Index of /code/art

Documentation

API documentation is available in the documentation) subdirectory. There are also api.html documents in some subdirectories, e.g. string/api.html, which provide summary information but have been mostly superceded by the generated API documentation.

Subdirectory summary

Code directories

• 3d: STL parsing
• art: core art framework files
• colourspace: colour and colour space manipulations
• components: higher level art components, e.g. "random pirate ship"
• core: fundamental operations and utilities
• examples: examples of API use
• geo: geometric objects and operations
• image: raw image file manipulation, PNG read/write (requires Saxon-PE)
• math: mathematical operations
• music: MusicXML parsing
• noise: noise functions
• sdf: signed distance functions and ray marching
• shapes: higher level paths, patterns, and grids
• string: some basic string functions
• structures: complex structures, e.g. FSA
• svg: SVG parsing, gradients, and filters
• tests: test suite
• tiling: isohedral tiling
• types: data type descriptors
• wfc: wave function collapse algorithm

Auxiliary directories

• COLOURS: SVG gradient definitions
• config: config file
• data: data files
• documentation: API documentation
• EFFECTS: SVG filter samples
• lib: jar files that some modules depend on
• Messages: error message catalogs

Licensing

The code here is generally licensed as CC-BY (https://creativecommons.org/licenses/by/4.0/).

Attribution should be to Mary Holstege and include a link to the code base at http://mathling.com/code/

Sources

Some of the same data is based on WordNet 3.0® and is made available under that license (see data directory). The UnicodeData.txt file is made available under the Unicode data license (see data directory).

The noise code is a port of noise-rs which is used under an MIT License (see noise directory).

Much of the colour space conversion code is a port of hsluv-c which is used under an MIT License (see colourspace directory).

Much of the SDF code is based in part on code from Inigo Quilez which is used under an MIT License with some operators from Karsten Schmidt which is used under an Apache license, and a few details from Electric Square Ltd., also under and MIT License (see sdf directory).

The gradients are based on gradient definitions from a variety of sources used under MIT, BSD, and CC Licenses (see COLOURS directory).

The Wave Function Collapse algorithm is a port of the WFC code, which is used under an MIT license. See wfc directory.

The Hyphae component is based on a port of Anders Hoff's Hyphae, which is used under an MIT license.

Some of the shape fills are based on ideas from Preet Shihn's rough.js library, which is used under an MIT license.

The Hobby splines are based on code ported and adapted from Jake Low's hobby.js licence, used under an ISC license. See geo/spline.xqy.

UnicodeData.txt is version 15.1.0 and used subject to Unicode license. See data/Unicode_license.txt.

oeis.stripped.txt is from the Online Encyclopedia of Integer Sequences as of 2025/04/07 and is used subject to the OEIS End-User License Agreement. See data/OEIS-LICENSE.txt.

Dependencies

Some of the operations depend on Java extensions provided by Saxon. They will not work with other processors.

PNG image operations depend on various Java libraries (java.io, javax.imageio, java.awt). These classes are part of the Java runtime environment.

IXML operations depend on Normal Walsh's NineML CoffeeSacks (and CoffeePot) version 3.2.9. See structures subdirectory. These libraries are available in the lib subdirectory, subject to an MIT license.

An alternative implementation of IXML operations depends on Gunther Rademacher's MarkupBlitz, which is Copyright (c) 2023-2025 Gunther Rademacher, and is available under the Apache license. See structures subdirectory.

Some of the mathematical operations depend on Apache Commons Math version 3.6.1. See math subdirectory. These libraries are available in the lib subdirectory, subject to the Apache License.

Maker functions

Many of the libraries have maker functions associated with them, marked with the art:maker annotation. These are intended for use with the text interface driver (still a work-in-progress and not currently part of the release). They provide a standardized callback interface for making things and generally provide a limited set of heavily defaulted options. They can be called directly, and can provide examples of how to use some of the APIs. All these functions are bleeding edge, and the details of the interfaces are certainly subject to some change.

The maker functions come in three basic signatures: direct makers, contextual makers, and relationship makers.

Direct makers make something directly. The signature is:

direct-maker(
  $dynamics as map(xs:string,item()*),
  $canvas as map(xs:string,item()*),
  $randomizers as map(xs:string,item()*),
  $parameters as map(xs:string,item()*)
) as map(xs:string,item()*)*

The parameters are:

• $dynamics: dynamic parameters setting standard and non-standard options
• $canvas: drawing space
• $randomizers: active randomizers for component
• $parameters: active parameters for component

Contextual makers modify something or make something new from it. The signature is:

contextual-maker(
  $context as map(xs:string,item()*)*,
  $dynamics as map(xs:string,item()*),
  $canvas as map(xs:string,item()*),
  $randomizers as map(xs:string,item()*),
  $parameters as map(xs:string,item()*)
) as map(xs:string,item()*)*

The parameters are the same except for the context:

• $context: context objects for the maker
• $dynamics: dynamic parameters setting standard and non-standard options
• $canvas: drawing space
• $randomizers: active randomizers for component
• $parameters: active parameters for component

Relationship makers combine two things something or make something new. The signature is:

contextual-maker(
  $base as map(xs:string,item()*)*,
  $related as map(xs:string,item()*)*,
  $dynamics as map(xs:string,item()*),
  $canvas as map(xs:string,item()*),
  $randomizers as map(xs:string,item()*),
  $parameters as map(xs:string,item()*)
) as map(xs:string,item()*)*

The parameters are the same except for the base and related group:

• $base: base context objects for the maker
• $related: related context objects for the maker
• $dynamics: dynamic parameters setting standard and non-standard options
• $canvas: drawing space
• $randomizers: active randomizers for component
• $parameters: active parameters for component

The canvas, randomizers, and parameters are the standard triad present in all components. The dynamic parameters include special options for the specific maker as well as several standard options. The makers do not require any of the standard options.

• "use": What kind of object is being made?
  • "thing": something to draw (or a collection of things)
  • "space": a space to draw something into (or a collection of spaces)
  • "location": a place to draw something at (or a collection of locations)
  • "modifier": for contextual makers; something that alters an object
  • "decorator": for contextual makers; something that is added to an object
• "gender": Dimensionality, to indicate whether colour applies to bounds or areas
  • "zone": treat as an area, so a red circle(zone) is red-filled
  • "stroke": treat as a line, so a red circle(stroke) is a red boundary
  • "neutral" (default): apply default treatment
• "size": exact sizing of the thing/space in pixels; if present should be no "scaling"
• "scaling": relative size of the object to the canvas; if present should be no "size"
• "location": point representing where the object should be drawn
• "colour": colour of the object
• "opacity": opacity of the object
• "width": line width

Status indicators

• Stable: has been used in a number of projects, not subject to much change (although major refactorings may impact it)
• New: has not been used in many projects, may not be well-exercised, probably not active
• Active: subject to active additions and modifications; usually used for libraries of operations where the capabilities are being expanded
• Incomplete: known incompletenesses that may not be being addressed at this time
• Limited: provides some limited capabilities, but not being actively updated
• Bleeding edge: hot-off-the presses, subject to wild flux in APIs and bug fixing
• Completed: not likely to change, is what it is warts and all; used for higher level components (e.g. "octopus")

Releases

20251115

This release is largely an accumulation of some small bug fixes. The major change is the integration of Markup Blitz for Invisible XML processing, and a reshuffling of those APIs to allow for the selection of processor. Currently CoffeeSacks and Markup Blitz are supported. Libraries are included, although it is up to you to include the right options when you invoke Saxon. See the makefile for examples. Markup Blitz is generally much faster and scales better, due to the separation of tokenization and parsing, but CoffeePot provides more control and better debugging capabilities.

This release also adds full text search to the website, encompassing the documentation as well.

• Incompatibilities

  • "http://mathling.com/core/statistics.xqy" is now new module "http://mathling.com/math/statistics.xqy" (math/statistics.xqy)

• Invisible XML (structures/ixml-blitz.xqy)

  • Integration of Markup Blitz: can be selected from IXML interface with using the "processor" option
  • Partition of some functions in to new module structures/ixml-parse.xqy
  • CoffeeSacks 3.2.9

• Math

  • New functions: stats:quantile(), stats:quantile-range() to compute weighted or unweighted quantile selections for a given fraction (math/statistics.xqy)
  • New function: mmath:close() to test whether values are within epsilon of each other (math/math.xqy)
  • New function: binary:is-power-of-two() to test whether integer is a power of two (core/binary.xqy)
  • seq:rotate() now handles negative offsets as rotation from end (core/sequences.xqy)

• Colours and rendering (svg/gradients.xqy)

  • New named palettes: "grasslands", "alps", "caribbean", "harem", "painted-desert", "night-garden", "machu-pichu", "barbados", "mossland"
  • New function: rgb:to-int-v to return integer RGB value from vector form of RGB point (colourspace/rgb.xqy)
  • New: "cover" resolution (A4 @300dpi)
  • Bug: Snapped SVG path drawing should snap start (XQuery only)
  • Bug: gradient:random() not applying exclusion properly
  • Bug: gradient names with operators in them failing on subsequent operations due to name-safing
  • Bug: gradient:gradient-sample() produces bad gradients with small gradients and high limits
  • Bug: XSL gradient:colours("X-reverse") double-reversed
  • Add gradient tests

Geometry (geo/euclidean.xqy)

* New function `geom:trace()` which can chain with other operations to provide intermediate tracing using descriptions of geometric objects
* `path:reverse()` now takes sequence of paths, the better to chain operations ([geo/path.xqy](https://mathling.com/code/art/documentation/geo/path.xqy.html))
* Aesthetic: arc edge end-points get snapped when when translating edge
* Adjustment to the logic of swapping in edge normalization
* Bug: `edge:chop()` sometimes computes incorrect splits ([geo/edge.xqy](https://mathling.com/code/art/documentation/geo/edge.xqy.html))
* Bug: `geom:as-polygon()` dropping properties
* Bug: incorrect calculation of tangent vectors on ellipses ([geo/ellipse.xqy](https://mathling.com/code/art/documentation/geo/ellipse.xqy.html))

Miscellaneous

* Add offset adjustment parameter to `fonts:text-as-glyphs()`
* Bug: mishandling of font lookup for characters in FF-FFF range
* Add `component-map()` method to all components to simplify their use

20250714

• Incompatibilities

  • shapes:scale-and-plaster() renamed to shapes:scale-and-plaster-solid() to accommodate new shapes:scale-and-plaster() function applied to faces (shapes/shapes.xqy)
  • Exclude all trivial (2-colour) gradients from gradient:random-gradient() (svg/gradients.xqy)
  • Use seq:extend-repeat() on all partial sequences (e.g. Katydid) in seq:sequence() (math/sequences.xqy)
  • Pass additional argument, symmetry number, to tile construction functions (wfc/simple-tiled-model.xqy)

• New modules

  • Implementation Separable Natural Evolution Strategy optimization "http://mathling.com/math/snes" (math/snes.xqy)
  • Venation algorithm "http://mathling.com/shape/venation" (shapes/venation.xqy
  • Recursive polygon splitting "http://mathling.com/shape/splits" (shapes/splits.xqy)

• Math, sequences (math/math.xqy and math/sequences.xqy)

