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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Edits and settings from the main window
Places the mirror plane for a flipped copy, turns a drawn curve into a curve object, bakes node meshes into the model, guesses storey heights, reads the sun settings, and hands a room to add-ons.
- ModelCraft
- 7 calculations
64-bit -
Element quantities for carbon and cost
Reads each element's volume, area and length and splits the volume between its materials, as the embodied carbon and cost calculations use them.
- BimCraft
- 5 calculations
64-bit Open item -
Entity info: volume, size, angle and area
Shows the volume and size of a selected group, component or mesh as it is placed, an arc's angle, the total area of selected faces, and the print check's size and volume.
- ModelCraft
- 5 calculations
64-bit -
Equipment list from drawing tags
Reads the equipment schedule hidden in a foodservice drawing's item tags: one row per item, its quantity and the sheets that show it.
- BimCraft
- 3 calculations
64-bit -
Estimate and quantity exports (CSV and XLSX)
The numbers written to the estimate CSV, the XLSX workbook, the material list and the spot elevation point file.
- TakeoffCraft
- 11 calculations
64-bit Open item -
Exact surface records for meshing
Reads each curved face's true surface (sphere, cone, torus, revolution, extrusion, spline) out of the kernel as plain numbers for the analysis mesher, and verifies it.
- PartCraft
- 3 calculations
64-bit -
Exact-kernel feature dimensions
Works out the lengths, angles and positions handed to the solid kernel for extrudes, revolves, holes, patterns, shells and chamfers.
- PartCraft
- 11 calculations
64-bit Open item -
Export of the 3D model to DXF and DWG
The coordinates, block placements and rotation angles written when the 3D model is exported to DXF R12 or handed to the DWG writer.
- CadCraft
- ModelCraft
- 6 calculations
64-bit Open item -
Face planes, areas, triangles and solid volume
The plane and area of a drawn face, the triangles it is split into, and the surface area and volume of a closed shape.
- CadCraft
- ModelCraft
- 4 calculations
64-bit Open item -
Factory layout checks
Checks equipment placed on a floor for overlaps, blocked access strips, narrow aisles, items outside the room and floor load, and measures the path between items.
- BimCraft
- 8 calculations
64-bit -
FBX import: axes, units and transforms
Turns an FBX file's axes and unit into Z up and meters, and builds each object's matrix from its translation, pivots, rotations and scaling.
- ModelCraft
- 7 calculations
64-bit Open item -
Feature line grades, arcs, offsets and crossings
Works out a feature line's lengths, grades and arcs, sets elevations by grade, offsets the line, and finds where it crosses an alignment.
- CivilCraft
- 15 calculations in 2 files
64-bit -
Field layout points from the model
Works out the points a crew sets out from the model (column feet, wall axis ends, anchor bolts, sleeves, chosen elements) in model or survey coordinates, in meters, millimeters or feet.
- BimCraft
- 3 calculations
64-bit -
Figures shown in the residential panels and schedules
Works out the numbers the residential tools show in Properties and on schedules: a roof plane's area, the cut list, board feet, cut and fill, a new stair's direction and a building's width on an elevation.
- BimCraft
- 7 calculations
64-bit -
Fillet and chamfer
Rounds or cuts the corner between two objects, between two segments of one polyline, or at every corner of a polyline.
- CadCraft
- 9 calculations
64-bit -
Finding joints between members
Finds where a beam end meets a column, where two members meet end to end in line or at an angle, and where a brace lands on another member.
- DetailCraft
- 5 calculations
64-bit -
Flowsheet variant metrics
Works out the heating, cooling and shaft power, the hourly operating cost and the hourly CO2 of one solved flowsheet variant, the numbers an optimization study ranks by.
- CadCraft
- BimCraft
- 1 calculation
64-bit -
Frame analysis: loads, releases, end forces and reactions
Turns loads into nodal forces, takes released ends out of each member, and works out member end forces, support reactions and the load and reaction totals of a solved frame.
- CadCraft
- BimCraft
- DetailCraft
- 13 calculations
64-bit -
Framing panels and cut lists
Lays out the studs, plates, headers, joists and rafters of a framing panel, lists the pieces to cut, and places them in the model as members.
- BimCraft
- DetailCraft
- 12 calculations
64-bit Open item -
Freeform bodies: subdivision surface and cage edits
Refines a control cage into a smooth surface, converts it to Bézier patches for the solid model, and moves, mirrors, extrudes and flattens cage vertices.
- PartCraft
- 19 calculations
64-bit -
Freeform cage edits from the workspace
Turns gizmo drags, clicks on the ground plane and edge extrusions in the Form workspace into new positions of the control cage that defines a freeform shape.
- PartCraft
- 4 calculations
64-bit -
GDSII layout read and placement
Reads an IC layout stream file and places every cell reference and array so the layout can be viewed and measured as drawing objects.
- CadCraft
- 3 calculations
64-bit -
Georeference written to the IFC file
Writes a model's place on the map into the file: the map conversion numbers, the coordinate reference system and its length unit.
- BimCraft
- 5 calculations
64-bit -
GIS feature geometry
Works out ring areas and winding, tests whether a point is inside a ring, sorts rings into polygons and holes, and moves layers between coordinate systems.
