Index of /code/art

Documentation

API documentation is in the various subdirectories, e.g. string/api.html as well as in the documentation directory.

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 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.

Status indicators

• Stable: has been used in a number of projects, not subject to much change
• 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

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" (geometric/intersection.xqy)
  • Refactoring: Shift distance functions from geom to point (geometric/euclidean.xqy, geometric/point.xqy)
  • Refactoring: geom:is-straight(), geom:is-straight-edge() to edge (geometric/euclidean.xqy, geometric/edge.xqy
  • New submodule: "http://mathling.com/geometric/simplify" (geometric/simplify.xqy)
    • sim:simplify(), sim:streamline(), sim:chaikin()
    • Refactor: geom:convex-hull() to simplify
  • New: Complex polygons (polygons with holes) geometric/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() (geometric/euclidean.xqy)
  • New: affine:apply-matrix3(), affine:projection3(), affine:projection() (geometric/affine.xqy)
  • New: point:sum(), point:counterclockwise() (geometric/point.xqy)
  • New: edge:osculating-circle(), edge:signed-curvature(), edge:curvature() (geometric/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() (geometric/path.xqy)
  • New: ellipse:ellipse-contains-ellipse() (geometric/ellipse.xqy)
  • New: solid:to-polyhedron(), solid:simple-polyhedron(), solid:extrude(), solid:glue(), solid:merge() (geometric/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/effect.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 documentation/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 (effect.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