  • New functions seq:odds(), seq:evens(), seq:extend-repeat()
  • Integrate OEIS sequence data (see Sources, above) in new functions seq:oeis-random-sequence(), seq:random-limited-oeis-sequence(), seq:oeis-sequence(), and in seq:sequence()
  • New functions mmath:rpow(), mmath:fpow(), mmath:modix-diff()

• Randomizers (core/random.xqy and types/distributions.xqy)

  • New function rand2:random-polar-points-on()
  • New accessors dist:ceiling(), dist:resample(), dist:drop()
  • New constructors dist:uniform-centered(), dist:normal-centered()

• Rendering and colouring (svg/gradients.xqy and svg/draw.xqy and art/draw.xqy)

  • New function gradient:any-random-gradient()
  • New gradient "coppery"
  • Smoother handling of gradient:luminance-range() to avoid overruns on colour values
  • Adjustments/improvements to conical gradient construction (svg/complex-gradients.xqy)
  • Support "none" in rgb:named-colour() as RGBA(0,0,0,0) (colourspace/rgb.xqy)
  • Hook for recentering within region bounds ("render.recenter") after 3D rendering
  • Performance optimization of colour space transformations
  • Performance optimization of pixel array processing
  • Angle-based arc edge drawing should snap calculated points
  • Add "rgbint" colour space option to ppm/png images (image/ppm.xqy and image/png.xqy)
  • Bug: point:destination() shouldn't lose Z values in 3D points
  • Bug: Avoid needless 3D points in points:destination(), shape:scale-and-center()
  • Bug: Remove projection properties after render in svg:draw() and art:draw()
  • Bug: Use of wrong perspective parameters (should be "perspective.p", "perspective.q", and "perspective.r")
  • Bug: account for box margin in scaling and centering calculations (shapes/shapes.xqy)
  • Bug: effect:colour() needs to rotate through colour sequence (svg/effects.xqy)

• Miscellaneous new features and functions

  • New interpretation of function shapes:scale-and-plaster() to apply to faces (shapes/shapes.xqy)
  • New functions generic consolidation functions path:consolidate-all(), path:consolidate-all-points(); specific consolidation functions deprecated (geo/path.xqy)
  • Extension of path:points-on() for fades
  • Add angle parameter to path:ngon()
  • New function knot:extend() to extend paths to ribbons (components/knots.xqy)
  • Walk types "steps-up", "steps-down", "lightning-up", "lightning-down" (shapes/paths.xqy)
  • New pattern patterns:wave() (shapes/patterns.xqy)
  • New modifier maker "symmetry" (geo/makers.xqy)
  • New mutations: "horizontal-reflect", "upwelling" (components/mutations.xqy)
  • New fills: fills:irregular-hachure-lines(), fills:irregular-crosshatch(), fills:irregular-zigzags(), fills:irregular-star() (shapes/fills.xqy)
  • New hex grid operations grids:right-straight(), grids:left-straight(), grids:hex-coordinates() (shapes/grids.xqy)
  • New function: paths:reverse-circle-spiral() (shapes/paths.xqy)
  • New background style: backgrounds:crisscross() (components/backgrounds.xqy)
  • New function: solid:as-face() (geo/solid.xqy)

• Miscellaneous fixes and enhancements

  • Adjust random parameters for "juliaN" and "juliaScope" mutations (components/mutations.xqy)
  • STL use file:resolve-path() when loading STL files (stl/stl.xqy)
  • Add support for faces to geom:bounding-box() (geo/euclidean.xqy)
  • Bug: WFC proper handling of F forms (wfc/simple-tiled-model.xqy)
  • Bug: constrained walk "random" mishandled (shapes/paths.xqy)
  • Bug: path:same() should return false() rather than error if number of edges different (geo/path.xqy)
  • New parameters for contours component "contours.granularity", "contours.smooth", "contours.connect", "contours.wobble" (components/contours.xqy)
  • New parameter for pixel sorting component "pixelsort.interval.min" (components/pixelsort.xqy)
  • Improve pixel-sorting performance
  • Add optional bounds parameter to conrec:as-path() for closing off polygons (geo/conrec.xqy)
  • Improvement: Use skip edges to close polygons in conrec for far edges
  • Bug: fix sense of test for unclosed polygons in conrec:extent()
  • Auto-scale data in treemap for squarification (geo/treemap.xqy)
  • Handle slots in mutated tiling (components/tiling.xqy)
  • Bug: incorrect index calculation in grids:down-left() (shapes/grids.xqy)

20241219

This release includes some major (incompatible) restructuring of the core libraries: various libraries have been moved from core to math and many of the functions in "http://mathling.com/core/utilities" (core/utilities.xqy) have been moved to new libraries. There are some new advanced mathematic capabilities, various drawing components, and more capable colouring and rendering.

• Incompatibilities

  • "http://mathling.com/core/roots.xqy" is now new module "http://mathling.com/math/roots.xqy" (math/roots.xqy)
  • "http://mathling.com/core/sequences" is now new module "http://mathling.com/math/sequences" (math/sequences.xqy)
  • Definite integral function has been moved from "http://mathling.com/core/utilities" to new module "http://mathling.com/math/integral" (math/integral.xqy)
  • Many functions in "http://mathling.com/core/utilities" have been moved to the new module "http://mathling.com/math" (math/math.xqy). Specifically the functions: is-prime(), logK(), log2(), decimal(), round(), trunc(), factorial(), binomial(), modix(), twixt(), clamp(), clamp-some(), sign(), zsign(), cbrt(), smoothstep(), mix(), intmix(), hypermix(), expmix(), remap(), intremap(), radians(), degrees(), remap-radians(), remap-degrees(), cos(), sinh(), cosh(), asinh(), and acosh(). The functions decimal(), round(), modix(), twixt(), clamp(), mix(), and intmix() remain, but are deprecated and will be removed in a later release.
  • Many functions in "http://mathling.com/core/utilities" have been moved to the new module "http://mathling.com/core/binary" (core/binary.xqy). Specificially the functions: unsignedLong(), xor(), or(), and(), lshift(), rshift(), count-bits(), count-digits(), bits-to-integer(), integer-to-bits(), as-base(), hex-to-integer(), integer-to-hex()
  • The interpolation functions have had their arguments rearranged so that the region argument always comes first, to allow for better chaining. (geo/euclidean.xqy)
  • core:do-randomize() has been moved to rand:random-value() (core/random.xqy)
  • rgb:to-int() now produces 32 bit integer values values compatible with PNGs (colourspace/rgb.xqy)

• New modules

  • New component for crystal lattices "http://mathling.com/components/lattice" (components/lattice.xqy)
  • iXML parsing and unparsing convenient wrappers (depends on CoffeeSacks and Saxon) "http://mathling.com/structures/ixml" (structures/ixml.xqy)
  • Finite state automata "http://mathling.com/structures/fsa" and "http://mathling.com/structures/fsa/mutating" (structures/fsa.xqy) (structures/mutating-fsa.xqy)
  • Basic math operations (from core) "http://mathling.com/math" (core/math.xqy)
  • Integer sequences and operators (from core) "http://mathling.com/math/sequences" (math/sequences.xqy)
  • Definite integrals (from core) "http://mathling.com/math/integral" (math/integral.xqy)
  • Solvers for systems of equations "http://mathling.com/math/solver" (math/solver.xqy)
  • Eigenvector decomposition (depends on Apache Commons Math and Saxon) "http://mathling.com/math/eigen" (math/eigen.xqy)
  • Binary operators (from core) "http://mathling.com/core/binary" (core/binary.xqy)
  • Complex gradients, such as conical gradients "http://mathling.com/svg/gradients/complex" (svg/complex-gradients.xqy)
  • Square-grid-based tiles "http://mathling.com/shape/gridtiles" (shapes/gridtiles.xqy)
  • Masking manipulations "http://mathling.com/shape/masking" (shapes/masking.xqy)

• Colouring and rendering (svg/gradients.xqy) (svg/draw.xqy) (art/draw.xqy)

  • New gradient aliases: "brassy", "golden", "silvery", "steely", "osloO", "rainO", "batlowWO", "naviaWO", "algaeO", "glassy", "verdigris-sheen", and "psychedelic"
  • Better gradient interleave and sampling including partial sampling support using ^ operator in names
  • Fix colour sampling calculations: in some circumstances rounding leads to too few colours
  • Properly make gradient names with operator symbols ID-safe
  • Allow gradient alias to be complex names
  • Support comment nodes in art:draw() and svg:draw()
  • Proper embedded metadata support in PNGs (no more sidecar documents) (image/png.xqy)
  • Add "render.opacity.min", "render.opacity.max" properties as hooks in draw:draw() for 3D rendering
  • Bug: don't do both projection and 3D rendering by default
  • Bug: Rounding in 3D rendering not always working correctly
  • New: draw:projection-draw()
  • Check for NaN/INF in fractal colouring methods (components/fractal.xqy)
  • Modify rgb:to-int() to produce 32 bit values compatible with PNGs (colourspace/rgb.xqy)
  • Add "background.scene.luminance" to modify background colour to a more contrasting luminence to the property value; set as a dynamic parameter (components/backgrounds.xqy)
  • Support colour functions on nibs to allow for path-varying colouring: new functions pens:colour(), pens:colour-at(), pens:constant-colour(), pens:fade-colour(), pens:taper-colour(), pens:wobble-colour() (shapes/pens.xqy)
  • New solid constructions and modifiers: solids:crystal(), solids:divide-body(), solids:divide-faces(), solids:divide-base() (shapes/solids.xqy)
  • New gradient modifier function gradient:gradient-offset()

• Geometric (geo/index.html)

  • Add graph support to geom:bounding-box(), geom:bounding-circle()
  • New geometric functions: edge:angle-between(), path:remove-useless(), path:angle(), path:inclination(), coord:hyperbolic()
  • Normalize polygons in simplify:regions() and simplify:convex-hull() which improved region finding
  • Better handling of polygons in path:chaikin()
  • Better point consolidation: avoid extra long dots
  • Add optional preserve-edges parameter to path:normalize()
  • Add optional spread parameter to arf:layout-as-graph()
  • New: stereographic modifier maker
  • Bug: Mutate centers of polyhedra also
  • Bug: box:quote() repeating box parameters multiple times
  • Bug: paths with no edges causes failure on path consolidation

• Miscellaneous bugs and improvements

  • Add optional parameter to util:doc(), util:unparsed-text(), util:unparsed-text-lines() to control whether to warn or not (core/utilities.xqy)
  • New utility functions: util:context-filter(), util:context-map(), util:for-each() (core/utilities.xqy)
  • New matrix operations: array:outer(), array:is-zero(), array:is-identity(), array:is-tridiagonal(), array:is-upper-triangular(), array:is-lower-triangular(), array:is-singular() plus array:vector() and matrix:as-array() (core/array.xqy) (core/matrix.xqy)
  • Other miscelleneous new functions: curves:polar-plot(), paths:round(), gradient:gradient-offset(), `bin:i32()
  • Add partial support for parsing "A" and "a" edges in SVG paths (svg/parse.xqy)
  • Integrate mixed functions into complex-functions component: cf:mixed-function() (components/complex-functions.xqy)
  • Better consolidation of paths:extended-star() output (shapes/paths.xqy)
  • Better font scaling adjustment with metrics.xml support for performance (components/fonts.xqy)
  • New font functions fonts:length() and fonts:text-as-glyphs() (components/fonts.xqy)
  • Increase $errors:QUOTE-LIMIT to 200 (core/config.xqy)
  • Add speckles.prune option to remove out-of-canvas speckles (components/speckles.xqy)
  • Bug: avoid duplicate roots in product functions in complex function component (components/complex-functions.xqy)
  • Replace absolute URIs in HTML JS tests with appropriate relative URIs (tests/index.html)
  • Fix errors in paths in quadtree and statistics tests
  • Various additions and updates to tests

20240727

This release includes a lot of work on the experimental maker functions: reworking handling of some of the dynamic parameters, adding more maker functions, and adding a new class maker function for relationships. The experimentation with the art shell (not released) that is driving this work has also produced a number of new modules. There are also some follow-up bug fixes from the change to default 3D rendering.