- CivilCraft
- 8 calculations in 2 files
64-bit Open item -
GIS import: reprojection and elevation units
Places the features of shapefiles, GeoJSON, KML and GeoPackage files in the project's coordinate system and converts their elevations to the project's unit.
- CivilCraft
- 4 calculations
64-bit -
Grid lines
Lays out grid lines by spacing and angle, finds where they cross for snapping, and decides which lines an elevation sees end on.
- BimCraft
- 6 calculations
64-bit -
Ground surface triangulation and contours
Builds the triangulated ground surface from points, breaklines and a boundary, and works out its contours, elevation bands and outline.
- BimCraft
- CivilCraft
- 17 calculations
64-bit -
Group modifiers: scale and array placements
Works out where each copy of a group or component sits when it has Scale and Array modifiers.
- ModelCraft
- 2 calculations
64-bit -
Groups, placements and the model file
How coordinates are carried when geometry is grouped, placed, exploded or turned into a mesh, and which numbers the model file holds.
- CadCraft
- ModelCraft
- 10 calculations
64-bit -
Heat-exchanger network design
Proposes the matches, heaters and coolers of a heat-exchanger network from stream data by the pinch design method, with the duty and end temperatures of each.
- CadCraft
- BimCraft
- 5 calculations
64-bit -
I/O channel counts with spare allowance
Counts the control system channels of each type on a P&ID and adds the spare allowance.
- CadCraft
- BimCraft
- 1 calculation
64-bit Open item -
IFC length unit and placement matrices
Finds how many millimeters one length unit of an IFC file is, and multiplies, inverts and applies the 4 × 4 placement matrices used when reading and placing elements.
- BimCraft
- 6 calculations
64-bit -
IFC measures in SI for USD
Converts IFC lengths, areas and volumes to meters, square meters and cubic meters when properties are written to USD.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 1 calculation
64-bit -
IFC units and placements
Reads the length and angle units of an IFC file and turns its placements, transformation operators, grid placements and map conversion into 4 × 4 matrices.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 13 calculations in 2 files
64-bit -
IGES files of NURBS curves and surfaces
Writes B-spline curves and surfaces to an IGES file in millimeters and reads them back, converting the file's unit.
- ModelCraft
- PartCraft
- 5 calculations
64-bit Open item -
Imported material parameters
Turns a glTF or FBX material's numbers (roughness, index of refraction, film thickness, emission strength) into the renderer's parameters and back.
- ModelCraft
- 4 calculations
64-bit Open item -
Inset, bevel and moves along normals
Places the new vertices of an inset or a bevel at the stated thickness or width from the old edges, and moves vertices along their normals.
- ModelCraft
- 7 calculations
64-bit -
Installation loads and cable lengths
Adds up the load on each electrical circuit of a building plan, works out its current, and measures each circuit's cable along the drawn routes.
- CadCraft
- 10 calculations
64-bit -
Interior elevations and their dimensions
Frames each wall of a room as an interior elevation, writes its width, height and level dimensions, and turns placed items.
- BimCraft
- 7 calculations in 2 files
64-bit -
Issue viewpoints in BCF files
Converts cameras and section planes between the viewer and the model's own coordinates, and writes and reads them in BCF issue files.
- BimCraft
- ModelCraft
- 8 calculations
64-bit Open item -
Join and stretch
Joins lines, arcs and polylines that line up or meet end to end into one object, and stretches the parts of objects inside a window.
- CadCraft
- 3 calculations
64-bit -
Keys dragged in the graph editor
Turns a drag on the curve editor's canvas into a key's new time and value, or a handle's new offset.
- ModelCraft
- 3 calculations
64-bit -
Knot vectors
Builds and checks the knot vectors that NURBS curves and surfaces are defined on.
- ModelCraft
- PartCraft
- 6 calculations
64-bit -
Lab results to stream composition
Turns lab results in mass, mole, ppm or mg/L terms into a proposed stream composition in mole fractions, and writes calculated compositions back in the lab's terms.
- CadCraft
- BimCraft
- 2 calculations
64-bit -
Length tags and tag schedules
Keeps a length tag on an element as an IFC property and lists tag values in schedules, in millimeters.
- BimCraft
- 3 calculations
64-bit -
Lengths and units for Library items
Reads lengths written as text (30", 2'-6 1/2", 762 mm) into millimeters and writes sizes back as short labels.
- CadCraft
- BimCraft
- 5 calculations
64-bit Open item -
Lengths as text: formats and typed lengths
Writes lengths and areas in the drawing's format (decimal, engineering, architectural, fractional, scientific) and reads lengths typed at the command line.
- CadCraft
- 9 calculations
64-bit Open item -
Lengths, areas and volumes as text
Turns a length in millimeters, an area or a volume into text in the display unit a person picked.
- BimCraft
- 9 calculations
64-bit -
Library configurator sizes
The size and connection positions shown for the chosen variant on a Library item's configure page.
Every app 64-bit, direct- 2 calculations
64-bit -
Library item placed as a block
Turns a Library item's plan into a block in the drawing's units and counts the Library items a drawing uses.
- CadCraft
- 4 calculations
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.