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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Sketch photo to drawing: sheet, perspective and scale
Finds the sheet of paper in a photo, straightens it, and places the traced lines and arcs in the drawing at a stated scale.
- ModelCraft
- CivilCraft
- 7 calculations in 2 files
64-bit Open item -
Sketch profiles as closed polygons
Turns the lines, arcs, circles and splines of a sketch into closed polygon loops, tests whether a point is inside them, and gives a loop's area.
- PartCraft
- 5 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 solver
Moves the points and radii of a sketch until every relation and dimension is met, and reports how many degrees of freedom are left and which relations conflict or repeat.
- PartCraft
- 11 calculations in 2 files
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 splines: length, nearest point, polyline and offset
The length of a sketch spline, the point on it nearest a given point, its points within a chord tolerance, and its offset curve.
- PartCraft
- 4 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 -
Skin weights and skinning
Works out how much each bone moves each vertex, and moves the mesh's points with the bones.
- ModelCraft
- 9 calculations in 3 files
32-bit in part Open item -
Skinning on the graphics card
Vertex skinning by bones on the GPU for the real-time view and the path tracer.
- ModelCraft
- 2 calculations
32-bit, display only -
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 -
Sky view and daylight factor
Works out how much of the sky each window sees and the daylight factor on a grid of points in a room.
- BimCraft
- 19 calculations
64-bit -
Slope stability
Finds the factor of safety of a circular slip surface by Bishop's simplified method or the ordinary method of slices, and searches for the critical circle.
- CivilCraft
- 6 calculations
64-bit Open item -
Smooth shading and texture placement
The normals that make faces joined by soft edges shade as one surface, and where an imported texture lies on a face.
- CadCraft
- ModelCraft
- 3 calculations
32-bit, display only -
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 -
Snapping to and measuring the sheet's own linework
Reads the vector lines of a PDF page or a CAD sheet, snaps picked points to them, and measures a whole connected path or closed loop from one click.
- TakeoffCraft
- 11 calculations in 4 files
64-bit Open item -
Solar array layout on roofs and ground
Finds the roof planes that can carry modules, fits modules inside a plane with a setback, and lays out ground rows with a spacing that avoids shade at the winter solstice.
- BimCraft
- CivilCraft
- 8 calculations
64-bit -
Solar array shading
Works out, for each hour of each month's representative day, the share of a solar array's sample points that the model shades from the direct sun, and the share of the beam light lost.
- BimCraft
- CivilCraft
- 4 calculations
64-bit -
Solar array site and saved summary
The latitude and longitude kept for a ground PV array and the numbers the file keeps for its plan.
- CivilCraft
- 2 calculations
64-bit -
Solar arrays on the model
Reads the roof planes from the model, plans an array on a roof or the ground, stores it in the file, and combines shading over the modules for the yield.
- BimCraft
- 7 calculations
32-bit in part Open item -
Solar one-line currents, devices and wires
Works out the current on each run of a solar one-line diagram and picks the overcurrent device and wire size from the tables the person gives.
- BimCraft
- 6 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 -
Solar yield estimate
Estimates the DC and AC energy a solar array gives in a year, month by month, with shading, temperature, losses and inverter clipping, and its performance ratio.
- BimCraft
- CivilCraft
- 8 calculations
64-bit Open item -
Solid modeling
Rebuilds a part from its feature history: extrudes, cuts, patterns and boolean operations.
- PartCraft
- 2 calculations
32-bit in part Open item -
Solvers shared by the process engine
The linear solve, Newton iteration, ODE integrator and bracketed root finder that the flowsheet, reactors and design specifications call.
- CadCraft
- BimCraft
- 4 calculations
64-bit Open item -
Solving an expression for one parameter
Finds the value of one parameter that makes an expression give a wanted result, the other parameters held.
- CadCraft
- BimCraft
- PartCraft
- 2 calculations
64-bit Open item -
Sound insulation ratings and the mass law
Works out the single-number airborne and impact sound ratings from sixteen third-octave values, and estimates a plain wall's sound reduction from its mass.
- BimCraft
- 6 calculations
64-bit Open item -
Spending on a person's own AI model
Adds up what calls to a person's own AI model have cost today and this month, and stops a call that could pass the limits the person set.
Every app 64-bit, stated limit- 4 calculations
64-bit -
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 -
Splines: curve points, fitting and editing
Evaluates a spline, builds one through fit points or from control points, turns it into points for drawing and measuring, and inserts control points without changing the curve.
- CadCraft
- 12 calculations in 2 files
64-bit Open item -
Splitting a model into printable pieces
Cuts a model too big for the printer into pieces that fit the bed, places connectors and part numbers on the cut faces, and lists the pieces.
- ModelCraft
- PartCraft
- 23 calculations in 2 files
32-bit in part 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 -
Sprinkler layout and hydraulic calculation
Places sprinkler heads on a grid in a room, builds the branch and main network, sizes the pipes and finds the pressure and flow the design area needs against the water supply.
- BimCraft
- 16 calculations in 3 files
64-bit Open item -
Stack plume rise and air dispersion screening
Works out the effective height of a stack plume, the worst-case and hour-by-hour ground concentrations at receptors, and the contours drawn on a plan.
- CadCraft
- BimCraft
- 10 calculations in 2 files
64-bit Open item -
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 part templates
Builds a parametric part for a standard bolt, nut, washer, pin, bearing or key at a size from the standards tables.
- PartCraft
- 4 calculations
64-bit Open item -
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 -
Standard sections: member solids, mass and parts list
Builds a steel member as a solid from a standard section, shows a section's mass per meter, and totals the placed parts into a parts list.
- CadCraft
- 4 calculations
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 -
Statistical comparison of rendered pictures
Decides whether two renderers give the same picture, and whether a test scene returns the expected brightness, by comparing block means against the pictures' own noise.
- BimCraft
- ModelCraft
- 5 calculations
64-bit -
Steel member checks on a solved frame
Runs the steel code checks along every member for every strength combination, finds the governing ratio, checks the deflection limit, and finds what gives way first.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations in 2 files
64-bit -
Steel member resistance to EN 1993-1-1
The design resistances of a rolled I or H section: classification, tension, bending, shear, buckling, lateral-torsional buckling and the combined checks.
- CadCraft
- BimCraft
- DetailCraft
- 11 calculations
64-bit Open item -
Steel member strength to AISC 360-16
The design strengths of a rolled I-shape in tension, compression, bending and shear, and the combined bending and axial check.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations
64-bit Open item -
Steel profiles: area, mass per meter and sizes
Looks up a steel section or builds a plate or custom profile, and gives its outline, area, mass per meter, width, depth and perimeter.
- DetailCraft
- 5 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: parameters from points
Finds where a 3D point of an edge lies on a free-form curve or surface, so the face it bounds can be laid out flat and triangulated.
- BimCraft
- ModelCraft
- PartCraft
- 5 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.