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.
-
Variant pack: parameter table, sizes and library bodies
Writes every configuration of a part as files: the parameter table as CSV and JSON, each variant's volume and size, and a library item with a body per variant.
- PartCraft
- 6 calculations in 2 files
64-bit -
Vector PDF output
Writes drawings to a PDF file: the page size, the millimeter scale, lines, circles and text positions.
- BimCraft
- DetailCraft
- 6 calculations
64-bit Open item -
Vectors, plane frames and transforms
The small vector and 4 × 4 matrix helpers that place sketches on planes and move, rotate and mirror parts.
- PartCraft
- 10 calculations
64-bit -
Vehicle swept paths
Drives a vehicle with up to three trailers along a path, forward or reversing, and reports its wheel paths, steering and articulation angles and the area its bodies sweep.
- CivilCraft
- 8 calculations
64-bit -
Vertical profile: grades and parabolic curves
Works out the design elevation and grade at any station from the PVIs and their vertical curves, and samples the existing ground along the alignment.
- CivilCraft
- 4 calculations
64-bit -
Vessel outline and inside volume
Works out the revolved outline of a vessel with its two heads, its height and inside volume, and where a nozzle sits on it.
- CadCraft
- BimCraft
- 4 calculations
64-bit Open item -
Viewports on a sheet
Works out the size and center of a viewport drawn on a sheet and the scale that fits a named view into it.
- CadCraft
- 2 calculations
64-bit -
Voxel grid and lattice struts
The solid cubes of a field grid for the solvers, and the strut lists of lattices.
- PartCraft
- 2 calculations in 2 files
64-bit -
Voxel grid of a part
Turns a part's surface triangles into the grid of cubes that the voxel stress, heat and generative studies use, and maps grid nodes to the part's faces for loads and supports.
- PartCraft
- 11 calculations
32-bit in part Open item -
Voxel remesh and snapping onto a surface
Rebuilds a mesh as an even closed mesh at a chosen voxel size, and moves vertices onto the nearest point of another surface.
- ModelCraft
- 5 calculations
32-bit in part Open item -
Voxel stress analysis: 32-bit steps in loads and results
The safety factor, the values under the result probe, and the direction of face loads in a voxel stress study.
- PartCraft
- 3 calculations
32-bit in part Open item -
Voxel stress analysis: elements, loads, reactions and modes
Builds the stiffness of the voxel elements, applies supports and loads, and works out reactions, element stresses, natural frequencies and the mesh's volume and mass.
- PartCraft
- 15 calculations
64-bit Open item -
Wall dimensions, heights and quantities
Reads a drawn wall's ends, length, thickness and height from the file and writes its shape, side areas, footprint and volumes.
- BimCraft
- 12 calculations
64-bit Open item -
Wall faces and plan frames from element meshes
Finds the faces of walls in plan so a placed item can sit against one, and the turned box of copied elements that the paste ghost and wall snap use.
- BimCraft
- 5 calculations
32-bit in part Open item -
Wall joins and plan outlines
Works out the plan outline of every drawn wall with its corners, tees and crossings cleaned, which becomes the wall's solid and closes rooms.
- BimCraft
- 9 calculations
64-bit -
Wall layers drawn in plans and sections
Works out the outline of each wall layer where a plan or a section cuts a wall, and the wall edges an elevation shows, as the linework drawn on screen and on sheets.
- BimCraft
- 11 calculations in 2 files
64-bit -
Wall, floor and roof framing layout
Works out where every stud, plate, header, joist, rafter, truss and collar tie goes, which lumber size a span needs, and the lengths and board feet written on each piece.
- BimCraft
- 21 calculations
64-bit Open item -
Wall-thickness check
Measures how thick the model is behind each triangle and lists the areas thinner than the printer's limit.
- ModelCraft
- 4 calculations
32-bit in part Open item -
Walls and openings from PDF pages and scans
Reads the lines and door-swing arcs of a plan page, scales them to millimeters from two picked points, and turns them into walls with door and window openings.
- BimCraft
- 9 calculations
64-bit -
Walls and openings traced from a drawing
Turns the lines and blocks of a DWG or DXF drawing into wall center lines, thicknesses, door and window positions, and a reference underlay.
- BimCraft
- 10 calculations
64-bit Open item -
Walls, doors and rooms proposed from a scan
Finds straight walls and door openings in a plan slice of a room scan and proposes them, with the rooms they close, for a person to accept.
- BimCraft
- 11 calculations in 2 files
32-bit in part Open item -
Water hammer and pump trip
Works out the pressure wave speed in a pipe and the head and flow over time after a valve moves or a pump loses power.
