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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Takeoff quantities from marks
The length, area, perimeter and count each mark measures at its sheet's scale, and the totals per item and per sheet that a takeoff reports.
- TakeoffCraft
- 6 calculations
64-bit -
Terrain from contours and terrain grids
Builds a ground surface from contour lines, or a flat grid to sculpt.
- ModelCraft
- 3 calculations
64-bit Open item -
Terrain import and GeoTIFF export settings
Works out the point spacing, the point count and the elevation scaling when an elevation grid or a LiDAR file is brought into a project, and the cell size offered when a surface is written as a GeoTIFF.
- CivilCraft
- 6 calculations
64-bit -
The model file and what it stores
Keeps members, grids, levels and loose bolts, and reads and writes the model file.
- DetailCraft
- 6 calculations
64-bit Open item -
Thinning point clouds to a spacing
Keeps one point per grid cell when a large point cloud is imported, and estimates how many points an import will keep.
- CivilCraft
- 4 calculations
64-bit -
TIFF scan resolution
Reads the resolution of a scanned drawing from a TIFF file as dots per inch.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- PartCraft
- 2 calculations
64-bit -
Traverse closure and compass adjustment
Runs a survey traverse from field angles or bearings and distances, reports its angular and linear misclosure and precision, and adjusts the stations by the compass rule.
- CivilCraft
- 4 calculations
64-bit -
Triangles inside a trimmed face
Adds points inside a triangulated face and keeps the triangles well shaped, for curved faces read from a .3dm file.
- ModelCraft
- PartCraft
- 6 calculations
64-bit Open item -
Triangulation of faces with holes
Splits a flat face, with any holes, into triangles.
- CadCraft
- ModelCraft
- TakeoffCraft
- 9 calculations
64-bit -
Triangulation of solid faces
Splits a face of an imported 3D solid, with its holes, into triangles; the triangles are what the solid's mesh is built from.
- CadCraft
- ModelCraft
- 6 calculations
64-bit -
Trim, extend and corner walls
Finds where two wall center lines meet and the new ends of a wall trimmed or extended to another.
- BimCraft
- 5 calculations
64-bit -
Truss member forces and timber checks
Works out the force in every member of a roof truss for each load case and combination, checks each member in tension or compression with bending, picks sizes, and estimates deflection and bearing reactions.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 20 calculations in 3 files
64-bit Open item -
Typed distances and coordinates while drawing
Places the next point of a run or outline from a typed distance, a distance and angle, or a pair of coordinates, and reads a typed spot elevation.
- TakeoffCraft
- 5 calculations in 2 files
64-bit -
Typed lengths and length readouts in 3D
Reads a length typed in feet, inches, fractions or metric units into meters, and writes lengths, areas and volumes in the model's unit.
- CadCraft
- ModelCraft
- 8 calculations
64-bit -
Typed lengths, angles and pitches
Turns what a person types (feet and inches, fractions, metric, a point or a polar step, a roof pitch) into millimeters and degrees, and formats areas, angles and pitches for display.
- BimCraft
- 6 calculations
64-bit Open item -
Typed lengths, stations and unit text
Reads lengths and stations as typed, and writes stations, areas, volumes and bearings as text.
- CivilCraft
- 8 calculations
64-bit Open item -
Typed points and door or window positions
Turns a typed length, step, polar entry or distance into the next wall point, and places a door or window along a wall from the pointer or a typed distance.
- BimCraft
- 2 calculations
64-bit -
Typed points, distances and angles
Turns what is typed or clicked at a prompt (x,y, @dx,dy, distance<angle, a distance along the cursor direction, an angle in degrees) into the point, length or angle a command uses.
- CadCraft
- 5 calculations
64-bit Open item -
Underground cable routes: cover, crossings, joints and trench quantities
Works out a cable route's length, its cover under the surface, its vertical separation from pipes and other routes it crosses, the joints it needs and the trench quantities.
- CivilCraft
- 10 calculations
64-bit -
USD transforms and placement
Works out where every object of a USD scene sits: each object's own transform, its place in the world, the change to meters with Z up, and the placement of instanced copies.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 11 calculations in 3 files
64-bit Open item -
User coordinate system set by command
Works out the origin and angle of the user coordinate system that UCS and the quarter-turn commands set, and what they print.
- CadCraft
- 4 calculations
64-bit Open item -
User coordinate systems
Converts points, directions and angles between a user coordinate system and world coordinates, and sets a coordinate system from points or from an object.
- CadCraft
- 5 calculations
64-bit -
Values stored from picks in the workspace
Turns a picked flat face, a click on a drawing view or a new section into the plane, point or offset that is saved in the part or assembly.
- PartCraft
- 4 calculations
64-bit -
Vectors, plane frames and transforms
The small vector and 4 × 4 matrix helpers that place sketches on planes and move, rotate and mirror parts.
- PartCraft
- 10 calculations
64-bit -
Vertical profile: grades and parabolic curves
Works out the design elevation and grade at any station from the PVIs and their vertical curves, and samples the existing ground along the alignment.
- CivilCraft
- 4 calculations
64-bit -
Viewports on a sheet
Works out the size and center of a viewport drawn on a sheet and the scale that fits a named view into it.
- CadCraft
- 2 calculations
64-bit -
Voxel grid and lattice struts
The solid cubes of a field grid for the solvers, and the strut lists of lattices.
- PartCraft
- 2 calculations in 2 files
64-bit -
Wall joins and plan outlines
Works out the plan outline of every drawn wall with its corners, tees and crossings cleaned, which becomes the wall's solid and closes rooms.
- BimCraft
- 9 calculations
64-bit -
Wall layers drawn in plans and sections
Works out the outline of each wall layer where a plan or a section cuts a wall, and the wall edges an elevation shows, as the linework drawn on screen and on sheets.
- BimCraft
- 11 calculations in 2 files
64-bit -
Water mains as objects: depths, fittings and take-off
Places each water main at the ground less the cover, derives the bends, tees, reducers and caps the layout implies, and lists pipe lengths and fitting counts.
- CivilCraft
- 5 calculations in 2 files
64-bit Open item -
Water treatment unit processes and sludge sizing
Works out head losses through screens and filters, settling removal, disinfection contact time, sludge age, and the size of an activated-sludge tank and clarifier.
- CadCraft
- BimCraft
- 10 calculations in 2 files
64-bit -
Weight totals in the status line and panels
Adds up the steel and reinforcing bar weights shown in the status line, the model summary and the selection panel.
- DetailCraft
- 3 calculations
64-bit -
Where dimensions are attached
Works out the points a new dimension stores: its two origins, the point on a circle for a radius or diameter, the legs of an angle, and the line position of baseline dimensions.
- CadCraft
- 5 calculations
64-bit -
Why a curve does not fit, and the radius or length that would
When an alignment's curves or a profile's vertical curves overlap, works out by how much and offers the largest radius or curve length that fits.
- CivilCraft
- 5 calculations
64-bit -
Window and door pieces, glass and hardware
Turns an opening, a layout of panes and a profile system into the profile pieces to cut with their angles, the glass sizes and the hardware and gasket quantities.
- CadCraft
- 9 calculations in 2 files
64-bit -
Wire harness and control cabinet layout
Reads the connections of a schematic, places modules along mounting rails, measures harness segments and records the wire count and bundle diameter of each segment.
- CadCraft
- 17 calculations in 4 files
64-bit Open item -
Worksheets: formulas, column rounding and totals
Works out each worksheet cell from an object's fields with a small formula language, rounds it to the column's decimals, and adds sums, counts, averages and extremes.
- CivilCraft
- 5 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.