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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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 -
Gravity pipe network: slopes, cover and automatic inverts
Works out each pipe's length, slope and least cover, each structure's rim and sump, and sets inverts that keep the minimum slope, cover and drop.
- CivilCraft
- 3 calculations
64-bit -
Ground modifiers: cut and fill, overlaps, level labels and junction checks
Reports the cut and fill each landscape object makes in the ground, where two of them overlap, the levels and gradients read off the surface, and where walls, steps and planted areas do not meet the levels beside them.
- CivilCraft
- 8 calculations in 2 files
64-bit -
Ground points from an unclassified point cloud
Finds which points of a drone or scanner cloud are ground, so a surface can be built from them.
- CivilCraft
- 5 calculations
64-bit -
Ground surface from contour lines and points
Checks contour lines, gives them elevations, and builds a ground surface from them, filling in the flat triangles that contours leave on ridges, valleys and hilltops.
- CivilCraft
- 8 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 -
Ground-mounted solar arrays on terrain
Places solar tables on the ground inside a region, spaces each row so the row in front does not shade it at the winter sun, and reports table positions, pile heights, ground slope, row pitch and installed power.
- CivilCraft
- 7 calculations
64-bit Open item -
Half floats in USD
Converts between 16-bit half floats and 32-bit floats for USD half types.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 2 calculations
32-bit in part Open item -
Hardscape: paving, paths, walls, ramps and steps
Sets out paving, paths, walls, curbs, ramps and steps on the ground, checks grades, risers and goings, and totals their quantities.
- CivilCraft
- 9 calculations
64-bit Open item -
Hours of direct sun on the ground and on walls
Counts the hours of direct sun each ground cell and each wall point of the building masses gets on chosen days, with the masses and the terrain casting shadows.
- CivilCraft
- 9 calculations
32-bit in part Open item -
IFC 4.3 infrastructure quantities and files
Reads the quantities, stations and alignment lengths of roads, railways, bridges and other infrastructure from an IFC file, totals them per class, and writes a new IFC 4.3 file.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 9 calculations
64-bit Open item -
IFC alignment curves and stations
Reads the alignment curves of an IFC 4.3 file as sampled 3D polylines, finds the point at a station, places elements along them and builds solids swept between cross sections.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 7 calculations
64-bit Open item -
IFC curves and profiles as point lists
Turns the curves and cross-section profiles of an IFC file into polylines: arcs, circles, ellipses, trimmed curves, B-splines, offsets, and the standard steel shapes with their fillets.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 10 calculations in 2 files
64-bit Open item -
IFC export: geometry and quantities gathered from the project
Turns the project's alignments, corridors, pads, walls, track, pipes and parcels into the meshes, lengths, areas and volumes that the IFC export writes.
- CivilCraft
- 15 calculations
64-bit Open item -
IFC export: numbers written to the file
Writes the whole project as an IFC file: coordinates, alignment parameters, lengths, areas, volumes and unit factors as text.
- CivilCraft
- 25 calculations
64-bit Open item -
IFC faces on curved surfaces
Tessellates faces that lie on cylinders, cones, spheres, tori, swept surfaces and B-spline surfaces into triangles.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 11 calculations
64-bit -
IFC geometry handed to the apps
Gives each app an element's triangles and the matrix that places them, in meters with Y up, moved near the origin.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 4 calculations
32-bit in part Open item -
IFC import: alignments, surfaces and units
Reads alignments, terrain surfaces and reference geometry from an IFC file into project coordinates and units.
- CivilCraft
- 13 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 openings, clippings and half-space cuts
Cuts openings and clipping solids out of an IFC element's mesh, so the element is drawn and measured with its voids.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 8 calculations
32-bit in part Open item -
IFC swept solids, primitives and faceted shapes
Builds the meshes of extruded, revolved and swept solids, swept disks such as rebar and pipes, the basic primitives, and faceted boundary shapes.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 10 calculations in 2 files
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 -
Inverse kinematics and joint trajectories
Joint angles that put a robot link at a target, and timed joint moves with their speeds, accelerations and peak torques.
Every app 64-bit, stated limit- 9 calculations in 2 files
64-bit -
Irrigation zones: flow, pressure and coverage
Adds up the flow of each irrigation zone, works out the pressure it needs at the valve and at the supply, the precipitation rate and run time, and checks head coverage.
- CivilCraft
- 20 calculations in 2 files
64-bit Open item -
Landscape grading: platforms, swales, slope classes and ponding
Shapes the proposed ground from platforms, berms, swales and free grading areas, and reads the surface for slope classes and ponds.
