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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Rib feature
Builds the region a rib fills from an open sketch line: the line extended past the body, swept to one side, and trimmed by the body.
- PartCraft
- 2 calculations
64-bit -
River model: stations, cut sections and reach lengths
Builds the river model a water surface profile is computed from: river stations, cross-sections cut from the ground, bank positions, reach lengths, flows along the reach and the unit constants.
- CivilCraft
- 7 calculations in 2 files
64-bit Open item -
Roof faces, ridges and areas from an outline
Works out the roof over a building outline: the plan of every roof face, the ridge, hip and valley lines with their heights, the eave and fascia lines, and the roof's area and line lengths.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 23 calculations in 2 files
64-bit -
Roof pitch and slope factors
Reads a roof pitch and turns plan lengths and areas into lengths and areas along the slope.
- TakeoffCraft
- 4 calculations
64-bit -
Roof planes over an outline
Works out the sloping faces, ridges, eave and area of a roof from the building's outline, a pitch and an overhang, and the roof's height over any plan point.
- BimCraft
- 8 calculations
64-bit -
Room outline and furniture placement
Reads a floor face as a room (outline, holes, area), finds nearby doors and windows, and builds the matrix that sets each planned piece on its footprint.
- ModelCraft
- 4 calculations
64-bit -
Rooms and building outline from walls
Finds the closed rooms and the outer outline that a set of wall outlines encloses, with each room's area, perimeter and centroid.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 11 calculations
64-bit -
Rooms handed to add-ons with their doors, windows and walls
Gives an add-on each room of a level with its outline, area and elevation, and decides which doors, windows and walls belong to the room's edge.
- BimCraft
- 1 calculation
64-bit -
Rotations, transforms and small linear algebra (motion)
Rotation matrices, roll-pitch-yaw angles, rotation vectors, rigid transforms and the dense solve used by the robot and linkage calculations.
Every app 64-bit, direct- 7 calculations
64-bit Open item -
Rounding for display and for money
Rounds a number to a fixed count of decimals, and writes a length in feet and inches to the nearest fraction of an inch.
- TakeoffCraft
- 4 calculations
64-bit -
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 -
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 -
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 -
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 -
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 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 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 -
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: 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 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 profiles for exact solids
Turns a sketch's lines, arcs, circles and splines into closed loops, decides which loops are holes, and hands the exact curves to the solid kernel.
- PartCraft
- 6 calculations
64-bit Open item -
Sketch splines: evaluation, fitting and exact pieces
Evaluates sketch splines and their derivatives, fits a spline through points, cuts an exact piece out of one, and gives the area a closed spline encloses.
- PartCraft
- 13 calculations
64-bit -
Sketch tools: trim, extend, offset, mirror, pattern, polygon, slot, project
Changes sketch geometry with the editing tools: new end points for trimmed and extended curves, offset copies, mirrored and patterned copies, polygons, slots and projected model edges.
- PartCraft
- 11 calculations
64-bit Open item -
SKP import: placements, texture coordinates and face loops
Reads component placements, texture coordinates and the direction of face loops from SKP files.
- ModelCraft
- 6 calculations in 2 files
64-bit -
Snap points picked in the 3D view
The 3D point a click gives when it snaps to a face, an edge, a midpoint, a face center, an axis direction or a locked direction. That point becomes model geometry.
- CadCraft
- ModelCraft
- 12 calculations
64-bit Open item -
Solar string sizing
Works out how many modules go in a string and how many strings on an inverter from the module and inverter ratings and the temperatures given.
- BimCraft
- CivilCraft
- 6 calculations
64-bit Open item -
Spline through fit points
Works out the control points and knots of a cubic spline that a drawing stores only by its fit points and end tangents.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- 5 calculations
64-bit Open item -
Spoken lengths, directions and extents
Works out the lengths, distances, directions and extents that CadCraft says when the drawing is described in words.
- CadCraft
- 9 calculations
64-bit Open item -
Spread between coarse and refined results
States how far a coarse live result is from the refined one, as a fraction.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 1 calculation
64-bit -
Stage lighting plot: positions, fixtures and loads
Measures the pipes and trusses fixtures hang on, spreads fixtures evenly along them, finds which position a fixture belongs to and totals the wattage.
- CadCraft
- 11 calculations in 3 files
64-bit -
Stair family from a sketch
Writes a sketched stair as a family recipe with its width, tread, total rise, tread counts and riser height as parameters.
- BimCraft
- 2 calculations
64-bit -
Stair risers, treads and stairwell
Works out how many risers a stair needs and how high each is, lays out the treads, landings, winders or spiral wedges, checks them against the limits, and cuts the stairwell in the floor above.
- BimCraft
- 12 calculations in 2 files
64-bit -
Staking reports
Lists stakes along an alignment at stations and offsets, or survey points measured against it, each with its coordinates, design and ground elevations and cut or fill.
- CivilCraft
- 5 calculations
64-bit -
Standard parts and library items
Works out the dimensions, mass and drawing of standard bolts, nuts, washers, pins, keys, bearings and gears, and turns parts and steel sections into library items.
- CadCraft
- PartCraft
- 9 calculations in 2 files
64-bit -
Starter door and window sizes
The width, height and sill of the starter door and window types, written in inches and stored in millimeters.
- BimCraft
- 2 calculations
64-bit -
Starter library: plants and entourage sizes
Builds a plant or entourage component at the size the plant list gives.
- ModelCraft
- 2 calculations
64-bit -
Steel section dimensions, areas and outlines
Gives the dimensions, published area and mass of every steel section in millimeters, the exact area from the dimensions, and the outline used to draw and sweep it.
- CadCraft
- BimCraft
- DetailCraft
- PartCraft
- 6 calculations
64-bit Open item -
STEP curves and surfaces: points from parameters
Works out the 3D point at a parameter on each kind of curve and surface a STEP file can hold, which is where the triangles of an imported solid get their corners.
- BimCraft
- ModelCraft
- PartCraft
- 14 calculations
64-bit -
STEP import: units, points and assembly placement
Turns the numbers of a STEP file into millimeters and radians and puts every solid where the file's assembly structure places it.
- BimCraft
- ModelCraft
- PartCraft
- 10 calculations
64-bit -
STEP import: welding and meters
Turns each solid read from a STEP file into one welded mesh in meters.
- ModelCraft
- 1 calculation
64-bit Open item -
Subdivide, loop cut, bisect, knife and grid fill
Places the new points when edges are cut evenly, when a plane or a knife line cuts faces, and when a quad or an open loop is filled with a grid.
- ModelCraft
- 5 calculations
64-bit Open item -
Superelevation: runoff, runout and lane slopes
Works out where the lanes of a road rotate into and out of each curve and the cross slope of each lane at any station.
- CivilCraft
- 5 calculations
64-bit -
Surfaces from curves: extrude, ruled, revolve and loft
Builds a surface by pulling a curve along a direction, spanning two curves, turning a profile about an axis or passing through a set of sections.
- ModelCraft
- PartCraft
- 7 calculations
64-bit Open item -
Symbols imported from another drawing
Turns a block of a DWG or DXF drawing into an electrical symbol in millimeters, with its connection points.
- CadCraft
- 4 calculations
64-bit -
Takeoff lengths and areas
Lengths, perimeters and areas of measured runs and outlines, with arcs and cut-outs.
- TakeoffCraft
- 6 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.