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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Scale feature for printing
Scales a body by a factor per axis about a chosen point, including a shrinkage allowance given as a percent.
- PartCraft
- 3 calculations
64-bit -
Scaled mesh for printing
Scales the part's mesh for shrinkage or by typed factors and writes it as STL or 3MF.
- PartCraft
- 3 calculations
32-bit in part Open item -
Scan clean-up and JPEG decoding
Reads a scanned image, turns it into black and white, finds how far the sheet is rotated and turns it straight.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- PartCraft
- 6 calculations in 2 files
64-bit Open item -
Scan compared with the model
Compares a point cloud with each model element's box and reports whether the element is built, partly built or missing, how far the scanned surface is from it, and the percent complete.
- BimCraft
- 5 calculations
32-bit in part Open item -
Scan registration
Finds the rigid move (rotation and shift) that lines one scan up with others, from picked point pairs or by iterative closest point, and reports the remaining error.
- CadCraft
- BimCraft
- 15 calculations
32-bit in part Open item -
Scanned drawings: size, scale, align, crop and trace
Places a scanned picture, scales and turns it from picked points, crops it, and turns its traced ink into lines, arcs and circles in drawing coordinates.
- CadCraft
- 9 calculations in 2 files
64-bit Open item -
Scattered plants, rocks and people: how many and where
Works out how many items a scatter set asks for from the area it covers and its density, and picks the points they stand on.
- BimCraft
- ModelCraft
- 4 calculations
64-bit -
Scene handed to the renderer
Turns what the view shows into the renderer's geometry: positions, normals and texture coordinates per color, with material displacement on meshes.
- ModelCraft
- 3 calculations
32-bit, display only -
Schedule risk (Monte Carlo)
The finish at P10, P50, P80 and P90, how often each task is critical, and which durations drive the finish.
Every app 64-bit, stated limit- 3 calculations
64-bit -
Schematic wires, pins and connections
Decides which wires and symbol pins of a schematic are connected, places wire numbers and junction dots, and positions symbols, pins and wires on the sheet.
- CadCraft
- 15 calculations in 4 files
64-bit -
Script result fields and meshes shown in the window
The scalar a script's field plot colors by, its range, and the outer surface of a result mesh.
- PartCraft
- 4 calculations
32-bit, display only -
Script workspace: the part handed to scripts and picked values
Hands the open part's mesh to scripts, and reports the point, node and field values under a click on what a script showed.
- PartCraft
- 4 calculations
32-bit in part Open item -
Sculpt brushes
Moves the vertices under a round brush: draw, clay, smooth, grab, inflate, crease, pinch and flatten, with a mask that protects vertices.
- ModelCraft
- 10 calculations in 2 files
32-bit in part Open item -
Seam allowance: the cut line
Draws the cut line round a pattern piece at each edge's seam allowance, with the corner rules pattern makers use (Apparel add-on).
- CadCraft
- 7 calculations
64-bit Open item -
Section caps: which elements are closed solids
Decides which elements have a closed surface, so the section view paints a cut face only where there is an inside to fill.
- BimCraft
- 2 calculations
32-bit, display only -
Section cut from the ground along any line
Cuts the ground surface along a polyline and gives the distance, offset and elevation at every triangle edge it crosses; also measures along, locates on and crosses polylines.
- CivilCraft
- 8 calculations
64-bit Open item -
Section view plane
The cutting plane of the live section view: its normal and position, and the range of its slider.
- PartCraft
- 2 calculations
32-bit, display only -
Section volumes in the 3D view
Works out the planes, corners and edges of the free-form section volumes that cut the 3D view.
- BimCraft
- 3 calculations
32-bit, display only -
Seismic loads and story drift to ASCE 7-22
The seismic base shear and story forces by the equivalent lateral force procedure, the building's period, the weight of each floor and the drift check.
- CadCraft
- BimCraft
- DetailCraft
- 11 calculations in 2 files
64-bit -
Sensor readings: values, times and limits
Reads sensor values and times from a CSV file or a live feed and flags a reading as high or low against the asset's limits.
- BimCraft
- 3 calculations
64-bit -
Settlement, flexible mats, pile groups and retaining walls
Estimates elastic settlement, analyzes a footing as a plate on springs, shares a load over a pile group and checks a cantilever retaining wall.
- DetailCraft
- 11 calculations
64-bit -
Shape keys: offsets, editing and blending
The vertex offsets stored for each shape key, the way a key is made from an edit or from imported positions, and the blended points of a mesh.
- ModelCraft
- 5 calculations in 2 files
32-bit in part Open item -
Shapes made by the draw commands
Works out the circles, arcs, polyline arcs, polygons, ellipses, construction lines and text positions that the draw commands store in the drawing.
- CadCraft
- 13 calculations
64-bit Open item -
Shared feature lines: units and geometry
Sends a feature line to the team and takes one back, converting between feet and meters when the two drawings differ.
- CivilCraft
- 2 calculations
64-bit -
Sheet and path of a point on a schematic
Finds which numbered path column of a sheet frame a device or wire sits in, for the place printed in cross-references and lists.
