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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PDF underlay in a plot
Plots the lines, curves, fills and text of a PDF underlay at its place in the drawing.
- CadCraft
- 1 calculation
64-bit Open item -
PDF underlay placement and PDF import
Places a PDF page at its true size in the drawing's units, and turns a page's lines, arcs, circles, fills and text into drawing objects.
- CadCraft
- 13 calculations in 2 files
32-bit in part Open item -
Pen sketch cleanup
Decides what a freehand stroke was meant to be (a line, circle, arc, rectangle or polyline) and makes that exact shape, then joins nearby ends.
- CadCraft
- MarkupCraft
- 9 calculations
64-bit -
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 -
People movement and travel distance
Works out how far the farthest point of each room is from an exit and simulates people walking out of or into the building, with times, queues and walked distances.
- BimCraft
- 12 calculations in 2 files
64-bit -
Photo material settings
Keeps the tile size, roughness and bump strength of a material made from a photo, as they are saved in the file.
- BimCraft
- 1 calculation
64-bit -
Photo to sketch: outline fitting and scale
Turns the outline of a flat part in a photo, or the lines of a pen drawing, into sketch lines, arcs and circles in millimeters.
- PartCraft
- 9 calculations
64-bit Open item -
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 -
Picture backgrounds: scale, placement and print
Sizes a picture placed under a drawing from two picked points and a distance, moves and turns it, places it in sheet views, and works out its size and matrix in a printed PDF.
- BimCraft
- 15 calculations in 3 files
64-bit Open item -
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 and duct runs: layout, lengths and sizing
Turns the pipe and duct lines a person draws into straight pieces, elbows, tees and reducers, measures their lengths and surface, and picks a pipe or duct size for a flow.
- BimCraft
- 23 calculations in 3 files
64-bit Open item -
Pipe route clearance size
Turns the outside diameter of a pipe size from the spec table into millimeters for the route finder, and states the bend radius in millimeters.
- BimCraft
- 1 calculation
64-bit -
Pipe run points with fall applied
Applies the fall of a sloped pipe run to its corner points and reads the outside diameter of the pipe.
- BimCraft
- 2 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 spec rules
Checks a pipe run's size and valves against its pipe spec and says how a branch is made and what bend radius the spec gives.
- BimCraft
- 3 calculations
64-bit -
Pipe spools, cut lists and spool sheets
Where a steel pipe run is cut into spools, the length of each cut piece, the pipe weight on the bill of materials, and the duct cut list.
- BimCraft
- 10 calculations in 2 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 in an IFC file as PCF components
Reads pipe segments, fittings and valves from an IFC file and gives their end points, bores, bend angles and center points in millimeters.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 4 calculations
64-bit -
Piping isometric drawing and its bill of materials
Draws pipe runs as a 30 degree isometric with the length of every leg, elevations and a bill of materials, and writes the drawing as SVG or DXF.
- BimCraft
- 8 calculations
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 -
Pit and solar table meshes in the 3D view
The 3D view geometry for open pits (haul ramp ribbons, bench rims) and ground solar tables.
- CivilCraft
- 4 calculations in 3 files
32-bit, display only -
Placing a linked model
Works out the matrix that puts a linked IFC model in the right place beside the open one, from both files' map positions or from two pairs of picked points.
- BimCraft
- 4 calculations
64-bit Open item -
Placing a model on the map
Builds and reads the map conversion that places a model on a map grid, and re-expresses it in another coordinate system.
- BimCraft
- 6 calculations
64-bit -
Placing a scanned sheet in the project
Works out the scale, rotation and position that put a scanned drawing into project coordinates, from a stated scale or from matched points, and converts traced lines with it.
- CivilCraft
- 12 calculations
64-bit Open item -
Placing and pasting elements in an IFC model
Works out where a placed library item or a pasted copy sits in the file: its position and direction relative to the story, its shape in the file's unit, and its plan outline.
- BimCraft
- 7 calculations in 2 files
64-bit Open item -
Placing scene trees and people
Lists where trees and people can stand, scatters them over a region with a minimum spacing, and builds each one's placement matrix.
- ModelCraft
- 7 calculations in 2 files
64-bit -
Plan as a vector PDF
Chooses the scale a level's plan prints at and turns plan millimeters into positions on the sheet.
- BimCraft
- 4 calculations
64-bit -
Plan drawing and section sheets for DXF and PDF
Turns the model into the linework and labels of the plan drawing and the cross-section sheets, as they are drawn on screen and written to DXF and PDF.
- CivilCraft
- 7 calculations in 2 files
64-bit -
Plan sheets and plan-and-profile sheets as PDF
Places the plan and the profile on paper at a stated scale and writes the page as a vector PDF.
- CivilCraft
- 14 calculations in 2 files
64-bit -
Plan symbol positions
Stores where a plan symbol sits and how it is turned, and moves symbols fixed to a wall when the wall moves.
- BimCraft
- 3 calculations
64-bit -
Plan view of elements drawn from their mesh
Cuts imported and library elements at the plan's cut height and joins the cut lines into outlines to draw.
- BimCraft
- 3 calculations
32-bit, display only -
Plan view: picked points, wall outlines and dimensions
Turns a pointer position into plan millimeters, and works out the dimension chain along each wall and the wall's plan outline with its door and window openings taken out.
- BimCraft
- 5 calculations in 2 files
64-bit -
Planar faces of a mesh
Groups a mesh's triangles into flat faces and traces each face's outline, for face picking, face profiles in DXF and merged faces in STEP.
- PartCraft
- 5 calculations
64-bit -
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 3D models for the 3D view
Reads a plant's own 3D model from a GLB file and scales it to a unit box so the 3D view can draw it at the plant's size.
- CivilCraft
- 4 calculations in 2 files
32-bit, display only -
Plant equipment solids, capacity and placement
Builds vessels, tanks, columns, pumps and exchangers of the Plant add-on from a few dimensions in millimeters, works out their capacity, and moves them to their place in the model.
- BimCraft
- 11 calculations in 3 files
64-bit Open item -
Plant equipment written as an IFC file
Writes the Plant add-on's equipment, with its solids and nozzle ports, as a standalone IFC4 file in millimeters.
- BimCraft
- 4 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 -
Plant sizes, spacing and symbols
The height, spread, spacing and supplied sizes of each plant species, and the 2D symbol and library item made from them.
- BimCraft
- ModelCraft
- CivilCraft
- 10 calculations
64-bit -
Plant symbols from SVG files and CAD blocks
Turns an SVG drawing or a CAD block into a plant symbol kept in the project, and scales it to each plant's spread on the plan.
- CivilCraft
- 3 calculations
64-bit -
Planting: bed and hedge fills, planted areas and their quantities
Fills beds, hedges and planted areas with plants at a spacing, counts each species, and totals areas, soil and mulch volumes and edging lengths.
- CivilCraft
- 11 calculations in 2 files
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 -
PLY import and export
Reads and writes PLY meshes with their colors, in meters with Z up.
- ModelCraft
- 5 calculations
32-bit in part 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 -
Point cloud slice and scan alignment
Cuts a point cloud at a level's height for drawing over it, and finds the turn and the lift that set a scan square to the building and its floor on a level.
- BimCraft
- 9 calculations
64-bit -
Points and faces picked for 3D measuring
Finds the corner, edge point or face under the pointer for the 3D Measure tool, the area of that face, and the bounding box of each element.
- BimCraft
- 3 calculations
32-bit in part 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.