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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Paper sizes, drawing scales and viewport aim
Turns a scale 1:n and the drawing's units into a viewport scale, picks the standard scale at which a view fits, and sizes the space a new sheet leaves for views.
- CadCraft
- 10 calculations
64-bit -
Parameter expressions
Evaluates the formulas typed for parameters and dimensions: arithmetic, units, trigonometry in degrees, rounding functions and comparisons.
- CadCraft
- BimCraft
- PartCraft
- 11 calculations
64-bit -
Parcels: deed calls, closure, area and legal description
Reads bearings and distances, runs deed calls into corners, reports the misclosure and precision, and works out a parcel's courses, area, perimeter, labels and legal description.
- CivilCraft
- 13 calculations in 2 files
64-bit Open item -
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 -
Pasted picture size
Sizes a pasted picture, or a copied area pasted at its true size, in drawing units.
- CadCraft
- 3 calculations
64-bit -
Pattern piece lengths, seam walking and areas
Measures the sew line of a pattern piece: edge lengths, the distance round the outline between two points, seam walking against another piece, and the perimeter and area per size.
- CadCraft
- 4 calculations
64-bit -
PCF piping files from and to pipe runs
Writes BimCraft's pipe runs as piping components with end points, bores, bend angles and corner points, and turns the components of a piping file back into runs.
- BimCraft
- 5 calculations
64-bit -
Photo material settings
Keeps the tile size, roughness and bump strength of a material made from a photo, as they are saved in the file.
- BimCraft
- 1 calculation
64-bit -
Picked points, object snaps and viewport views
Turns a pointer position into drawing coordinates, finds the object snap under it, and works out the center, scale and twist of a sheet viewport after it was panned or zoomed.
- CadCraft
- 7 calculations
64-bit -
Pictures: size, placement and clip
Works out where a picture's corners lie, its pixel size when attached or pasted, and its clip boundary in pixel coordinates for saving.
- CadCraft
- 6 calculations in 2 files
64-bit -
Pinch analysis
Works out the minimum hot and cold utility, the pinch temperature, the composite curves, the area target and the minimum number of exchangers for a set of process streams.
- CadCraft
- BimCraft
- 5 calculations
64-bit -
Pipe route clearance size
Turns the outside diameter of a pipe size from the spec table into millimeters for the route finder, and states the bend radius in millimeters.
- BimCraft
- 1 calculation
64-bit -
Pipe run points with fall applied
Applies the fall of a sloped pipe run to its corner points and reads the outside diameter of the pipe.
- BimCraft
- 2 calculations
64-bit -
Pipe runs: layout, 3D solid and schedule
Lays out a pipe run with its elbows, reducers and branches, builds its 3D solid, and adds up pipe lengths, weights and fittings for the schedule.
- CadCraft
- 31 calculations in 4 files
64-bit Open item -
Pipe spec rules
Checks a pipe run's size and valves against its pipe spec and says how a branch is made and what bend radius the spec gives.
- BimCraft
- 3 calculations
64-bit -
Pipe spools, cut lists and spool sheets
Where a steel pipe run is cut into spools, the length of each cut piece, the pipe weight on the bill of materials, and the duct cut list.
- BimCraft
- 10 calculations in 2 files
64-bit Open item -
Pipe stress support helpers
Works out the pressure thrust on a blind end, picks a spring hanger from the maker table and flags a stop that closes.
- CadCraft
- BimCraft
- 3 calculations
64-bit -
Piping in an IFC file as PCF components
Reads pipe segments, fittings and valves from an IFC file and gives their end points, bores, bend angles and center points in millimeters.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 4 calculations
64-bit -
Placing a scanned sheet in the project
Works out the scale, rotation and position that put a scanned drawing into project coordinates, from a stated scale or from matched points, and converts traced lines with it.
- CivilCraft
- 12 calculations
64-bit Open item -
Plan drawing and section sheets for DXF and PDF
Turns the model into the linework and labels of the plan drawing and the cross-section sheets, as they are drawn on screen and written to DXF and PDF.
- CivilCraft
- 7 calculations in 2 files
64-bit -
Plan view: picked points, wall outlines and dimensions
Turns a pointer position into plan millimeters, and works out the dimension chain along each wall and the wall's plan outline with its door and window openings taken out.
- BimCraft
- 5 calculations in 2 files
64-bit -
Planar faces of a mesh
Groups a mesh's triangles into flat faces and traces each face's outline, for face picking, face profiles in DXF and merged faces in STEP.
- PartCraft
- 5 calculations
64-bit -
Plant readings: units, comparison and trends
Converts live plant readings to SI units, compares them with the model, thins long trends for plotting and summarizes a series.
- CadCraft
- BimCraft
- 5 calculations
64-bit Open item -
Planting: bed and hedge fills, planted areas and their quantities
Fills beds, hedges and planted areas with plants at a spacing, counts each species, and totals areas, soil and mulch volumes and edging lengths.
- CivilCraft
- 11 calculations in 2 files
64-bit 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 -
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: 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 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 -
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 -
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 -
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 -
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 -
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 -
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 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 -
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 -
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 -
Redline items placed in the drawing
Maps the marks of a redline package from sheet fractions to drawing coordinates and sizes the revision clouds drawn round accepted items.
- CadCraft
- 4 calculations
64-bit -
Reference picture size and position
Places a copied area of a sheet in the model at its true size.
- DetailCraft
- 4 calculations
64-bit -
Reference planes, axes and points
Works out a reference plane, axis or point from the faces, edges, planes and points it is defined by.
- PartCraft
- 9 calculations
64-bit -
Refrigeration copper tube sizes
Gives the outside diameter, wall and inside diameter of a refrigerant line from its trade size.
- BimCraft
- 1 calculation
64-bit -
Regulation limits in force and how values are written
Gives an app's tools the tightest limit of a rule across the ticked regulation packs, and writes required and found values in problems and on the code summary sheet.
- CadCraft
- BimCraft
- CivilCraft
- DetailCraft
- 4 calculations in 2 files
64-bit Open item -
Rendered picture size
Works out the width and height in pixels of a picture an assistant asks the Render dialog for.
- BimCraft
- 1 calculation
64-bit -
Revision overlay: lining up two sheets and moving the takeoff
Fits the move, turn and scale that lays an old sheet over its revision from two pairs of picked points, and carries the marks and the scale across.
- TakeoffCraft
- 7 calculations in 3 files
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
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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.