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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People flow and evacuation time
How fast people pass doors, corridors and stairs, which way each room empties, and how long it takes everyone to reach an exit.
Every app 64-bit, stated limit- 6 calculations
64-bit -
Picked points, object snaps and viewport views
Turns a pointer position into drawing coordinates, finds the object snap under it, and works out the center, scale and twist of a sheet viewport after it was panned or zoomed.
- CadCraft
- 7 calculations
64-bit -
Pictures: size, placement and clip
Works out where a picture's corners lie, its pixel size when attached or pasted, and its clip boundary in pixel coordinates for saving.
- CadCraft
- 6 calculations in 2 files
64-bit -
Pinch analysis
Works out the minimum hot and cold utility, the pinch temperature, the composite curves, the area target and the minimum number of exchangers for a set of process streams.
- CadCraft
- BimCraft
- 5 calculations
64-bit -
Pipe runs: layout, 3D solid and schedule
Lays out a pipe run with its elbows, reducers and branches, builds its 3D solid, and adds up pipe lengths, weights and fittings for the schedule.
- CadCraft
- 31 calculations in 4 files
64-bit Open item -
Pipe stress checks
Turns a routed pipe run into a beam model, solves weight and thermal expansion, and checks sustained, expansion and occasional stresses against the allowables a person gives.
- CadCraft
- BimCraft
- 11 calculations
64-bit Open item -
Pipe stress support helpers
Works out the pressure thrust on a blind end, picks a spring hanger from the maker table and flags a stop that closes.
- CadCraft
- BimCraft
- 3 calculations
64-bit -
Pipe, duct and gas networks
Heads, pressures, flows and velocities in a steady network of pipes, pumps and fittings.
Every app 64-bit, stated limit- 9 calculations in 2 files
64-bit Open item -
Piping network, pumps and compressors
Works out the flows and pressures in a liquid or gas piping network with pumps and valves, the suction head available to a pump, and the head, power and surge margin of a compressor.
- CadCraft
- BimCraft
- 11 calculations in 2 files
64-bit Open item -
Planar linkages (closed loops)
The pose of four-bars, slider-cranks and other planar linkages, their sweep, velocity ratios, mobility and Grashof class.
Every app 64-bit, stated limit- 9 calculations
64-bit Open item -
Plant readings: units, comparison and trends
Converts live plant readings to SI units, compares them with the model, thins long trends for plotting and summarizes a series.
- CadCraft
- BimCraft
- 5 calculations
64-bit Open item -
Plate element for slabs and walls
The stiffness of one four-node plate of a slab or wall, and the membrane forces, bending moments and shears inside it.
- CadCraft
- BimCraft
- DetailCraft
- 12 calculations
64-bit -
Plotting: sheet scale, PDF, SVG and PNG output
Scales the model onto paper and writes the sheet as a PDF, an SVG or a PNG.
- CadCraft
- 13 calculations
64-bit Open item -
Point cloud positions and read-in values
Turns the points of a scan file into the kept cloud (positions, intensities, size) that the apps measure, slice and snap to.
- CadCraft
- BimCraft
- 6 calculations
32-bit in part Open item -
Points and heights picked in the 3D view
Turns a click in the 3D tab into a point or a height in drawing units, and lays the 2D drawing on the ground as edges the 3D snaps use.
- CadCraft
- 5 calculations
64-bit -
Polar and object snap tracking
Pulls the pointer onto a ray at a set angle from a base point, or onto the crossing of two such rays, and returns that point for the drawing.
- CadCraft
- 3 calculations
64-bit Open item -
Polygon mesh: attribute layers (UV, color, crease, weights)
The extra values a mesh keeps per vertex, corner, face or edge, such as texture coordinates, colors, edge crease and skin weights.
- CadCraft
- ModelCraft
- 4 calculations
32-bit in part Open item -
Polygon mesh: normals, areas, triangles and volume
The normal, area, center and flatness of a mesh face, the triangles the mesh is cut into, and the area and volume reported for a mesh.
- CadCraft
- ModelCraft
- 7 calculations
64-bit -
Polygon mesh: shading normals
The normal at each face corner that makes a mesh shade smooth or faceted on screen.
- CadCraft
- ModelCraft
- 1 calculation
32-bit, display only -
Polygon triangulation (ear clipping)
Splits a flat polygon with holes into triangles, for caps of extruded sections and faces with holes.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 9 calculations
64-bit -
Pressure vessel thickness and support formulas
Works out required shell, head and cone thickness, allowable pressures, nozzle reinforcement areas, saddle and skirt stresses and wind and seismic loads on a vessel.
