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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Real-time view and render bench
Draws the real-time 3D view, bakes its bounce light, times the path tracers and writes the standalone viewer's scene.
- BimCraft
- ModelCraft
- 4 calculations in 4 files
32-bit, display only -
Render hand-off manifest
The camera, sun, lamps, materials, exposure and frame numbers written into the package that an outside render engine reads.
- BimCraft
- ModelCraft
- 8 calculations
64-bit Open item -
Rendered picture: mixing, post and color
The pixel values of a high-quality render as shown and as saved to an 8-bit or 16-bit picture, after light mixing, denoising, exposure, bloom, the view transform and the sRGB curve.
- BimCraft
- ModelCraft
- 14 calculations in 5 files
32-bit in part Open item -
Rendered picture: sample sums and color tables
Adds up the light samples of a CPU render into the picture and applies .cube color tables to it.
- BimCraft
- ModelCraft
- 5 calculations in 2 files
32-bit, display only -
Rendered pictures
Draws still pictures and video frames of the model: the fast render, the path-traced render and the textures of the material library.
- BimCraft
- ModelCraft
- 4 calculations in 4 files
32-bit, display only -
Rigid body simulation
Drops, stacks and collides boxes and spheres under gravity and records where each one is at every frame, to be baked into keys.
- ModelCraft
- 12 calculations
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 and furniture placement
Reads a floor face as a room (outline, holes, area), finds nearby doors and windows, and builds the matrix that sets each planned piece on its footprint.
- ModelCraft
- 4 calculations
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 -
Samples per pixel reported after a render
Works out the average and the largest number of samples a pixel received in an adaptive path-traced render, shown on the finish line.
- BimCraft
- ModelCraft
- 1 calculation
32-bit in part 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 -
Scattered plants, rocks and people: how many and where
Works out how many items a scatter set asks for from the area it covers and its density, and picks the points they stand on.
- BimCraft
- ModelCraft
- 4 calculations
64-bit -
Scene handed to the renderer
Turns what the view shows into the renderer's geometry: positions, normals and texture coordinates per color, with material displacement on meshes.
- ModelCraft
- 3 calculations
32-bit, display only -
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 -
Sculpt brushes
Moves the vertices under a round brush: draw, clay, smooth, grab, inflate, crease, pinch and flatten, with a mask that protects vertices.
- ModelCraft
- 10 calculations in 2 files
32-bit in part Open item -
Shape keys: offsets, editing and blending
The vertex offsets stored for each shape key, the way a key is made from an edit or from imported positions, and the blended points of a mesh.
- ModelCraft
- 5 calculations in 2 files
32-bit in part Open item -
Sheet nesting
Lays parts out on sheets or a roll, reports the sheets used and the efficiency, checks the result, reads part outlines from DXF and writes the nest as DXF.
- CadCraft
- BimCraft
- ModelCraft
- PartCraft
- 19 calculations
64-bit Open item -
Shift calendar working time
The hours a production line is on in a weekly shift calendar, used by the material flow simulation.
- ModelCraft
- 3 calculations
64-bit -
Site surroundings in local meters
Converts the buildings, parcels and zones found around an address from longitude and latitude to meters east and north of the address point, as suggestions a person can add to the model.
- BimCraft
- ModelCraft
- CivilCraft
- 4 calculations
64-bit -
Sizes for new curves and meshes, remesh grid
Chooses a round starting size for a new curve or mesh from what the view shows, and checks that a voxel remesh is not too fine.
- ModelCraft
- 4 calculations in 2 files
64-bit -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 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 -
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 -
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 -
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 -
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 -
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
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.