• Documentation improvements

  • Add function index for each module
  • Mark deprecated functions in red

• Incompatibilities

  • background:border() renamed to background:frame() (components/backgrounds.xqy)
  • Swap argument order in util:repeat() (core/utilities.xqy)
  • string:capitalize() lowercases non-initial letters (core/string.xqy)

• New modules:

  • Geometric merger operations "http://mathling.com/geo/mergers" (geo/mergers.xqy)
  • Fractal generation component "https://mathling.com/art/fractal" (components/fractal.xqy)
  • Embroidery component "https://mathling.com/art/embroidery" (components/embroidery.xqy)
  • Expanding echoes "http://mathling.com/shape/echoes" (shapes/echoes.xqy)
  • Droste effect "http://mathling.com/shape/droste" (shapes/droste.xqy)
  • Circular intersection reflections "http://mathling.com/shape/reflect" (shapes/reflect.xqy)
  • Unicode name/category lookup "http://mathling.com/string/unicode" (string/unicode.xqy)
  • Adhoc functions with integration into core functions "http://mathling.com/type/adhoc-function" (types/adhoc-function.xqy, core/functions.xqy)

• Rendering

  • Better 3D rendering of 2D objects: e.g. ellipse center needs projection
  • Extend shapes:scale-and-center(), shapes:fitting-scale-and-center(), and shapes:center() to take either a flat space or a block and adjust either 2D or 3D
  • Draw ellipses as svg:circle when possible
  • Bug: 3D rendering processing fails with GEOM-BADREGION on certain delegating objects
  • Bug: avoid error in rendering when path has no points

• Geometry (geo/euclidean.xqy)

  • New: geometric merger operations (geo/mergers.xqy)
  • New geom:bounding-block(), geom:points-on(), geom:flatten(), geom:process-polygonlike(), geom:process-pathlike()
  • New: path:subsegments(), path:has-segments() to break paths into subsegments (geo/path.xqy)
  • New edge:end() as settor (geo/edge.xqy)
  • Add new optional close argument to path:as-polygon() (default false)
  • georand:polar-random-points-in() takes either circle or sphere, producing 2D or 3D results as appropriate (geo/random.xqy)
  • Handle dispatching of ellipse-arc and block in geom:bounding-box()
  • point:with-properties() takes sequence
  • box:edge() looks for "edge" property first
  • Bug: geom:process-xxx() functions not honouring delegators
  • Bug: don't include skip edges in interpolations
  • Bug: Reverse of skip edge should be a skip edge
  • Bug: Fix path:streamline() handling of leading and trailing skip edges
  • Bug: path:simplify() should not trim skip edges
  • Bug: Z/z closes current segment, not whole path (svg/parse.xqy)
  • Bug: Don't parse multi-segment paths as polygons (svg/parse.xqy)
  • Bug: Avoid NaNs in path:with-edge-ts() and path:path-point() when path is length 0
  • Bug: Avoid divide by zero in solid:face-centroid() when all zs are 0
  • Bug: geom:delegate() loses exception list in recursive calls

• Miscellaneous new functions and features

  • seq:every-nth() (core/sequences.xqy)
  • core:edge() (art/core.xqy)
  • util:timestamp() (core/utilities.xqy)
  • shapes:triangulate() (shapes/shapes.xqy)
  • ppm:p6-bytes() and png:png-bytes() to return octets (image/ppm.xqy, image/png.xqy)
  • Support adhoc functions in fractal:newton() (components/fractal.xqy)
  • Add scale parameter to effect:texture() (svg/effects.xqy)
  • Make image wrappers that embed image data directly, or link to external images (image/image.xqy)
  • Operator + for colour+colour combinations (svg/gradients.xqy)
  • "raw" modifier for canvas resolution for border size 0 (art/core.xqy)
  • fills:hachure-lines() et all handle ellipses via interpolation (shapes/fills.xqy)
  • background:terrain() and background:crosshatch() support spaces with arbitrary offsets as minimum point; modernize to fit with new rendering (components/backgrounds.xqy)

• Miscellaneous bugs

  • Bug: dist:max() settor should recalculate Zipf and Binomial tables
  • Bug: fills:hachure-lines() shouldn't add useless zero-length edges
  • Bug: Off-by-one error in grid:navigable-hex-grid()
  • Bug: Fonts component mishandles codepoints with more than 2 hex digits
  • Bug: Error in component table for algorithm mode parameter function

20240521

This release includes a great number of maker functions, a lot of new solids, and the replacement of simple projection with automatic depth-ordered 3D rendering by default. The configuration option $config:RENDER controls this (core/config.xqy).

• Incompatibilities:

  • Solid operators merge(), glue(), revolve(), extrude(), and onion() moved from http://mathling.com/geometric/solid to http://mathling.com/shape/solids (shapes/solids.xqy)
  • Remove automatic delegation of complex polygons; handling varies (geo/euclidean.xqy)
  • Change SDF mapping of points to pure points (with no radius) (sdf/sdf.xqy)
  • images:image() is now images:random-image() and images:svg() is images:random-svg() (components/images.xqy)
  • edge:skip() only returns skip edge if it is useful (start!=end)

• Deprecations

  • spline:spline() is deprecated; prefer spline:open-spline() or spline:closed-spline() as appropriate

• New modules

  • Depth-ordered opacity-mapped 3D rendering geo/render3d.xqy
  • Pens for drawing shapes along paths shapes/pens.xqy
  • Rough sketch styling of base geometric objects shapes/sketchy.xqy
  • Candle flame components/candle.xqy
  • Quadtree geo/quadtree.xqy
  • Read font glyphs created by convert -font and make polygons components/fonts.xqy
  • Solid operators (refactored) shapes/solids.xqy

• Solid geometry geo/solid.xqy, shapes/solids.xqy

  • Archimedean solids (truncated-tetrahedron, cuboctahedron, truncated-cube, truncated-octahedron, rhombicuboctahedron, truncated-cuboctahedron, snub-cube, icosidodecahedron, truncated-dodecahedron, truncated-icosahedron, truncated-icosidodecahedron, rhombicosidodecahedron, snub-dodecahedron
  • Kinds of known solids: solid:solids(), solid:regular-polyhedra()
  • Generate constructor: solid:regular-polyhedron()
  • Other interesting solids: solid:great-icosahedron(), solids:borromean-rings(), solids:hex-knot-star(), solids:hex-knot-links(), solids:toroid-7-3-11()
  • Modify various operators (e.g. speckles) to apply to solids generally
  • Refactor: solid:merge(), solid:glue(), solid:revolve(), solid:extrude(), solid:onion() to new module
  • solid:volume() for generic polyhedra
  • New: solid:as-polygon(), solid:depth-ordered-faces()
  • Oversight: solid:scale() on sphere returns radius not error
  • Apply 2D shapes to polyhedra faces: shapes:plaster(), shapes:scale-and-plaster() shapes/shapes.xqy
  • More documentation

• Drawing and rendering

  • Automatic depth-ordered 3D rendering replacing simple projection by default, controlled by $config:RENDER variable (core/config.xqy)
  • New module for 3d rendering geo/render3d.xqy
  • Faces ordered by depth with mapped opacity solid:ordered-translucent-faces() geo/solid.xqy
  • Path edges ordered by depth with mapped opacity path:ordered-translucent-edges() geo/path.xqy
  • Bug: complex-polygon drawing function should draw inner polygons, unfilled
  • Drawing projection automatically decimalizes result

• Signed distance functions sdf/sdf.xqy

  • New: sdf:cache(), sdf:opRenderVolumetric()
  • New: sd3:sdSphere() with center sdf/sd3.xqy
  • New: sd2:sdPoint() and sd2:sdSignPoint() sdf/sd2.xqy
  • Change SDF mapping of points to pure points (no radius)
  • Add hooks for "add" and "add-into" operators
  • Optimizations to some SDF operators

• Images

  • Add images.granularity to images module components/images.xqy
  • Rename images:image() to images:random-image() and images:svg() to images:random-svg()
  • Add optional space parameter to image:image(), images:image(), and images:svg()
  • Add image:bounding-box(), image:delegate()
  • Add greyscale-value support to dithering image/dithering.xqy
  • Better greyscale-value support in png/ppm image/ppm.xqy image/png.xqy
  • Performance improvements to image read

• Paths and edges

  • New: paths:focus-fill(), paths:fit(), paths:triangulate(), paths:starr-rose() shapes/paths.xqy
  • Bug: paths:essbend() mispositioning second control point
  • Improve handling of skip edges in path modifiers
  • New spline variants: spline:open-spline(), spline:closed-spline(), spline:open-hobby-spline(), spline:closed-hobby-spline(), spline:open-natural-spline(), spline:closed-natural-spline() geo/spline.xqy
  • New: path:points-on(), path:triangle-chain(), path:consolidate-by-colour-and-opacity(), path:depth-ordered-edges() geo/path.xqy
  • Bug: path:consolidate() creating multiple redundant paths
  • Better performance on path:path-points()
  • New: edge:is-skip() geo/edge.xqy
  • Add edge:vertices() and (rough) edge:bounding-box()support for ellipse arc
  • edge:skip() only returns skip edge if it is useful (start!=end)
  • Bug: Edge case in edge arc normalization where angle difference is -180
  • Edge/point inclination/angle clean-up
  • Bug: Return 0 for length of a skip edge
  • Bug: mishandling of arc interpolation for flipped arcs
  • Bug: bounding box calculation for arc edges very wrong
  • Bug: missing properties from normalized arcs

• Core utilities core/utilities.xqy

  • New: map operators util:append-into(), util:include-filter(), util:exclude-filter()
  • New: index mapping util:remap(), util:intremap()
  • New: util:doc(), util:unparsed-text(), util:unparsed-text-lines(): check and warn if file doesn't exist, don't throw error
  • Change: util:exclude() and util:include() to allow non-string keys
  • Change: util:quote() always wrap multiple-item sequences in parentheses
  • Support multiple maps in second parameter to util:merge-into()
  • Performance improvements to util:rangeindexes()
  • Bug: util:cbrt() mishandling negative numbers
  • Bug: util:include() shouldn't add empty entries for non-existent keys
  • Bug/change: util:annotations() was dropping annotations with no parameters; now it sets a boolean in the output map
  • New: seq:interleave() core/sequences.xqy
  • New: wrapper:body-with-properties() to push properties into body types/wrapper.xqy
  • Improved slot:quote() types/slot.xqy
  • Allow zero value in sparse array/matrix to be empty sequence core/sparse.xqy, core/matrix.xqy
  • Bug: Issue with quaternion to-angles() at (0; √2/2, 0, √2/2); rounding err or leads to NaN core/quaternion.xqy, core/vquaternion.xqy
  • Bug: error formatting throwing error if error message contained a dollar sign ($) core/errors.xqy