- CadCraft
- BimCraft
- 19 calculations in 2 files
64-bit Open item -
Printing patterns at full size
Lays pattern pieces on one large page or on tiled home-printer pages at 1:1, with a test square to check the print scale (Apparel add-on).
- CadCraft
- 6 calculations
64-bit -
Process diagram entities
Lays out the process flow diagram, node boundaries and live value labels that the P&ID add-on and the Plant tab add to a drawing.
- CadCraft
- BimCraft
- 4 calculations
64-bit -
Process emissions (CO2 equivalent)
Works out the CO2-equivalent emissions of vented and burned streams, fired heaters and electric units, per second and per year.
- CadCraft
- BimCraft
- 4 calculations
64-bit -
Properties in DWG and DXF: transparency, lineweights, dimension variables
Converts transparency, lineweights and dimension style settings between the drawing's values and the whole-number or text forms DWG and DXF keep.
- CadCraft
- 9 calculations
64-bit -
Properties panel: measures and geometry edits
Shows an object's length, angle, area, circumference, chord and sweep, and changes the object when one of them is typed.
- CadCraft
- 10 calculations in 2 files
64-bit -
Property package and flashes
Works out phase splits, bubble and dew points, enthalpy, entropy and volume of a mixture for the flowsheet and the calculators.
- CadCraft
- BimCraft
- 18 calculations in 2 files
64-bit Open item -
Protection curves and grading
Relay and fuse operating times, grading margins between devices, and the cable damage time.
Every app 64-bit, stated limit- 6 calculations
64-bit Open item -
Pure-fluid properties from CoolProp
Gives enthalpy, entropy, heat capacity, density and saturation values of a pure fluid, and builds a component from them.
- CadCraft
- BimCraft
- 5 calculations
64-bit Open item -
Push/pull, move, stretch, follow me and intersect
The new positions of vertices when a face is pushed or pulled, geometry is moved or stretched, a face is swept along a path, or faces are cut where they cross.
- CadCraft
- ModelCraft
- 9 calculations
64-bit -
Reaction mechanisms in a closed vessel
Reads a reaction mechanism file and follows the species concentrations and temperature of a closed, constant-volume vessel over time.
- CadCraft
- BimCraft
- 8 calculations
64-bit -
Reactors
Works out the outlet of conversion, equilibrium, plug-flow and stirred-tank reactors, with their heat duty.
- CadCraft
- BimCraft
- 10 calculations
64-bit -
Redline items placed in the drawing
Maps the marks of a redline package from sheet fractions to drawing coordinates and sizes the revision clouds drawn round accepted items.
- CadCraft
- 4 calculations
64-bit -
Registered scans written as LAS and E57
Moves every point of the registered scans by its scan's matrix and writes the result as a LAS 1.2 or an E57 file.
- CadCraft
- BimCraft
- 6 calculations
32-bit in part Open item -
Regulation limits in force and how values are written
Gives an app's tools the tightest limit of a rule across the ticked regulation packs, and writes required and found values in problems and on the code summary sheet.
- CadCraft
- BimCraft
- CivilCraft
- DetailCraft
- 4 calculations in 2 files
64-bit Open item -
Release, fire, explosion and toxic screening
Works out how much escapes through a hole, how far fire radiation, blast overpressure and a toxic or flammable cloud reach, and the chance of harm from a dose.
- CadCraft
- BimCraft
- 19 calculations in 3 files
64-bit Open item -
Relief valve sizing, depressuring and flare loads
Works out the orifice area a relief valve needs for gas, liquid, steam or two-phase flow, the heat input from a fire, the back pressure in the outlet line and flare header, flare radiation distance and the pressure of a vessel as it is vented.
- CadCraft
- BimCraft
- 17 calculations in 2 files
64-bit Open item -
Rigid-body dynamics of a mechanism
Joint torques for a given motion, the mass matrix, joint accelerations for given torques, energy, and a simulated motion over time.
Every app 64-bit, stated limit- 6 calculations
64-bit -
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 -
Room outline, walls and openings
Builds the room a cabinet job sits in: its corners, the frame of each wall, inside tests, distances to walls, and the doors and windows along the walls.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 19 calculations in 2 files
64-bit Open item -
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 -
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 -
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 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 -
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 -
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 -
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 -
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
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.