- CivilCraft
- 6 calculations
64-bit Open item -
Landscape IFC export
Writes plants, beds, hedges, planted areas, hardscape and freeform objects to an IFC file in meters.
- CivilCraft
- 7 calculations
64-bit Open item -
Landscape sections and detail drawings
Cuts a section line through the ground, walls, paving, planted areas, steps and plants and lays the result out to scale on a sheet, and draws wall, paving and step details from their numbers.
- CivilCraft
- 11 calculations in 3 files
64-bit -
LandXML export and import
Writes points, surfaces, alignments, profiles, pipe networks and feature lines as LandXML, and reads them back.
- CivilCraft
- 16 calculations
64-bit Open item -
LAS and LAZ point coordinates
Reads a LiDAR file's header and turns each stored point into x, y, z in the file's coordinates.
- CadCraft
- BimCraft
- CivilCraft
- 4 calculations
64-bit -
Library 3D preview
The 3D view of an item on its Library page and on the configure page.
Every app Display only- 3 calculations in 2 files
32-bit, display only -
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 -
Line study file (.DON) export and import
Writes an overhead line study as a .DON XML file in meters and decanewtons for another line program, and reads such a file back into a line.
- CivilCraft
- 7 calculations
64-bit -
Lineweights in a DWG file
Converts a lineweight between its value in hundredths of a millimeter and the index a DWG file stores.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- 2 calculations
Exact -
Linework checks for linked landscape objects
Checks a line or outline taken from other linework before a landscape object uses it, and detects when that source has moved.
- CivilCraft
- 3 calculations
64-bit -
Load flow and short-circuit currents
Bus voltages, branch flows and losses of an AC network, and fault currents by symmetrical components.
Every app 64-bit, stated limit- 12 calculations in 3 files
64-bit Open item -
Lumped system models
Operating point and response over time of electrical, thermal, hydraulic and mechanical networks built from lumped elements.
Every app 64-bit, stated limit- 12 calculations in 3 files
64-bit Open item -
Magnetic and electric field solvers
The field of wire segments, the mutual inductance of loops, and 2D finite-element magnetic and electric fields with energy, capacitance and force.
Every app 64-bit, stated limit- 12 calculations in 2 files
64-bit Open item -
Map coordinate reprojection
Moves points, and a model's position on the map, between coordinate systems.
- BimCraft
- CivilCraft
- 3 calculations in 2 files
64-bit -
Map layers: web Mercator, tile grids and world files
Converts longitude and latitude to web Mercator and back, lays out the tiles of a map service, reads a picture's world file, and writes the box of a map request.
- CadCraft
- BimCraft
- CivilCraft
- 10 calculations
64-bit Open item -
Map pictures warped onto the plan
Picks the tile level for the screen and cuts a map picture into pieces that are each drawn with one affine transform.
- CadCraft
- BimCraft
- CivilCraft
- 3 calculations
32-bit, display only -
Mass-haul diagram
Works out the mass ordinate at each section, the balance points, the volume moved in each balanced stretch and its average haul distance.
- CivilCraft
- 5 calculations
64-bit -
Massing options placed on a lot
Reads alternative building footprints, places each inside the buildable envelope, and writes the envelope back as a file in millimeters.
- CivilCraft
- 6 calculations
64-bit Open item -
Massing window read-outs and typed height
The footprint and floor-area read-outs of a building mass, the zoning coverage field, and what happens to a typed height.
- CivilCraft
- 3 calculations
64-bit -
Measure tool
The lengths, bearings, grades, total length, ground length and area of what the person measures in plan, and the difference between two points on a profile.
- CivilCraft
- 2 calculations
64-bit Open item -
Model points written to USD
Writes the vertices and edges of a model into USD meshes and curves.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 2 calculations
32-bit in part Open item -
Number text in USD files
Writes numbers into .usda text and decides which attribute types are 32-bit and which are 64-bit.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 3 calculations in 2 files
32-bit in part Open item -
Numbers in a DWG file, read and written bit for bit
Reads and writes the number codes of a DWG file: full and compressed 64-bit values, whole numbers of several sizes and object handles.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 16 calculations in 2 files
64-bit -
Numbers sent between people editing together
How a number in an edit is written into a Studio Live message and read back on the other side.
Every app 64-bit, direct- 5 calculations
64-bit -
Numbers typed into the property grid
Turns what a person types or drags in a Properties row into the number handed to the app.
Every app 64-bit, direct- 3 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
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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.