• Miscellaneous geometry

  • New: point:one-of()
  • Delegation: Change delegation to look for object-specific delegator function first
  • Delegation: mutation of a ref with existing transform needs to add mutation to transform
  • Delegation: handle case on def where mutation of location is not OK
  • Delegation: geom:with-properties() shouldn't delegate wrapper objects
  • Delegation: add exception for defs that contain XML bodies
  • Delegation: improper handling of map transform property on ref
  • Streamlining transforms: Don't add in translate operators when offset is 0, etc. geo/transform.xqy
  • Rework Delaunay triangulation: better performance geo/delaunay.xqy
  • Bug: Poisson disk sampling with box offset from origin created infinite loop geo/random.xqy
  • Bug: lower bound edge case in Poisson disk sampling
  • Bug: incorrect perimeter approximation for ellipses geo/ellipse.xqy

• Miscellaneous

  • New: flower:flower(), flower:flowers() for Starr roses components/flowers.xqy
  • New: add focus-fill colouring option for flowers and roses components/flowers.xqy
  • Refactor squishy component (secondary function API change) components/squishy.xqy
  • Bug: Outer speckles on straight lines should use normal vector components/speckles.xqy
  • New patterns:maze(), patterns:maze-xxx() bias and k functions shapes/patterns.xqy
  • Add optional offsets parameter to shape:scale-and-center(), shape:fitting-scale-and-center() shapes/shapes.xqy
  • New text:estimated-bounding-box() and delegator function types/text.xqy
  • Bug: gradient:colours() not handling interleaved reverse gradients properly svg/gradients.xqy
  • Bug: out of date gradient XSL files; update to latest ScientificColourMaps version; change gradient lookup to prefix SVG file

20240131

(Refreshed 20240202.)

This release includes a number of new capabilities in the area of paths, shapes, and patterns, a reworking of hyperbolic geometry, and some more refactoring of the geometry code.

• Incompatibilities

  • Remove deprecated geom:xxx-distance() functions
  • Remove deprecated dist:weighted-distribution-of()
  • Moved geom:signed-distance(), geom:shortest-distance() to sdf:signed-distance() and sdf:shortest-distance() sdf/sdf.xqy
  • Moved geom:projection(), geom:isometric(), geom:stereographic() to new module geo/projection.xqy
  • Renaming: paths:dusty-path() paths:dusty()
  • Renaming: paths:taper-path() to paths:taper()
  • Renaming: paths:sweep-path() to paths:sweep()
  • Renaming paths:stroke-path() to paths:stroke()
  • Renaming paths:bend-path() to paths:bend()
  • Change $rand:DECIMAL-DIGITS to 3
  • Change in order of parameters in hyperbolic functions (scale after points)
  • Folded hyper:sorted-hypers() into hyper:tesselate() and made it private
  • Change seq:primes() to return first n primes; use seq:primes-to() to get primes less than or equal to n (old seq:primes())

• New deprecations

  • geom:random-point() et al (moved to geo/random.xqy)
  • geom:to-edges() (moved to geo/edge.xqy)

• New modules

  • Drawing shapes into pixel arrays geo/pixels.xqy
  • Point randomization geo/random.xqy
  • Fills shapes/fills.xqy
  • Guilloché patterns shapes/guilloche.xqy

• Pixel arrays and image processing

  • New module for drawing into pixel arrays geo/pixels.xqy
  • Performance of draw:draw-point-matrix() and related
  • Add images.pixel-function option components/images.xqy
  • Allow colour values not just colour points in image matrix
  • Add "greyscale" and "greyscale-value" as valid colour space parameters

• Random distributions

  • Refactoring point randomization from euclidean.xqy to geo/random.xqy
  • New: georand:random-polar-points(), georand:poisson-disk-sample()
  • New: dist:constant-index-of(), dist:normal-index-of(), dist:skewed-index-of(), dist:bernoulli-index-of(), dist:binomial-index-of(), dist:binomial-poisson-index-of(), dist:poisson-index-of(), dist:gamma-index-of(), dist:beta-index-of(), dist:binomial-beta-index-of(), dist:exponential-index-of(), dist:markov-index-of() geo/random.xqy

• Geometry geo/euclidean.xqy

  • Refactoring random points from euclidean.xqy to geo/random.xqy
  • Refactoring signed/shortest distance from euclidean.xqy to sdf/sdf.xqy
  • Refactoring projections from euclidean.xqy to geo/projection.xqy
  • Reworking of hyperbolic geometry: more variants, auto-centering, default scale geo/hyperbolic.xqy
  • New geom:invert(), geom:ellipse-invert()
  • New: point:sqdistance(), v:sqdistance() geo/point.xqy, core/vector.xqy
  • New: edge:slope() geo/edge.xqy
  • New: path:star() geo/path.xqy
  • New: ellipse:destination() geo/ellipse.xqy
  • Extension: geom:bounding-circle() takes sequence of regions
  • Bug: check $config:CANVAS-GEOMETRY in edge:angle()
  • Bug: drawing of bare cubic edges (not in path) brokwn
  • Bug: geom:reflect() on arcs incorrect

• Paths shapes/paths.xqy

  • New: paths:horizontal-modulated-torus-knot(), paths:vertical-modulated-torus-knot(), paths:dashed(), paths:dotted(), paths:constrained-walk(), paths:hex-constrained-walk(), paths:pure-hex-constrained-walk(), paths:extended-star(), paths:essbend()
  • paths:dusty(), paths:taper(), paths:sweep(), paths:stroke() take multiple paths as parameter
  • Bug: paths:taper-path() infinite recursion for unspecified inclination

• Shapes, patterns, grids, etc.

  • New: shape:fitting-scale-and-center() shapes/shapes.xqy
  • New: grids:exact-array(), grids:diagonal-array() shapes/grids.xqy
  • New: patterns:hvedges() shapes/patterns.xqy
  • New: fills:hachure-lines(), fills:crosshatch(), fills:zigzag(), :star() shapes/fills.xqy
  • New: guilloche:guilloche(), guilloche:knot-guilloche(), guilloche:stack() shapes/guilloche.xqy
  • New: systems:contextual-lsystem(), systems:curve() with delegation shapes/system.xqy
  • Bug: off-by-one in grid:hex-grid()

• SDF sdf/sdf.xqy

  • New: sd2:circle() (with center), sd2:donut(); use new sd2:circle() in sdf:regionToSDF()
  • New: sdf:signXXX() for sign-only SDF for in/out/on testing
  • New: sdf:opDrift()
  • New: SDF "colouring" option to translate "cix" attribute to material selection
  • Handle skip edges in sdf:toSDF()
  • Improved parameter annotations
  • Bug: edge case in sdf:toSDF() with union of 1

• Miscellaneous

  • New: arr:as-array(), arr:array(array(array(*))) core/array.xqy
  • New: util:index-of()core/utilities.xqy
  • New: transform:is-identity() geo/transform.xqy
  • New: text:shrink() types/text.xqy
  • New gradient:random-large-gradient() tied "largerandom" svg/gradients.xqy
  • New: isohedral:describe() tiling/isohedral-tiling.xqy
  • New parameters: flowers.rose.precision, fish.eye.colour, mutations.random.augment, random+none tiling colour mode components/flowers.xqy, components/fish.xqy, components/mutations.xqy, components/tiling.xqy
  • Bug: Off-by-one on seq:rotate() vis-a-vis comment core/sequences.xqy
  • Miscellaneous optimizations, minor bug fixes, additional maker functions, documentation, tests

20231012

A small refresh update to pick up some 3D extensions, fixes, and clean-up of the parametric L-system code.

• L-Systems shapes/systems.xqy

  • New rendering functions: sys:random(), sys:forwards3D(), sys:move3D(), sys:rotate3D(), sys:set-inclination(), sys:up(), sys:down(), sys:reverse-inclination(), sys:flip-inclination(), sys:flip()
  • Builtin parametric bindings for full set of rendering functions (see $this:PARAMETRIC-CALLBACKS)
  • Allow functional names in parametric systems to include all letters (not just lowercase ones) as well as digits and underbar
  • Include arity in key for function lookup
  • Add parametric variable hooks $lrand_, $arand_, $wrand_, $irand_ for randomized values from builtin randomizers
  • Add inclination to drawing context, with associated parameters and randomizers
  • Tests for new capabilities tests/test-systems.xqy

• Colours svg/gradients.xqy

  • Upgraded to ScientificColourMaps v8.0.1 which tweaks some of the existing gradients and adds "glasgow", "lipari", "managua", and "navia"
  • Deprecate gradient:xxx-random() in favour of gradient:xxx-shuffle() and "-random" modifier in favour of "-shuffle"

• Paths shapes/paths.xqy

  • New: paths:taper-path(), paths:taper:segments(), paths:stroke-segments()
  • Add 3D support to paths:stroke-path()
  • Bug: shape:scale-and-center() mishandling circles shapes/shape.xqy

• Miscellaneous

  • Bug: geom:bounding-sphere() incorrectly used geom:bounding-box() for most 2D objects geo/euclidean.xqy
  • Allow geom:bounding-box() to apply to polyhedra (ignores z coordinate) geo/euclidean.xqy

20231001

With Saxon 12.3 the need for additional JAR files (see 20230424 release notes) is gone. Saxon-JS problems with heap errors and string "too large" errors still apply (see 20230722 release notes). Some of the heap errors now show up with XSL as well (e.g. the fish example). Saxon-JS remains unusable except for very small and constrained examples that do not use many packages. XSL is still broadly usable.

Major changes and incompatibilities

• L-System code has been extensively refactored, streamlined, and extended. Support for parametric systems has been added, as have a collection of drawing functions to make modifying rendering callbacks more straightforward as well as to provide some builtins for parametric systems. Specific L-systems have been moved to the http://mathling.com/art/lsystems module. Various API incompatibilities exists (see details) See shapes/systems.xqy and components/lsystems.xqy.

• Refactoring of geometric delegation to make use of generic geom:delegate() function which honours "delegate" methods on objects. Refactoring of some of the structured components, such as http://mathling.com/art/octopus to leverage this new method. See geo/euclidean.xqy.

• Incompatibility: the default drawing map for solids now uses 2-angle projection rather than 3-point perspective. The results are easier to control and more likely to be useful as-is. The default angles are -45 and 90.

• (Bleeding Edge) Experimental 'maker' functions for various components, paths, an objects. The goal is to hook these into an Invisible XML driver art shell (not yet releases). The API and parameter usage in these maker functions is definitely subject to some change. In particular colour-handling is still up in the air. They can be used as exemplars of how to drive some of these components, however. Currently makers are all annotated with art:maker(somename). Makers may probably ultimately come in a few flavours, depending on intention as arrangements, spaces, or objects.

