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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People movement and travel distance
Works out how far the farthest point of each room is from an exit and simulates people walking out of or into the building, with times, queues and walked distances.
- BimCraft
- 12 calculations in 2 files
64-bit -
Photo to sketch: outline fitting and scale
Turns the outline of a flat part in a photo, or the lines of a pen drawing, into sketch lines, arcs and circles in millimeters.
- PartCraft
- 9 calculations
64-bit Open item -
Picture backgrounds: scale, placement and print
Sizes a picture placed under a drawing from two picked points and a distance, moves and turns it, places it in sheet views, and works out its size and matrix in a printed PDF.
- BimCraft
- 15 calculations in 3 files
64-bit Open item -
Pipe and duct runs: layout, lengths and sizing
Turns the pipe and duct lines a person draws into straight pieces, elbows, tees and reducers, measures their lengths and surface, and picks a pipe or duct size for a flow.
- BimCraft
- 23 calculations in 3 files
64-bit Open item -
Pipe stress checks
Turns a routed pipe run into a beam model, solves weight and thermal expansion, and checks sustained, expansion and occasional stresses against the allowables a person gives.
- CadCraft
- BimCraft
- 11 calculations
64-bit Open item -
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 -
Piping isometric drawing and its bill of materials
Draws pipe runs as a 30 degree isometric with the length of every leg, elevations and a bill of materials, and writes the drawing as SVG or DXF.
- BimCraft
- 8 calculations
64-bit Open item -
Piping network, pumps and compressors
Works out the flows and pressures in a liquid or gas piping network with pumps and valves, the suction head available to a pump, and the head, power and surge margin of a compressor.
- CadCraft
- BimCraft
- 11 calculations in 2 files
64-bit Open item -
Placing a linked model
Works out the matrix that puts a linked IFC model in the right place beside the open one, from both files' map positions or from two pairs of picked points.
- BimCraft
- 4 calculations
64-bit Open item -
Placing a model on the map
Builds and reads the map conversion that places a model on a map grid, and re-expresses it in another coordinate system.
- BimCraft
- 6 calculations
64-bit -
Placing and pasting elements in an IFC model
Works out where a placed library item or a pasted copy sits in the file: its position and direction relative to the story, its shape in the file's unit, and its plan outline.
- BimCraft
- 7 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 -
Plan as a vector PDF
Chooses the scale a level's plan prints at and turns plan millimeters into positions on the sheet.
- BimCraft
- 4 calculations
64-bit -
Plan sheets and plan-and-profile sheets as PDF
Places the plan and the profile on paper at a stated scale and writes the page as a vector PDF.
- CivilCraft
- 14 calculations in 2 files
64-bit -
Plan symbol positions
Stores where a plan symbol sits and how it is turned, and moves symbols fixed to a wall when the wall moves.
- BimCraft
- 3 calculations
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 equipment solids, capacity and placement
Builds vessels, tanks, columns, pumps and exchangers of the Plant add-on from a few dimensions in millimeters, works out their capacity, and moves them to their place in the model.
- BimCraft
- 11 calculations in 3 files
64-bit Open item -
Plant equipment written as an IFC file
Writes the Plant add-on's equipment, with its solids and nozzle ports, as a standalone IFC4 file in millimeters.
- BimCraft
- 4 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 -
Plant symbols from SVG files and CAD blocks
Turns an SVG drawing or a CAD block into a plant symbol kept in the project, and scales it to each plant's spread on the plan.
- CivilCraft
- 3 calculations
64-bit -
Plate element for slabs and walls
The stiffness of one four-node plate of a slab or wall, and the membrane forces, bending moments and shears inside it.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations
64-bit -
Plotting: sheet scale, PDF, SVG and PNG output
Scales the model onto paper and writes the sheet as a PDF, an SVG or a PNG.
- CadCraft
- 13 calculations
64-bit Open item -
Point cloud slice and scan alignment
Cuts a point cloud at a level's height for drawing over it, and finds the turn and the lift that set a scan square to the building and its floor on a level.
- BimCraft
- 9 calculations
64-bit -
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 -
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 -
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 -
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 -
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 -
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 -
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 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 -
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 -
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 -
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 -
Redline package coordinates
The positions written into a redline package that lists each markup on its sheet.
- MarkupCraft
- 2 calculations
64-bit -
Reference geometry, sweep paths and extrude extents
Finds points on edges for reference planes, axes and points, chains curves into a sweep path, and works out how far an extrude runs when it stops at a face, a vertex or the next face.
- PartCraft
- 9 calculations
64-bit -
Regulation checks of rooms, doors, windows and outlets
Works out what the model has for each rule of the active regulation pack: room area and least dimension, window area and openable area as a share of the floor, escape openings, egress door width, outlet spacing along the walls.
- BimCraft
- 11 calculations in 2 files
64-bit -
Regulation limits read from the pack's tables
Looks up the footing size, stud spacing and height, header span, joist and rafter span and wall insulation a regulation pack asks for, and compares the model with them.
- BimCraft
- 10 calculations
64-bit Open item -
Reinforcing bars and the bending schedule
Places the bars in a pad footing and works out their bends, cut lengths, counts and weights for the bending schedule.
- DetailCraft
- 13 calculations
64-bit Open item -
Release, fire, explosion and toxic screening
Works out how much escapes through a hole, how far fire radiation, blast overpressure and a toxic or flammable cloud reach, and the chance of harm from a dose.
- CadCraft
- BimCraft
- 19 calculations in 3 files
64-bit Open item -
Relief valve sizing, depressuring and flare loads
Works out the orifice area a relief valve needs for gas, liquid, steam or two-phase flow, the heat input from a fire, the back pressure in the outlet line and flare header, flare radiation distance and the pressure of a vessel as it is vented.
- CadCraft
- BimCraft
- 17 calculations in 2 files
64-bit Open item -
Render hand-off manifest
The camera, sun, lamps, materials, exposure and frame numbers written into the package that an outside render engine reads.
- BimCraft
- ModelCraft
- 8 calculations
64-bit Open item -
Replacement schedule and cost over the building's life
Lists when each part of the building is replaced over a study period, what that costs with inflation and discounting, and how much embodied carbon the replacements add.
- BimCraft
- 6 calculations in 2 files
64-bit 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.