakeoffCraft
- 5 calculations
64-bit Open item -
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 -
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 -
Printing patterns at full size
Lays pattern pieces on one large page or on tiled home-printer pages at 1:1, with a test square to check the print scale (Apparel add-on).
- CadCraft
- 6 calculations
64-bit -
Process diagram entities
Lays out the process flow diagram, node boundaries and live value labels that the P&ID add-on and the Plant tab add to a drawing.
- CadCraft
- BimCraft
- 4 calculations
64-bit -
Process emissions (CO2 equivalent)
Works out the CO2-equivalent emissions of vented and burned streams, fired heaters and electric units, per second and per year.
- CadCraft
- BimCraft
- 4 calculations
64-bit -
Project objects exported as GIS layers
Turns survey points, contours, alignments, pads, corridor lines, pipes and structures into GIS features with their attribute values, in grid coordinates.
- CivilCraft
- 6 calculations
64-bit -
Project: stand-in ground, volumes and saved points
Holds the project and the results derived from it: a flat stand-in ground for a road with no survey, cut and fill inside the daylight lines, and the points written to the project file.
- CivilCraft
- 3 calculations
64-bit -
Properties in DWG and DXF: transparency, lineweights, dimension variables
Converts transparency, lineweights and dimension style settings between the drawing's values and the whole-number or text forms DWG and DXF keep.
- CadCraft
- 9 calculations
64-bit -
Properties panel: measures and geometry edits
Shows an object's length, angle, area, circumference, chord and sweep, and changes the object when one of them is typed.
- CadCraft
- 10 calculations in 2 files
64-bit -
Property package and flashes
Works out phase splits, bubble and dew points, enthalpy, entropy and volume of a mixture for the flowsheet and the calculators.
- CadCraft
- BimCraft
- 18 calculations in 2 files
64-bit 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 -
Pure-fluid properties from CoolProp
Gives enthalpy, entropy, heat capacity, density and saturation values of a pure fluid, and builds a component from them.
- CadCraft
- BimCraft
- 5 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 -
Quadratic tetrahedron element matrices
Works out the stiffness, mass, heat and load matrices of each 10-node tetrahedron used by the stress, vibration, heat and buckling studies on a tetrahedral mesh.
- PartCraft
- 18 calculations in 2 files
64-bit -
Quantities handed to TakeoffCraft
Lays the model's walls, openings, roofs, foundations, cabinets and devices as marks on scaled plan sheets inside a PDF, so TakeoffCraft measures every quantity from the marks.
- BimCraft
- 8 calculations
64-bit Open item -
Quantities sent in a bid package
Sends each scope line's quantity and unit to the bidding service.
- TakeoffCraft
- 2 calculations
64-bit Open item -
Quantity totals and schedules from IFC properties
Adds up the quantities and number properties of IFC elements by group, lists rooms with their areas and volumes, and decides whether a property changed between two versions.
- BimCraft
- 6 calculations in 4 files
64-bit 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 -
Radio links, fiber budgets and tower loads
Works out free-space loss, Fresnel zone clearance over the terrain, link margin, fiber loss, link availability, and the wind forces and leg loads of a tower.
- CivilCraft
- 13 calculations
64-bit Open item -
Railing posts, balusters and rails
Works out where a railing's posts and balusters stand, how long its rails are, and the solids that are written into the model.
- BimCraft
- 3 calculations
64-bit Open item -
Railway cant, cant ramps and track quantities
Works out equilibrium cant, cant deficiency and excess, the cant ramps and their gradients and rates, each rail's height along the line, the track cross section, and the quantities of rail, sleepers, ballast and sub-ballast.
- CivilCraft
- 13 calculations
64-bit Open item -
Railway turnouts, crossovers and clearance envelopes
Works out the geometry of a turnout and a crossover from the frog number, the speed on the diverging route, the extra width a vehicle needs on a curve, and whether two clearance outlines overlap.
- CivilCraft
- 7 calculations
64-bit 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 -
Ramps: flights, landings and quantities
Splits a ramp's rise into sloped flights with landings between them, and works out each flight's slope, length and volume.
- BimCraft
- 5 calculations
64-bit Open item -
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 -
Rates exported as a price table
Writes each priced item's material and labor rates as a price table another app can read.
- TakeoffCraft
- 2 calculations
64-bit Open item -
Rates, percentages and extended amounts
Reads a typed unit rate and percentage, and works out quantity × rate to the cent.
- TakeoffCraft
- 6 calculations in 2 files
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 -
Reaction mechanisms in a closed vessel
Reads a reaction mechanism file and follows the species concentrations and temperature of a closed, constant-volume vessel over time.
- CadCraft
- BimCraft
- 8 calculations
64-bit -
Reactors
Works out the outlet of conversion, equilibrium, plug-flow and stirred-tank reactors, with their heat duty.
- CadCraft
- BimCraft
- 10 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 -
Real-time view and render bench
Draws the real-time 3D view, bakes its bounce light, times the path tracers and writes the standalone viewer's scene.
- BimCraft
- ModelCraft
- 4 calculations in 4 files
32-bit, display only -
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
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.