Additional Details

• L-systems shapes/systems.xqy
  • New L-systems: lsys:algae(), lsys:anklets(), lsys:boxes(), lsys:cracks(), lsys:daisy-chain(), lsys:double-penrose(), lsys:hex-crystal(), lsys:island(), lsys:island-and-lakes(), lsys:koch-island(), lsys:parametric-tree() lsys:peano(), lsys:peano-offset(), lsys:pentagram(), lsys:quartet(), lsys:gappy-quartet(), lsys:seaweed(), lsys:seaweed-wreath(), lsys:terdragon-boundary(), lsys:zigzag() components/lsystems.xqy
  • New: parametric L-systems (depends on eval) with system:parametric-lsystem(), system:parametric-lsystem-translate(), system:parametric-lsystem-translate-curve()
  • New: callback support functions: system:start(), system:end(), system:set-randomizers(), system:enable-randomizers(), system:disable-randomizers(), system:forwards(), system:forwards(), system:move(), system:move(), system:rotate(), system:set-angle(), system:left(), system:right(), system:reverse(), system:set-length(), system:adjust-length(), system:shorten(), system:lengthen(), system:set-width(), system:adjust-thickness(), system:widen(), system:narrow(), system:set-colour(), system:next-colour(), system:previous-colour(), system:set-kind(), system:make-path(), system:start-path(), system:start-path(), system:end-path(), system:circle(), system:circle(), system:ngon(), system:triangle(), system:square(), system:pentagon(), system:hexagon(), system:start-polygon(), system:end-polygon(), system:push(), system:pop(), system:start-branch(), system:end-branch(), system:no-op(), system:trace(), system:compose(), system:compose()
  • New: Add colour index operators to standard interpretation: , and ;. New property system.colours defines the palette.
  • New: Infer polygons when paths start/end are same if system.infer.polygons is true
  • Incompatibility: changes to the API for callback functions: only the rendering stack is provided. Additional keys capture passed parameters and randomizers, etc.
  • Incompatibility: the "current" key is no longer available in the default rendering map: use stack:top() instead.
  • Incompatibility: Reorder args in system:lsystem-curve()
  • Incompatibility: Remove system:simple-lsystem-curve(), system:stochastic-lsystem-curve()
  • Incompatibility: Use length to drive ellipse radius, not width in default interpretation of @
  • Incompatibility: system:lsystem() delegates to either system:simple-lsystem() or system:stochastic-lsystem() as appropriate; similarly with system:lsystem-curve()
  • Bug: Disabling randomizers didn't work if default randomizers were overridden
  • Bug: change lsys:koch-snowflake() to be 60 degree closed version
• New, misc.
  • Path ghosting types/ghosts.xqy
  • Iterated complex function flow lines shapes/flows.xqy
  • Add text path support to text object types/text.xqy
  • geom:collect() gather actual geometric objects from nest of slots, defs, and wrappers geo/euclidean.xqy
• Components, misc.
  • New: Pirate ship components/ship.xqy
  • New: Flowers (roses and vines) components/flowers.xqy
  • New: Images, for random image selection and creation as image object, matrix, or SVG embed (for SVG images) components/images.xqy
  • Refactoring of octopus components/octopus.xqy to use new delegate and draw hooks to replace octopus:rescale() et al with simpler octopus:style() + octopus:draw() as draw hook (thus: automaticly applied)
  • Refactoring of harmonograph components/harmonograph.xqy to use new delegate and draw hooks
  • Refactoring of knots component to use draw hook components/knots.xqy
• Arrangements components/arrangements.xqy
  • New: arrangement:star(), arrangement:pie(), arrangement:rays(), arrangement:pseudospiral()
  • Bug: arrangement:circle() using wrong angle calculation
  • Bug: incorrect null modifier handling
  • Bug: fix handling of paths with teeny edges in rays and tangents components/speckles.xqy
• Tiling components/tiling.xqy
  • Incompatibility: the order of arguments of tiling:colour-function() has been flipped to be more consistent
  • Bug: mishandling missing colours in tiling:colour-function()
  • Bug: Wrong cardinality on return type of isohedral:wild-complex-edges tiling/isohedral-tiling.xqy
• Miscellaneous
  • Support parsing transforms on SVG paths svg/parse.xqy
  • draw:as-attributes()` handle transform property containing transform object geo/transform.xqy and svg/draw.xqy
  • New sequence seq:hamming-weight() OEIS sequence A000120 core/sequences.xqy
  • New paths:dusty-path() shapes/paths.xqy
  • Allows constrained patterns to take non-box constraints shapes/patterns.xqy
  • Add convenience methods for dist:cast(): dist:integer(), dist:double() etc. types/distributions.xqy
  • Make path:edges() work on raw edges too (so path consolidation methods work on raw edges too) geo/path.xqy
  • Bug: core:inner-canvas() not honouring offsets properly art/core.xqy
  • Bug: cs:cmyk-to-rgb() mishandles k=1 case colourspace/colour-space.xqy
  • Bug: typo in image extension check image/image.xqy

20230722

The Saxon 12 and Saxon-JS issues mentioned in 20230424 still apply. The Saxon-JS issues are further exacerbated by heap errors during export and "too large" errors at run time. Saxon-JS is really not usable yet except for very small and constrained examples that do not use many packages.

• Geometry
  • Refactoring: intersections in new namespace "http://mathling.com/geometric/intersection" (geo/intersection.xqy)
  • Refactoring: Shift distance functions from geom to point (geo/euclidean.xqy, geo/point.xqy)
  • Refactoring: geom:is-straight(), geom:is-straight-edge() to edge (geo/euclidean.xqy, geo/edge.xqy
  • New submodule: "http://mathling.com/geometric/simplify" (geo/simplify.xqy)
    • sim:simplify(), sim:streamline(), sim:chaikin()
    • Refactor: geom:convex-hull() to simplify
  • New: Complex polygons (polygons with holes) geo/complex-polygon.xqy
  • New: geom:bounding-sphere(), geom:stereographic(), geom:stereographic3D(), geom:apply-matrix3(), geom:projection(), geom:process-polygons(), geom:process-areas(), geom:process-solids(), geom:process-paths(), geom:delegate() (geo/euclidean.xqy)
  • New: affine:apply-matrix3(), affine:projection3(), affine:projection() (geo/affine.xqy)
  • New: point:sum(), point:counterclockwise() (geo/point.xqy)
  • New: edge:osculating-circle(), edge:signed-curvature(), edge:curvature() (geo/edge.xqy)
  • New: path:quadrangle(), path:ngon(), path:osculating-circle(), path:simplify(), path:simplify-points(), path:streamline(), path:chaikin(), path:chaikin-points(), path:normalize(), path:consolidate-points-by-colour(), path:consolidate-points-by-colour-and-opacity() (geo/path.xqy)
  • New: ellipse:ellipse-contains-ellipse() (geo/ellipse.xqy)
  • New: solid:to-polyhedron(), solid:simple-polyhedron(), solid:extrude(), solid:glue(), solid:merge() (geo/slot.xqy)
  • New: coord:stereographic(), coord:stereographic3D() (geo/coordinates.xqy)
  • New: v:distance(), v:valid() (core/vector.xqy)
  • geom:region-center() supports slot/wrapper
  • edge:inclination() with just edge argument
  • edge:tangent() supports arc and ellipse
  • solid:insphere() supports block
  • geom:edges() takes region sequence not just singleton
  • path:path() handles sequence of points
  • spline:spline() excludes points with infinite coordinates
  • geom:length() add support for polygons
  • Bug: solid:properties() missing case for generic polyhedron
  • Bug: solid:with-properties() missing case for generic polyhedron
  • Bug: solid:circumsphere() missing case for generic polyhedron
  • Bug: point:distinct() should return () for empty sequence of points
  • Bug: wrong reserved properties for ellipsoid, polyhedra
  • Bug: Error name "BAD-SOLID" to "GEOM-BADSOLID"
  • Bug: solid:same() generic polyhedron should be less sensitive to vertex reordering
  • Bug: solid:points(), solid:vertices(), solid:face-indexes() should give error for ellipsoids
  • Bug: make sure all faces counter-clockwise on Platonic solids (relative to center)
  • Bug: geom:length() mishandling box/space
  • Bug: edge:line-intersection() fails in some cases because test of -0=0 fails (?!)
  • API: reorder points in box:vertices() to be consistent with counterclockwise polygon
• Polynomials (types/polynomial.xqy, types/cpolynomial.xqy)
  • New: cosh/sinh polynomials
  • New: poly:as-real(), poly:is-constant(), zpoly:is-real(), zpoly:as-real-polynomial(), zpoly:as-polynomial(), poly:times(), zpoly:times(), zpoly:ztimes(), poly:zvaluev(), zpoly:zvaluez()
  • Handle sin/cos ops in roots (core/roots.xqy)
  • Bug: wrong anti-derivative for cos(z)
• Numbers
  • New: complex:asin(), complex:acos(), vcomplex:asin(), vcomplex:acos(), complex:asinh(), complex:acosh(), vcomplex:asin(), vcomplex:acosh(), complex:modsq(), vcomplex:modsq(), complex:vector(), complex:as-vector() (core/complex.xqy, (core/vcomplex.xqy)
  • New: Quaternion rotations: q:quaternion() (from angles), q:from-vector(), q:rotation-between(), q:rotation3(), q:to-angles() (core/complex.xqy, (core/vquaternion.xqy)
• Sequences (core/sequences.xqy)
  • New: seq:continued-fraction(), seq:convergents(), seq:numerators(), seq:denominators(), seq:modp(), seq:modz(), seq:unmodp(), seq:unmodz()
  • seq:sequence() supports "counter" + other new functions
  • Bug: seq:sequence() incorrect handling of "prime-sequence"
• Utilities (core/utilities.xqy)
  • New: util:some(), util:every(), util:none(), util:extreme()
  • Bug: Handle edge case in util:linspace() n=1, inclusive
• Randomizers:
  • New random distributions: gamma, beta, binomial, binomial-beta (types/distributions.xqy)
  • API change: dist:weighted-distribution-of() to dist:weighted-index-of() (types/distributions.xqy)
  • New: $rand:STD-UNIT (core/random.xqy)
• Colours
  • New: tone:shade(), tone:shadev() (colourspace/tonemap.xqy)
  • API extension: effect:colour() take sequence of colours, rotates through them (svg/effects.xqy)
• Patterns, shapes, and grids
  • Refactoring: patterns:center() and patterns:scale-and-center() to shapes (shapes/patterns.xqy, shapes/shapes.xqy)
  • New: paths:stroke-path(), paths:looping-meander(), paths:bend(), paths:bend-path() (shapes/paths.xqy)
  • New: grids:hexagon() (shapes/grids.xqy)
  • Bug: patterns:scale-and-center() support width != height better (shapes/patterns.xqy)
  • Bug: paths:meander() should use just sin() not derivative; paths:looping-meander() uses derivative (shapes/paths.xqy)
  • Bug: grids:hex-point() maybe returns empty (not error) (shapes/grids.xqy)
• Music:
  • New: music:parse() and associated objects (music/music.xqy)
  • API change: music:note(), music:rest() additional parameter for note index (music/music.xqy)
  • New: music-based noise (mnoise:noise-pitch(), mnoise:noise-pitch-vector(), mnoise:noise-density(), mnoise:noise-density-vector(), mnoise:noise-extreme(), mnoise:noise-extreme-vector()) (music/noise.xqy)
• Images
  • New: ppm:p6-array() reading P6 into array (image/ppm.xqy)
  • New: imagematrix:sample() (image/matrix.xqy)
  • Better performance on row/column/diagonal selection
• Drawing (svg/draw.xqy, art/draw.xqy)
  • Add no-op draw:project to default drawing map
  • Bug: wrong draw:dump-dynamic-parameters in XSLT drawing map
  • Bug: better handling of empty values in dumped maps
• New libraries and components
  • KML (http://mathling.com/geometric/kml) basic KML to object parsing (geo/kml.xqy)
  • Statistics (http://mathling.com/core/statistics) stats:mean(), stats:median(), stats:mode(), stats:std() (core/statistics.xqy)
  • Density maps (http://mathling.com/shape/density) density:chloropleth(), density:dots(), density:dot-diagram() (shapes/density.xqy)
  • Quotient (http://mathling.com/type/polynomial/quotient): quotient of polynomials or complex polynomials (types/quotient.xqy)
  • Function unifier (http://mathling.com/core/functions) for polynomials, complex polynomials, and quotients (core/functions.xqy)
  • Component: smooth meanders (components/meanders.xqy)
  • Component: random complex-functions (e.g. for use with fractals) (components/complex-functions.xqy)