- CadCraft
- BimCraft
- 6 calculations in 2 files
64-bit Open item -
Water mains as objects: depths, fittings and take-off
Places each water main at the ground less the cover, derives the bends, tees, reducers and caps the layout implies, and lists pipe lengths and fitting counts.
- CivilCraft
- 5 calculations in 2 files
64-bit Open item -
Water mains network: heads, flows and pressures
Solves a looped water network for the head and pressure at every node and the flow, velocity and head loss in every pipe, then runs fire-flow and extended-period cases on it.
- CivilCraft
- 12 calculations
64-bit Open item -
Water supply and duct network sizing
Works out the flow, velocity, friction and pressure in each pipe or duct of a network, the size each needs, and the pressure left at every outlet.
- CadCraft
- BimCraft
- 31 calculations in 4 files
64-bit Open item -
Water treatment unit processes and sludge sizing
Works out head losses through screens and filters, settling removal, disinfection contact time, sludge age, and the size of an activated-sludge tank and clarifier.
- CadCraft
- BimCraft
- 10 calculations in 2 files
64-bit -
Weibull life data
Weibull shape and scale fitted to failure times, with confidence bounds, mean life and B10 life.
Every app 64-bit, stated limit- 6 calculations
64-bit Open item -
Weight totals in the status line and panels
Adds up the steel and reinforcing bar weights shown in the status line, the model summary and the selection panel.
- DetailCraft
- 3 calculations
64-bit -
Welding of imported geometry
How the points of an imported file (OBJ, glTF, Collada, DXF, DWG) are joined into shared vertices and its polygons into faces.
- CadCraft
- ModelCraft
- 2 calculations
64-bit Open item -
Where a moved solid stops against another
Shortens a move so that solids do not pass into each other, and returns the distance actually moved.
- CadCraft
- ModelCraft
- 7 calculations
64-bit Open item -
Where a remnant's number is written
Finds the roomiest spot inside a remnant for its number, and the text height that fits there.
- CadCraft
- PartCraft
- 1 calculation
32-bit in part Open item -
Where an IFC model point is on the earth
Turns a point of an IFC model into map grid coordinates when the file has a map conversion, or into an approximate longitude and latitude from the site's reference point.
- BimCraft
- 5 calculations
64-bit -
Where dimensions are attached
Works out the points a new dimension stores: its two origins, the point on a circle for a radius or diameter, the legs of an angle, and the line position of baseline dimensions.
- CadCraft
- 5 calculations
64-bit -
Why a curve does not fit, and the radius or length that would
When an alignment's curves or a profile's vertical curves overlap, works out by how much and offers the largest radius or curve length that fits.
- CivilCraft
- 5 calculations
64-bit -
Wide polylines, text masks and ellipses as drawn and plotted
Builds the outlines that a polyline with width, a text background mask and an ellipse become when the drawing is put on screen or on a plotted page.
- CadCraft
- 6 calculations
64-bit -
Window and door pieces, glass and hardware
Turns an opening, a layout of panes and a profile system into the profile pieces to cut with their angles, the glass sizes and the hardware and gasket quantities.
- CadCraft
- 9 calculations in 2 files
64-bit -
Wire antenna (method of moments)
Input impedance, segment currents, radiation pattern and directivity of thin-wire antennas.
Every app 64-bit, stated limit- 8 calculations
64-bit -
Wire harness and control cabinet layout
Reads the connections of a schematic, places modules along mounting rails, measures harness segments and records the wire count and bundle diameter of each segment.
- CadCraft
- 17 calculations in 4 files
64-bit Open item -
Wire lengths through a harness or a cabinet
Works out the cut length of every wire from its route through a harness drawing or between two modules in a cabinet, and the diameter of each bundle.
- CadCraft
- 4 calculations
64-bit -
Worksheets: formulas, column rounding and totals
Works out each worksheet cell from an object's fields with a small formula language, rounds it to the column's decimals, and adds sums, counts, averages and extremes.
- CivilCraft
- 5 calculations
64-bit Open item -
Zoning envelope and limit checks
Works out the buildable area of a lot from its setbacks, the height a sky-exposure plane allows, and the coverage and floor area ratio of the masses on the lot against the limits the person typed.
- CivilCraft
- 8 calculations
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
-
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.
-
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.
-
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
-
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.
-
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.
-
Stated tolerances
Where a tolerance is used it is written down, scaled to the size of the geometry and applied the same way everywhere.
-
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.
-
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.
-
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.