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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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 files of NURBS curves and surfaces
Writes B-spline curves and surfaces, with their trims, to a STEP file in millimeters and reads such files back.
- ModelCraft
- PartCraft
- 7 calculations
64-bit -
STEP import: triangles for curved faces
Turns each face of an imported STEP solid into triangles that stay within a chord tolerance of the true surface and share their edge points with the neighboring faces.
- 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 -
STL and 3MF files for the printer
Writes the checked mesh as a binary STL or a 3MF file.
- ModelCraft
- PartCraft
- 3 calculations
32-bit in part Open item -
STL import and export
Reads and writes STL triangles, with a unit on import and millimeters on export.
- ModelCraft
- 6 calculations
32-bit in part Open item -
Stock simulation and machining time
Simulates the stock being cut by every tool move, reports material removed, stock left and gouges, and estimates the machining time.
- PartCraft
- 8 calculations
64-bit -
Storm drainage: rational method, pipe sizing and grade lines
Works out the runoff reaching each pipe, the pipe size that carries it, and the hydraulic and energy grade lines through the network.
- CivilCraft
- 9 calculations
64-bit Open item -
Storm hydrographs routed through the pipe network
Carries each catchment's runoff over time down the pipes and reports the peak flow, its time and the attenuation at every pipe and structure.
- CivilCraft
- 6 calculations
64-bit Open item -
Straight stair geometry
Works out the risers, treads, pitch and the stringer and tread parts of a straight steel stair from its rise, going and width.
- DetailCraft
- 4 calculations
64-bit -
Stress analysis
Linear static stress and displacement of a part on a voxel grid.
- PartCraft
- 3 calculations
32-bit in part Open item -
Stress, displacement and error results on tetrahedra
Turns the solved displacements into stresses, principal stresses, strain, reactions, the reported maxima, the safety factor and the estimated error of the mesh.
- PartCraft
- 11 calculations in 2 files
32-bit in part Open item -
Structural members and their cut list
Places steel sections along sketch lines, works out the miter, butt and fitted cuts where members meet, and lists each piece's length and end angles in the cut list.
- PartCraft
- 10 calculations
32-bit in part Open item -
Study set-up: element size and the mesh handed to the solver
Prepares a simulation or generative study for solving: the automatic element size, the estimated element count, the design box, and the copy of the body's mesh the solver works on.
- PartCraft
- 4 calculations
32-bit in part 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 -
Subdivision surfaces
Smooths a mesh by Catmull-Clark subdivision, with sharp and semi-sharp creases, and finds where its vertices lie on the limit surface.
- ModelCraft
- 6 calculations
32-bit in part Open item -
Sun gain through windows
Works out the heat the sun brings through each window over one clear day: the gain at each time step, the peak and the daily total.
- BimCraft
- 4 calculations
64-bit -
Sun position
Works out where the sun is for a date, time and place: azimuth, altitude with refraction, declination and the equation of time.
- CivilCraft
- 3 calculations
64-bit -
Sun position and light on a tilted plane for solar
Gives the sun's direction for each solar hour and the direct, sky and ground-reflected light falling on a module plane, from a clear-sky model or typed monthly totals.
- BimCraft
- CivilCraft
- 8 calculations
64-bit -
Sun position for shadows
The sun's altitude and azimuth for a date, clock time, latitude, longitude and time zone, and the direction shadows are cast from.
- CadCraft
- BimCraft
- ModelCraft
- CivilCraft
- 5 calculations
64-bit -
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 -
Supplier stock and lead-time check
Reads a supplier's stock list and checks each quantity the model needs against it: how much is short, and how long the wait is.
- TakeoffCraft
- DetailCraft
- 12 calculations in 2 files
64-bit -
Supports preview and material estimate
Finds the faces that overhang past an angle, places simple column or tree supports under them, and estimates the support material.
- ModelCraft
- 5 calculations
64-bit -
Surface display meshes, curvature map and zebra stripes
Makes the triangles that draw a surface body and colors a mesh by curvature or by zebra stripes.
- PartCraft
- 3 calculations
32-bit, display only -
Surface exported as a GeoTIFF elevation grid
Samples a surface on a regular grid and writes it as a GeoTIFF with one elevation band.
- CivilCraft
- 4 calculations
32-bit in part Open item -
Surface features built with the kernel
Makes freeform surface bodies and turns them into solids: patches, lofts, network surfaces, offsets, thickened and stitched surfaces.
- PartCraft
- 8 calculations
64-bit -
Surface mesh from a distance grid (dual contouring)
Turns a distance grid into a closed triangle mesh, one vertex per surface cell.
- PartCraft
- 5 calculations
32-bit in part Open item -
Surface through a network of curves
Builds one B-spline surface that passes through a grid of profile curves and guide curves, and reports how far it strays from them.
- PartCraft
- 19 calculations
64-bit -
Surface triangulation
Builds a triangulated surface from survey points and breaklines, then its elevations, contours and slopes.
- BimCraft
- CivilCraft
- 6 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 -
Survey levels from text and the survey check
Reads spot levels written as text or block attributes into points with a height, and checks a surveyor's drawing for unit, origin, flat-contour, outlier and duplicate problems.
- CadCraft
- BimCraft
- CivilCraft
- 6 calculations
64-bit -
Survey network adjustment
Adjusts a survey network or a leveling run by least squares, closes a traverse by the compass rule, and reports residuals, the variance factor and error ellipses.
- CivilCraft
- 10 calculations
64-bit Open item -
Survey point files: reading and writing
Reads survey points from CSV or text files, counts them by description group, and writes them back as a PNEZD file.
- CivilCraft
- 3 calculations
64-bit -
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 -
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 -
Tapered, revolved and swept solids
Builds a solid from a 2D outline: an extrusion with tapered sides, a revolution about an axis, or a sweep along a path.
- CadCraft
- 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 -
Tetrahedral mesh of a part
Builds the tetrahedral analysis mesh of a solid from its surface triangles: element sizes, inside and outside, cut points on the surface, boundary vertices on the true faces, and the mesh quality and volume that are reported.
- PartCraft
- 20 calculations
64-bit -
Tetrahedral stress, vibration and buckling solve
Assembles the stiffness of the tetrahedral model, applies supports and loads, and solves for displacements, natural frequencies and the pre-stress of a buckling study.
- PartCraft
- 12 calculations in 2 files
64-bit -
Text from drawings as stroked edges
The line segments that draw the text of an imported drawing in the 3D model, and the width of a string.
- CadCraft
- ModelCraft
- PartCraft
- 3 calculations
64-bit -
Text positions: search hits and the OCR text layer
Works out where a found word sits on the sheet, the cloud drawn round it, and where the words read from a scanned page are placed.
- MarkupCraft
- 6 calculations in 2 files
64-bit -
Text width from built-in font metrics
The width of a text string, used to size and wrap text boxes in the markup.
- MarkupCraft
- 2 calculations
64-bit -
Texture bake inputs
Gathers the triangles, normals and ray distance that the texture bake (ambient occlusion, curvature, normals, lighting) reads to make pictures.
- ModelCraft
- 2 calculations
32-bit, display only -
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 -
Thermal window temperature range and balance read-outs
The temperature range of a thermal plot, the probed temperature and the heat balance figures.
- PartCraft
- 3 calculations
32-bit in part 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 -
Thread dimensions and modeled threads
Works out a thread's diameters and profile from its size, picks the size that fits a round face, and builds the helical solid of a modeled thread.
- PartCraft
- 8 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.