- CadCraft
- 2 calculations
64-bit -
Sheet compare picture
Mixes the renderings of an old and a new sheet into one picture that colors what was removed and what was added.
- MarkupCraft
- 1 calculation
32-bit, display only -
Sheet metal base and edge flanges
Builds the cross-section of a sheet metal flange (bend arcs, leg, tip) and its bend reliefs from thickness, bend radius, angle and length.
- PartCraft
- 4 calculations
64-bit -
Sheet metal bends and flat pattern
Works out the bent profile of a sheet metal base, the bend allowance of every bend, and the flat pattern with its bend lines, size and area.
- PartCraft
- 13 calculations in 2 files
64-bit Open item -
Sheet nesting
Lays parts out on sheets or a roll, reports the sheets used and the efficiency, checks the result, reads part outlines from DXF and writes the nest as DXF.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 19 calculations
64-bit Open item -
Sheet scale read from the sheet's text
Finds scale notations in a PDF sheet's text and picks the listed scale to offer for the sheet.
- TakeoffCraft
- 3 calculations
64-bit -
Sheet scale, typed lengths and measured values
Turns a sheet's scale into real lengths and areas: the calibration from a preset or from two picked points, the reading of a typed length, and the length, area, perimeter and count shown for a measurement.
- MarkupCraft
- 15 calculations in 2 files
64-bit Open item -
Sheet scale: presets, calibration and drawing units
Sets how many real feet one unit on the sheet stands for: from a named scale, from two picked points and a typed distance, or from a DWG or DXF drawing's own units and viewport.
- TakeoffCraft
- 10 calculations in 4 files
64-bit Open item -
Shift calendar working time
The hours a production line is on in a weekly shift calendar, used by the material flow simulation.
- ModelCraft
- 3 calculations
64-bit -
SHX font text: strokes and width
Turns the shapes of a loaded .shx font into strokes, and gives a text's width and the position of each stroke in the drawing.
- CadCraft
- 7 calculations in 2 files
64-bit -
Simulation and flow result plots
Draws the colored cut plane, the surface colors and the streamlines of a result, and makes the finer mesh the colors are drawn on.
- PartCraft
- 4 calculations in 3 files
32-bit, display only -
Simulation numbers shown as text
How the simulation window rounds the numbers it prints and puts into input boxes.
- PartCraft
- 2 calculations
64-bit -
Simulation workspace: plot values and the hover probe
Prepares the values a result plot colors by and reads the result under the pointer.
- PartCraft
- 8 calculations
32-bit in part Open item -
Single-part shop drawing
Draws one part with its holes, copes and section, and prints its dimensions, cut angles and weight.
- DetailCraft
- 5 calculations
64-bit -
Site ground, building pads and cut and fill
Builds the site's ground from survey points, grades building pads into it, works out the cut and fill volumes, drapes paving on it and writes the ground to LandXML.
- BimCraft
- 17 calculations
64-bit Open item -
Site outline, building placement and levels
Stores the site boundary with its area and perimeter, places the building on the site, adds or splits levels, and turns a site-study mass into walls and floors.
- BimCraft
- 11 calculations in 2 files
64-bit Open item -
Site surroundings in local meters
Converts the buildings, parcels and zones found around an address from longitude and latitude to meters east and north of the address point, as suggestions a person can add to the model.
- BimCraft
- ModelCraft
- CivilCraft
- 4 calculations
64-bit -
Size of a copied area
Works out how big a copied area of a sheet is on paper and in the real world, the pixel size it is rendered at, and the scale and turn that fit it to two picked points.
- CadCraft
- BimCraft
- MarkupCraft
- DetailCraft
- 5 calculations
64-bit -
Sizes for new curves and meshes, remesh grid
Chooses a round starting size for a new curve or mesh from what the view shows, and checks that a voxel remesh is not too fine.
- ModelCraft
- 4 calculations in 2 files
64-bit -
Sketch editor drawing
Draws the sketch, its dimensions and their labels on the canvas over the 3-D view.
- PartCraft
- 2 calculations
32-bit, display only -
Sketch editor: typed sizes and dimension values
Takes the numbers a person types in the sketch editor (a dimension's value, the sizes of a shape being drawn) and turns them into stored values and point coordinates.
- PartCraft
- 8 calculations
64-bit Open item -
Sketch exchange macro and import
Writes the drawing as a .swb sketch macro with its coordinates in meters, and reads an exported sketch back as geometry, constraints and dimensions.
- CadCraft
- 8 calculations
64-bit Open item -
Sketch geometry and measured values
Works out radii, arc angles, the current value of a dimension, sketch fillets and the size of a sketch.
- PartCraft
- 9 calculations
64-bit -
Sketch intersections of lines, arcs and circles
Finds where sketch lines, arcs and circles cross each other; trim, extend and offset use the points.
- PartCraft
- 7 calculations
64-bit -
Sketch intersections with splines
Finds where a sketch spline crosses a line, an arc, a circle or another spline.
- PartCraft
- 3 calculations
64-bit -
Sketch photo to drawing
Finds a sheet of paper in a photo, straightens it, and turns the pen lines on it into lines and arcs at a stated scale.
- CadCraft
- 6 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.