20230424

• Saxon 12 issues

  • The handling of component configuration bundles (art/components.xqy) is incompatible in some way with Saxon 12 performance tracing for some reason.
  • Attempts to use image/png.xqy (including via wfc/image-tiled-model.xqy or wfc/overlapping-model.xqy and similarly for XSL packages) will fail without additional JAR files (e.g. JDOM2) on the classpath.

• Saxon-JS issues

  • Saxon-JS has serious performance issues when there is a non-trivial number of functions or packages in scope, which is generally the case here. The compiled JSON file can easily get too large to load or will run unusably slowly.
  • You cannot write PPM or PNG files in Saxon-JS: the EXPath file module is not available in that context.
  • Direct annotation of function items is not available, as it depends (for XSLT) on eval (i.e. saxon:xquery()) which is not available in that context.

• Major changes

  • XSL packages for all modules; XSL versions of all tests and examples
  • Status markers and auto-generated API documentation on all modules index.html
  • Reworking of the handling of component configuration bundles

• Major incompatibilities: Mutation functions, modifier functions, and noise functions

  • As with SDF functions, these have all been changed to use callables rather than function items directly. It is necessary to use callable:function() to get an actual function item to call.
  • Mutation and noise functions now come in vector as well as point forms, with the vector form being the default usage, which should improve performance for complex compositions of functions. New methods mutation:as-vector(), mutation:as-point(), noise:as-point(), noise:as-vector() to switch modalities. (components/mutations.xqy, components/modifiers.xqy, noise/)

• Other incompatibilities:

  • mutation:random-mutation() and mutation:random-mutations() changed order of arguments to make compatible with general usage (components/mutations.xqy)
  • Move: components/systems.xqy is now shapes/systems.xqy with namespace changed from "http://mathling.com/art/systems" to "http://mathling.com/shape/systems"
  • point:orientation() arguments order interpreted so that first two points are edge and orientation is of third point relative to that edge (geo/point.xqy); calls should flipped 2nd and 3rd parameters
  • Deprecated: geom:point(), geom:x(), geom:y(), geom:px(), geom:py(), geom:midpoint() Use point functions instead. Not present in XSL package. (geo/euclidean.xqy)
  • Move all annotations names to "http://mathling.com/art" namespace (types/distributions.xqy, string/aho.xqy, string/entity.xqy)

• Major new capabilities:

  • Function caching (depends on Saxon memo-function annotation in XQuery) (core/cache.xqy)
  • Polynomials with complex coefficients (including support for roots) (types/cpolynomial.xqy)
  • Polynomials over sin(x) and cos(x) (support for derivatives, values, not for roots) (types/polynomial.xqy)
  • Hyperbolic tesselation (geo/hyperbolic.xqy)
  • Hyphae component (components/hyphae.xqy)
  • Creating sequences by name with seq:sequence() (core/sequences.xqy)
  • Sequence modifiers: seq:mirror(), seq:alternate(), seq:shift(), seq:modix()
  • Hexagon grid subdivision and operations: grid:hex-triads(), grid:hex-subgrid(), grid:hex-points(), grid:hexagons(), grid:excluded() (shapes/grids.xqy)

• Other new things:

  • Geometric:
    • edge:skip() (geo/edge.xqy)
    • vector:destination(), vector:mutate() (core/vector.xqy)
    • path:consolidate(), path:consolidate-by-colour(), path:consolidate-by-width(), path:consolidate-points() (geo/path.xqy)
    • point:sorientation() orientation of point triplets as a numerical sign (geo/point.xqy)
    • New, faster implementation of geom:convex-hull() (geo/euclidean.xqy)
  • Shapes:
    • patterns:scale-and-center(), patterns:center() (shapes/patterns.xqy)
    • paths:meander(), paths:circle-spiral() (shapes/paths.xqy)
  • Complex numbers: (core/complex.xqy, core/vcomplex.xqy)
    • complex:sum(), complex:eq(), vcomplex:sum(), vcomplex:eq()
  • Effects: (svg/effects.xqy)
    • New modifier: effect:distant-light()
    • New effect: "topography"
  • Noise:
    • noise:trace-bounds(), noise:cache() (noise/modifiers.xqy)
    • noise-map:flat-static(), noise-map:sphere-static() (noise/noise-map.xqy)
    • tests/test-noise.xqy testing noise functions and modifiers
  • SDF: (sdf/sdf.xqy)
    • sdf:opRepeat2(), sdf:opMirrorRepeat2(), sdf:opGridRepeat2(), sdf:opPolarRepeat2()
  • Miscellaneous:
    • util:zsign() see bugs (core/utilities.xqy)
    • mask:ref() (types/mask.xqy)
    • poly:multiply() (types/polynomial.xqy)
    • arr:blur(), arr:horizontal-blur(), arr:vertical-blur() (core/array.xqy)
  • New mutations: bipolar, elliptic, circular, parabolic, sphere (components/mutations.xqy)
  • Gradients: Add $gradient:DIVERGING-GRADIENTS list (svg/gradients.xqy)
  • New examples: examples/contours.xqy, examples/tree.xqy (examples/)
  • Drawing: add hook for "describe" on drawn object
  • Some BaseX hooks for randomizers, eval

• Bug fixes, clean-ups, and tweaks

  • Workaround for bad callback lookup in XSL: component:expand()
  • Improper/suboptimal imports in components/fflame, components/splitttree, noise/*, string/entity
  • Replace use of deprecated functions on components/astronomy
  • Testing
    • Bug in testlib comparator function causing incorrect reporting of success (D'oh!)
    • Add some decimal rounding on some tests so they don't fail for irrelevant floating point differences
  • Sequences:
    • Errors in seq:primes(), seq:prime-factors(), seq:foreach-combination(), seq:lazy-caterer(), seq:thue-morse(), seq:binomial()
    • Typo in tests/test-sequences.xqy seq:foreach-permutation()
    • Missing call to local:testThueMorse() in tests/test-sequences.xqy
  • Drawing:
    • Missing type in art/draw causing broken rendering in Art XML
    • Missing/broken support for all matrix types in XSL draw:colour-buckets()
    • Missing types in draw XSL metadata dumping methods causing malformed metadata
    • Incorrect function reference in SVG draw for metadata dumping method
    • Fix sort key on parameter bundle dumping
    • Incorrect drawing call in mask
    • Lookup failing for some gradients in XSL
    • Map sorting of dumped maps might fail for certain unusual maps
  • Geometry:
    • Edge intersections use $config:tolerance instead of $config:ε
    • solid:ry(), solid:rz() using wrong accessor for spheres
    • solid:ordered-edges() and solid:edges() reporting inverted edges
    • transform:translate() and transform:rotate() check for no-ops
    • delaunay:base-triangle() check for empty point list
    • marching:contours-by-function() wrong cardinality on parameter
    • Missing types in geo/translate.xsl leading to improper formatting
    • sd3:sdPyramid() misbehaves because util:sign(-0) should be 0 but ends up negative as $v=0 fails (?!); however, some of the complex functions fail if util:sign(-0) is not negative (?!) so add util:zsign() for sd3:sdPyramid()
  • Missing types in XSL effects methods creating malformed effect definitions
  • Missing types in XSL gradient methods creating malformed gradient definitions
  • Bad accessor used in simplex:noise4() raising type error
  • Apply box:min-point() offsets to grid:hex-grid() calculations
  • Astronomy component misused core:randomize() wrt keys
  • Flowfield component mishandled mutation modifiers in named fields
  • Some clean up of isohedral tiling code (needs more)

20230224

• Major incompatibility: SDF functions

  • Since XSL doesn't support function annotations, to support annotations in function libraries like SDF, a new callable wrapper has been introduced. It is necessary to use callable:function() to get at the actual function now. Other functions-that-produce-annotated functions (noise, modifiers) will get this treatment going forward. However, callable:function() will work on bare functions too, so it is advisable to just use it with these modules to future-proof code.

• Other incompatibilities

  • Namespace changed from http://mathling.com/art/colour-space to http://mathling.com/colour/space
  • Moved components/paths.xqy to shapes/paths.xqy; namespace changed from http://mathling.com/art/paths to http://mathling.com/shape/paths
  • Split grid functions out of components/paths.xqy into shapes/grids.xqy with namespace http://mathling.com/grid
  • Renamed SDF smooth operators to round (e.g. sdf:opSmoothUnion => sdf:opRoundUnion)
  • Remove $geom:ORIGIN* (use $point:ORIGIN* instead)
  • Remove deprecated function rand:uniform-distribution-of (use dist)
  • dist:markov() with 1 argument now uses 1 as start (not a random index, which creates circular imports)
  • util:clamp() now requires both arguments; use util:clamp-some() for open ranges

• Documentation

  • XQDocs for all modules, to varying degrees of detail

• XSL APIs

  • Ports to XSL of some of the core libraries (more to come!)

• Examples

  • Rendering examples in XQuery and XSLT
  • Randomization and loops

• Complete reworking of drawing functions

  • Drawing operations for various objects not in that object's module

• Major new objects and capabilities

  • Blocks: axis aligned 3D blocks (see geo/box.xqy)
  • Coordinate mappings such as bipolar (see geo/coordinates.xqy)
  • Patterns: patterns:fir(), patterns:nested-arc(), patterns:diamonds(), patterns:voronoi() (see shapes/patterns.xqy)
  • Clipping regions (see types/reach.xqy)
  • Navigable hex grids (see shapes/grids.xqy)
  • New colour palettes from https://nrennie.github.io/PrettyCols/

• Sequences (see core/sequences.xqy)

  • New sequences: seq:primes(), seq:prime-factors(), seq:factors(), seq:recaman(), seq:gerrymander2(), seq:inventory()
  • Sequence operators: seq:μ(), seq:mobius(), seq:lodumo(), seq:binomial(), seq:ordinal()
  • More error checking on sequence arguments

• SDF changes (see sdf/)

  • Reorganization as described in incompatibilities
  • Make SDFs easier to use when you don't need scaling (i.e. not raymarching)
  • Add sdf:make-point-render() and sdf:make-vector-render() which return functions to do the ray-casting (avoids repeated camera angle calculations etc.)
  • Additional SDF operators (chamfered, smooth, and stepped)

• New art components and capabilities

  • Backgrounds: background:terrain() shadowed height field
  • Shadowy people (see components/people.xqy)
  • Squishy blob fills (see components/squishy.xqy)
  • Barnsley ferns (see components/barnsley.xqy)

• Miscellaneous new functions

  • util:annotations() (see core/utilities.xqy)
  • dist:weighted-distribution-of() (see types/distributions.xqy)
  • curve:plot() curve:multi-plot() (see geo/curves.xqy)
  • splittree:find(), splittree:parent(), splittree:split-tree3() (see geo/splitree.xqy)
  • effect:displace() (see svg/effects.xqy)
  • gradient:luminance-range() (see svg/gradients.xqy)
  • english:word-syllable() and mode 'syllables' (see components/english.xqy)
  • path:simplify(), path:chaikin() (see geo/path.xqy)
  • edge:closest-point() (see geo/edge.xqy)

• Bug fixes

  • Off-by-one sequence length fix: jacobsthal(), katydid(), grasshopper()
  • Arc bounding box raised assertion failure on degenerate arc
  • Handle edge cases for ellipse:circle-center-of(), ellipse:circle-from()

• Tests

  • More sequence, SDF, utilities, geo tests
  • XSLT tests

20221219

• Major new components and capabilities

  • Quaternions (core/quaternion.xqy, core/vquaternion.xqy)
  • MusicXML basic parsing (music/music.xqy)
  • Text wrapper and text layout within rectangles (types/text.xqy, string/string.xqy)
  • Pseudospirals (components/paths.xqy)
  • Randomized components
    • Polynomial spirals (components/polyspiral.xqy)
    • Arrangements: initial gathering of basic point arrangements by name (components/arrangements.xqy)
    • Modifiers: gathering of modifier functions (double to double) by name (components/modifiers.xqy)
    • Refraction: Snell's law refraction calculations; various material parameters (components/refraction.xqy)
    • Pixel sorting: pixel sorting (components/pixelsort.xqy)
    • Crosshatch: crosshatching of various kinds (components/crosshatch.xqy)
    • English: gibberish with English letter distributions (components/english.xqy)
    • Old key: old-fashioned block keys (components/oldkey.xqy)

• Effects and filters

  • New builtin effects: sandstone and sandpaper
  • New effect composition modifiers: overlay, blend-multiply, blend-screen, blend-darken, blend-lighten, compose-over, compose-in, compose-out, compose-atop, compose-xor
  • Make effect building API more compositional; add effect:blur(), effect:perturb()
  • Bug: effect prefixes using wrong regex; not working properly

• Colours and gradients

  • Fix name confusion cube_1_0 vs cube1_0
  • New palette: plant-dyes plus associated colour names
  • Add variables capturing key palette/gradient aspects: $gradient:SMALL-GRADIENTS, $gradient:SPLIT-GRADIENTS, $gradient:CYCLIC-GRADIENTS, $gradient:LINEAR-GRADIENTS
  • Bug: werner_reds, werner_blues, werner_browns misnamed in gradient:starts-darker() so not properly accounted for
  • Make gradient building API more compositional; make modifiers in names fully compositional
  • gradient:random-colour() selecting random colour from gradient with optional reluminance bounds
  • gradient:colours() to reluminate colours from gradient within luminance bounds
  • gradient:circularize() to extend set of colours to make circular gradient
  • Escape rgb() colour names in URL references
  • Clamp values in CMYK-to-RGB conversion to avoid errors
  • New: cs:greyscale-value-to-rgb(), cs:greyscale-value-to-xyz(), cs:rgb-to-greyscale-value(), cs:rgb-to-greyscale(), tone:cmyk-snap()
  • Bug: Wrong accessor used for ambient light; diffuse lighting could be off
  • Bug: error in RGB-to-CMYK conversion

• Images

  • New: Image wrapper with data URL escaping and embedding (image/image.xqy)
  • New: image matrix convolutions, plus edge-detection, sharpen, and blur (image/convolution.xqy)
  • New: pixel sorting (image/pixelsort.xqy)

• Randomizers

  • core:randomize() will return keys corresponding to random index if available
  • Add selector distribution to multimodal distributions (not just uniform)
  • New: dist:zipf-index-of(), dist:weighted-index-of()

• Geometry

  • More refactoring (see specifics below)
  • Add solid geometry objects to more generic geometric operations (e.g. geom:points())
  • Add more pass-throughs to generic geometric operations for wrappers, slots, and masks
  • Extend and improve region intersection; add tolerance
  • New: geom:apply-transforms(), geom:circle-intersection(), transform:matrix()
  • geom:points(), geom:vertices() take sequence of regions, not singleton
  • Add option to conrec functions to return polygons
  • Improved error reporting
  • Bug: fix off-by-one point check in spline:spline()
  • Bug: signed distance was 0 limited for edges, paths, and polygons
  • Bug: polygon-contains(circle) wrong sense of comparison
  • Bug: polygon-intersects(circle) incomplete
  • Points:
    • New: point:midpoint(), point:angle(), point:inclination(), point:pcoordinate(), point:centroid()
    • Handle INF and NaN better in points
  • Solids:
    • New: solid:n-faces(), solid:points()
  • Edges:
    • geom:edge-angle() => edge:angle()
    • geom:edge-inclination() => edge:inclination()
    • geom:edge-length() => edge:length()
    • geom:edge-intersects() => edge:linear-intersects()
    • geom:quad-intersects() => edge:quad-intersects()
    • geom:cubic-intersects() => edge:cubic-intersects()
    • geom:arc-intersects() => edge:arc-intersects()
    • geom:arc-midpoint() => edge:arc-midpoint()
    • geom:interpolate-edge() => edge:interpolate-edge()
    • geom:interpolate-edge-using() => edge:interpolate-edge-using()
    • geom:interpolate-quadratic() => quadratic:interpolate-quadratic()
    • geom:interpolate-quadratic-using() => quadratic:interpolate-quadratic-using()
    • geom:interpolate-cubic() => cubic:interpolate-cubic()
    • geom:interpolate-cubic-using() => cubic:interpolate-cubic-using()
    • geom:interpolate-arc() => arc:interpolate-arc()
    • geom:interpolate-arc-using() => arc:interpolate-arc-using()
    • New: edge:edge-intersects(), edge:tangent(), edge:to-edges(), edge:slice(), edge:chop(), edge:point-distance(), edge:linear-t(), edge:quad-t(), edge:cubic-t(), edge:arc-t(), edge:edge-t(), edge:arc-intersection()
  • Ellipses and circles
    • geom:ellipse-point() => ellipse:ellipse-point()
    • geom:interpolate-circle() => ellipse:interpolate-circle()
    • geom:interpolate-circle-using() => ellipse:interpolate-circle-using()
    • geom:interpolate-ellipse() => ellipse:interpolate-ellipse()
    • geom:interpolate-ellipse-using() => ellipse:interpolate-ellipse-using()
    • geom:circle-center-of() => ellipse:circle-center-of()
    • geom:circle-from() => ellipse:circle-from()
    • New: ellipse:bounding-box(), ellipse:circle-circle-intersection(), ellipse:ellipse-intersects-ellipse(), ellipse:bounding-box(), ellipse:tangent-angle(), ellipse:interpolate(), ellipse:interpolate-using()
    • Bug: incorrectly using degrees instead of radians for ellipse rotation in ellipse:contains-point()
  • Boxes and rectangles:
    • geom:box-intersects() => box:box-intersects(), rect:box-intersects()
    • New: box:intersects-box()
  • Paths and polygons:
    • geom:path-point() => path:path-point()
    • geom:polygon-contains-point() => path:polygon-contains-point()
    • geom:slice-path() => path:slice()
    • Subsume geom:polygon-intersects-polygon() into geom:region-intersects()
    • New: path:polygon-center(), path:tangent(), path:bounding-box(), path:edge-intersections(), path:path-t()

• Complex numbers

  • New: vector form API
  • New: z:abs(), z:sinh(), z:cosh(), z:ppow(), z:exp()
  • Incompatibility: z:complex-rφ() now takes radians; z:complex-rφd() takes degrees

• Tweaks

  • Canvas: change resolution to naming system (e.g. medium+reverse+45+border); new core:inner-canvas()
  • Utilities: new util:intmix(), util:hypermix(), util:expmix(), util:factorial(), util:binomial()
  • trace() function in mutations, modifiers, and SDF functions
  • Wrappers: wrapper:shapes() to extract geometric drawable shapes (exclude def, ref, element metadata, etc.)
  • Drawing: use function lookup to find drawing functions; don't draw empty paths; supper stroked paths
  • Voronoi: allow non-rectangular bounds; use shorter "infinite" edges
  • Backgrounds: border frames, circle crosshatching
  • Mountains: add smoothing
  • Speckles: speckles:tangents(); more controls; better ray calculation for singleton point
  • Mutations: typo in name of perspective parameter; add new randomized parameters for various mutations; new mutation:trace(), mutation:translate()
  • Paths: new paths:hex-grid(), better handling of border edges in grids
  • Sequences: new seq:padovan(), seq:fractal(), seq:golomb(), seq:lazy-caterer(), seq:jacobsthal(), seq:jacobsthal-lucas(), seq:pascal-row(), seq:pascal(), seq:katydid(), seq:grasshopper(), seq:k-combinations(), seq:foreach-k-combination()

• Misc

  • Various minor bug fixes and additional tests, examples, and documentation

20220731

• Major new algorithm: Wave Function Collapse (wfc/)

• Mutations:

  • Additional mutation functions (pillow, crumble, rotate, flowfield, supershape, flower, conic, parabola, bent2, dist2)
  • Fixes to some mutations (arch, gaussian, blur, ring/ring2)
  • Parameter drift extents
  • Add randomization framework to mutation naming system

• Other new:

  • Mask type for drawing masks ('types/mask.xqy`)
  • Extended helix functions
  • $config:POINT-IS-PIXEL to control how points get rendered by default
  • Shift wave component to use wrapper
  • More examples and docs

• Refactoring of geometry code

  • Partition basic affine support operations to geo/affine.xqy
  • Consolidation and clean-up of affine code in general
  • Shifting edge intersection point operations to geo/edge.xqy; some renaming, e.g. geom:slice-edge() => edge:slice()
  • Shift box code to geo/box.xqy to avoid twisted imports; external interface unchanged

• Geometry additional:

  • Better handling of precision issues with edge operations
  • New: edge:quad-t(), edge:cubic-t()
  • More passthroughs for wrappers and slots in geometry operations
  • New: transform:parse-matrix()
  • Slightly better arc handling; new: edge:as-point-arc()
  • Bug: box:mutate() and some arc transforms lose properties

• Colours

  • Make Werner colour names more consistent with other colour names
  • Support gradient merges and interleaves in naming system

• Other bugs:

  • Missing abs() in complex:is-real()
  • For consistency path angle should return 270 not -90
  • Missing cast in one branch or util:unsignedLong
  • rgb:to-int() inverted the coordinates, causing colour changes
  • rand:n-partition() used wrong subroutine, incorrect results

20220626

• Major new components and features

  • STL 3D model files[1] (3d/)
  • PNG read/write [2] (images/png.xqy)
  • CONREC (contouring algorithm) implementation[3] (geo/conrec.xqy)
  • Exponential random distribution (types/distibutions.xqy)
  • Parametric, polar, and dependent curve plotting (geo/curves.xqy)
  • Polynomials (values, definite integrals, derivatives, anti-derivatives) (types/polynomial.xqy)
  • Filter manipulation functions (svg/effects.xqy)

  • Randomized components:

    • Backgrounds: neutral backgrounds with crosshatching, stippling, etc. (se components/backgrounds.xqy)
    • Cellular: Cellular automatons[4] (components/cellular.xqy)
    • Contours: random contours (components/contours.xqy)
    • Egg: egg shapes based on universal egg equation[45 (components/egg.xqy)
    • Divisions: rectangular subdivisions (components/divisions.xqy)
    • Fractal flame: fractal flame implementation[6] (components/fflame.xqy)
    • Waves: symmetrically damped waves (components/waves.xqy)
    • Glyphs (components/xtrs.xqy)
    • Harmonographs (components/harmonograph.xqy)

  • Various spirals and curves (components/paths.xqy)

    • harmonographs and damped pendulums, damped sine waves, torus-knot-driven wiggles, modulated Lissajous, Rose curve, trefoil, Maurer rose, granny knot, harmonograph, Euler's spiral, polynomial spiral, Cotes' spiral, Poinsot spiral, reciprocal spiral, equiangular spiral, epispiral, cochleoid spiral, atom spiral, circle involute, lituus, Gielis curve (super ellipse), super rose, super spiral, logarithmic spiral, Fermat's spiral, tractrix, Doppler curve, conchospiral, Lamé curve

• Colours and gradients:

  • Upgrade to version 7 of Scientific Colour Maps
  • Add palettes and colours from Werner's Nomenclature of Colours
  • Other new palettes (svg/gradients.xqy)
  • Add RGBA constructor that takes string values
  • Add RGB to integer and integer to RGB functions
  • gradient:average-luminance() to compute relative brightness of a set of colours
  • Clean up and extend the gradient manipulation code
  • Fix cardinality errors in gradient expansion functions

• Random distributions:

  • dist:post-shift() to add a value to the output of the core algorithm
  • dist:simple-sums() method for constructing a cumulative weight table from an ordered set of raw weights
  • Add keys hook for automating getting values from random indexes (art/core.xqy)
  • Add explicit double cast to override the implicit integer cast of some of the distributions (e.g. Zipf)

• Types:

  • Wrappers: Generic bundling of objects with dynamic parameters; refactor components to use wrappers, support wrapper passthroughs in various contexts
  • Noise-based colouring, for applying a colour shift against a gradient based on a noise field

• Isohedral tiling:

  • Add parameter to tiling:create-tiles to control the extent of the bounds and override the default
  • Add boundary settor to tiles, so that we can apply affines, for example

• Geometry:

  • ARF inprovements: use radius not diameter for default scaling and add explicit radius parameter, lower Δt and iterations to improve performance, more controls over graph layout, edge case checks
  • Add support for various solids to geometric operations (correct ellipsoid support is WIP)
  • Change affine operations to take sequences of regions, for easier use
  • Generic geom:area(), geom:length(), geom:n-faces(), geom:region-point() functions
  • geom:tangent() and geom:normal() for 2D linear, quad, or cubic edge, plus associated geom:tangent-angle() and geom:normal-angle() (angle of the tangent or normal vector)
  • point:valid() to check for point coordinates that are infinite or NaN
  • More solid geometry operations on faces: solid:normal(), solid:face-area(), solid:face-centroid()
  • Method for conversion of one of the Platonic solids to the generic polyhedron

• Framework

  • Improved support for merging information from components; refactoring of components to make use of this
  • Support selecting keys based on random index in core:randomize()
  • High level generation of dynamic random values: core:random-parameter-map(), core:random-parameters()
  • Hooks for colour buckets drawing
  • Limited SVG path parsing support
  • Fix metadata passthrough in SVG drawing functions

• Signed distance functions

  • Improvements to sdf:toSDF()
  • Sequence operations to reduce function stacking: sdf:opUnion(), sdf:opIntersect()

• Components

  • Mutation functions: add weight into calculations mut:drift(), handle missing parameters
  • Systems: add quadratic Gosper curve
  • Array arrangements: ability to return boxes, allow use of boxes or slots for sizing

• Incompatibilities

  • Adjustments and additions to standard resolutions (pic, page, poster, rev-pic, rev-poster)
  • SDF octohedron renamed octahedron
  • Flip argument order on util:min-key() and util:max-key()
  • geom:region-center() honours a center property
  • Change solid:edges() to return distinct edges; add solid:ordered-edges() to get the full set of edges (including shared), in face order
  • Change order of output arguments in transform:describe() to better match SVG transform property

• Various fixes:

  • Fixes to dodecahedron: add missing face, fix ordering of some faces, fix scaling
  • Better handling of some edge cases in geom:region-center(), fix bug in center of 4-sided polygon
  • Check some edge cases in quad length calculations
  • Better area calculations for triangles
  • Fix mishandling of rotated ellipses in geom:ellipse-point()
  • Fix cardinality errors within core:dump-randomizer() and $core:EVAL11
  • Fix systems:pentaplexity() to use parameters for scaling and generations
  • Raise error if light direction is origin (gives NaN values)
  • Handle degenerate edges in SDF; avoid NaNs
  • More tests and examples

• Possible future mayhem:

  • Refactoring of spirals and related curves from components/paths.xqy
  • Refactoring of more geometric operations to push more to the individual geometric types

[1] Requires functions from the http://expath.org/ns/file and http://expath.org/ns/binary namespaces.

[2] Depends on Saxon Java API extensions; metadata saved in a secondary file due to lacunae in Java PNG implementation.

[3] See Paul Bourke "CONREC: A Contouring Subroutine" (http://paulbourke.net/papers/conrec/) for more information.

[4] See https://en.wikipedia.org/wiki/Elementary_cellular_automaton for more information.

[5] See Valeriy G. Narushin, Michael N. Romanov, and Darren K. Griffin " A universal formula for avian egg shape" (https://www.biorxiv.org/content/10.1101/2020.08.15.252148v1) for more information.

[6] See Scott Draves & Erik Reckase "The Fractal Flame Algorithm" (https://flam3.com/flame_draves.pdf) for more information.

20220308

• Geometry:

  • More refactoring of edge/point/circle code (shifting to specific type module)
  • Some support for Platonic solids and generic polyhedra
  • Signed distance function for region types
  • ARF graph layout
  • Point maps (hash map for points)
  • Additional circle/polygon intersection support (needs more tests)
  • Isometric projection
  • Pass-through slot bodies in various geometric operations
  • Fix bug in box:max-y for spaces
  • Fix bug in geom:project return type
  • Fix cardinality bug in some instances of mutate()

• Sequences:

  • Consolidate some sequence/set operations in sequences.xqy (Fibonacci, combinations and permutations)
  • Additional sequences: deBruijn, Thue-Morse, Feibenbaum, ruler

• Utilities:

  • Add Poisson and binomial Poisson distributions
  • Matrix operations
  • Stack data structure
  • Base conversions
  • util:logK() and util:log2() (log base K and log base 2)
  • rand:mutual-prime-pair() (pair of mutually prime integers)
  • util:modix handle negative numbers to preserve sequentiality
  • Include canvas edge in paths:array() calculations
  • Fix mishandling of pre-multiplier in resampling
  • Bugs in skewed normal distribution
  • Cardinality errors in some random functions
  • Fix function annotation mechanism

• Drawing/Colour/Effects:

  • Add configuration for SVG vs DSL drawing so components can be agnostic
  • Integrate projection into drawing functions for solids
  • Diffuse lighting model
  • Effect manipulations: merging, renaming, changing lighting colour or point light source, changing extent, changing turbulence
  • gradient:random-gradient() select a random well-known gradient or its reverse
  • Doc fix: tonemapping should take place over linear RGB (XYZ space)

• Components:

  • Functions to array points on circular arc, helix, spirals of various types
  • Mutation function library
  • L-systems
  • Trees
  • Smooth curls
  • Flowfields
  • Mutated torus knots
  • Frustrated N-gons
  • Mountain ranges

20211222

• Additions, extensions, and bug fixes to geometry code:

  • geo:region-intersects between most region types
  • geo:region-contains between some region types
  • geo:shortest-distance from point to region
  • geo:intersection between edges
  • geo:bounding-circle of region (Weltz' algorithm)
  • geo:bounding-box of region
  • geo:region-center
  • geo:regions edge following to construct polygons from edge graph
  • Graph object (graph.xqy)
  • Squarified tree construction (treemap.xqy)
  • Delaunay triangulation (delaunay.xqy)

• Drawing code

  • Simple geometric object to SVG rendering (draw.xqy)
  • SVG filter construction/manipulation (effects.xqy)

• Miscellaneous

  • Read PPM image data into non-sparse matrix, much faster
  • ACES, Hablic, Reinhard tonemapping (tonemap.xqy)
  • Add missing prefixes to $EDGE-START and $EDGE-END in tiling code
  • Enpsulate entity/string dictionary saving methods
  • Linear, quadratric, and cubic root calculations (roots.xqy)
  • Complex numbers (complex.xqy)

20211020

• Major refactoring of geospatial code, with some additional operations for splinning and reversing edges, among others. As a consequence of this a number of edge and path functions have shifted from euclidean.xqy to edge.xqy or path.xqy in some cases with a slight renaming. Example: geom:linear-edge-point is not edge:linear-point. In addition a few functions have moved to utilities.xqy (remap-degrees, remap-radians).

• Handle error cases in edge:quad-length better.

• Change geom:inclination to define it as 90° not 0° when the points are the same.

• Change geom:destination to avoid small round-off errors in Z values from inclination imprecision.

• Add split tree and well-separated pair decomposition and spanning edges on WSPDs. (Depends on bug-fix in Saxon 10.6 to work.)

• Add support for dithering of raw images.

• Add support for complex numbers.

• Add modules for signed distance function calculation, with various rendering and lighting calculations, with tests.

• Add SVG gradient collection and module for manipulating SVG gradients.

• Add permutation and combination calculations to utilities.xqy.

• Slight refactoring of random distributions code to avoid tangled imports.

• ε is now defined globally in config.xqy

• util:twixt will reorder out-of-order arguments.

20210814

• Bug fix to rand:skewed(): incorrect calculation of standard deviation.

• Bug fix to rand:flip(): scaling error.

• Reimplementation and API change to rand:random-selection() to give more precise probability mapping.

• Additional/cleaned-up randomizer tests: advice on optimizer flags for Saxon EE

• util:rangeindex() + tests