#  [](https://www.npmjs.com/package/@thi.ng/geom)  [](https://mastodon.thi.ng/@toxi) > [!NOTE] > This is one of 215 standalone projects. LLM-free, human-made and > cared for software, maintained as part of the > [@thi.ng/umbrella](https://codeberg.org/thi.ng/umbrella/) ecosystem and > anti-framework. > > 🚀 Please help me to work full-time on these projects by [sponsoring > me](https://codeberg.org/thi.ng/umbrella/src/branch/develop/CONTRIBUTING.md#donations). > Thank you! ❤️ For the Clojure version, please visit: [thi.ng/geom-clj](https://thi.ng/geom-clj) - [About](#about) - [Shape types](#shape-types) - [Hiccup support](#hiccup-support) - [SVG support](#svg-support) - [Polymorphic operations](#polymorphic-operations) - [Shape factory functions](#shape-factory-functions) - [AABB](#aabb) - [Arc](#arc) - [Bezier patch](#bezier-patch) - [Circle](#circle) - [Cubic](#cubic) - [Group](#group) - [Line](#line) - [Path](#path) - [Plane](#plane) - [Polygon](#polygon) - [Polyline](#polyline) - [Quad](#quad) - [Rect](#rect) - [Sphere](#sphere) - [Triangle](#triangle) - [Constants & presets](#constants--presets) - [Curve subdivision kernels](#curve-subdivision-kernels) - [Polygon tessellation algorithms](#polygon-tessellation-algorithms) - [Vertex convolution kernels](#vertex-convolution-kernels) - [Support packages](#support-packages) - [Related packages](#related-packages) - [Status](#status) - [Installation](#installation) - [Dependencies](#dependencies) - [Usage examples](#usage-examples) - [API](#api) - [Authors](#authors) - [License](#license) ## About Functional, polymorphic API for 2D geometry types & SVG generation. This project is a partially ported from the [Clojure version of the same name](http://thi.ng/geom-clj). All polymorphic operations built on [@thi.ng/defmulti](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/defmulti). ### Shape types The following 2D/3D shape primitives are provided. All these types are implemented as basic data container classes with additional eponymous factory functions (e.g. `Circle` (class) => `circle()` (function)), which are encouraged to be used instead of calling class constructors directly. For many shapes there're [multiple ways to create them](#shape-factory-functions), please also check linked sources and/or docs. > [!IMPORTANT] > Support for 3D shapes is WIP and currently limited to the various operations > provided by this package, but does not _yet_ find any usage outside (e.g. for > visualization). Sill, even the ops supported so far can be useful for many > use cases... | Shape/Form | Description | Hiccup support | |--------------------------------------------------------------------------------------------------------|---------------------------------------|---------------------| | [AABB](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/aabb.ts) | 3D Axis-aligned bounding box | ✅⁽¹⁾ | | [Arc](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/arc.ts) | 2D elliptic arc | ✅ | | [BPatch](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/bpatch.ts) | 2D cubic bezier patch (4x4 points) | ✅ | | [Circle](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/circle.ts) | 2D circle | ✅ | | [ComplexPolygon](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/complex-polygon.ts) | 2D polygon w/ holes | ✅ | | [Cubic](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/cubic.ts) | 2D cubic bezier | ✅ | | [Cubic3](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/cubic3.ts) | 3D cubic bezier | ✅⁽¹⁾ | | [Ellipse](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/ellipse.ts) | 2D ellipse | ✅ | | [Extra](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/extra.ts) | Custom embedded hiccup/SVG data | ✅ | | [Group](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/group.ts) | group of 2D shapes | ✅ | | [Group3](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/group3.ts) | group of 3D shapes | ✅⁽¹⁾ | | [Line](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/line.ts) | 2D line segment | ✅ | | [Line3](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/line3.ts) | 3D line segment | ✅⁽¹⁾ | | [Path](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/path.ts) | 2D path (w/ optional holes/sub-paths) | ✅ | | [Path3](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/path3.ts) | 3D path (w/ optional holes/sub-paths) | ✅^(1),(2) | | [Plane](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/plane.ts) | 3D plane | ✅⁽¹⁾ | | [Points](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/points.ts) | 2D point cloud | ✅ | | [Points3](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/points3.ts) | 3D point cloud | ✅⁽¹⁾ | | [Polygon](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/polygon.ts) | 2D simple polygon (no holes) | ✅ | | [Polygon3](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/polygon3.ts) | 3D simple polygon (no holes) | ✅ | | [Polyline](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/polyline.ts) | 2D polyline | ✅ | | [Polyline3](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/polyline3.ts) | 3D polyline | ✅⁽¹⁾ | | [Quad](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/quad.ts) | 2D quad (4-gon) | ✅ | | [Quad3](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/quad3.ts) | 2D quad (4-gon) | ✅⁽¹⁾ | | [Quadratic](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/quadratic.ts) | 2D quadratic bezier | ✅ | | [Quadratic3](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/quadratic3.ts) | 3D quadratic bezier | ✅⁽¹⁾ | | [Ray](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/ray.ts) | 2D ray | ✅ | | [Ray3](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/ray3.ts) | 3D ray | ✅⁽¹⁾ | | [Rectangle](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/rect.ts) | 2D rectangle | ✅ | | [Sphere](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/sphere.ts) | 3D sphere | ✅⁽¹⁾ | | [Text](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/text.ts) | Basic stub for text labels | ✅⁽³⁾ | | [Triangle](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/triangle.ts) | 2D triangle | ✅ | | [Triangle3](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom/src/triangle3.ts) | 3D triangle | ✅⁽¹⁾ | - ⁽¹⁾ valid hiccup format, but currently still missing **external** tool/library support - ⁽²⁾ only lines, cubic & quadratic curve segments supported - ⁽³⁾ merely treated as a point in space (e.g. used for placing text labels), no geometry of text itself ### Hiccup support > [!NOTE] > Sidebar with background information for advanced usage only. Most users can safely ignore this. With very few exceptions these all are implementing the [`IToHiccup` interface](https://docs.thi.ng/umbrella/api/interfaces/IToHiccup.html) and so can be easily converted (via [hiccup](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/hiccup)) to a variety of other formats, incl. [conversion to SVG](#svg-support). By design, for more flexibility and for performance reasons, the hiccup flavor used by this package is **not** compatible with that used by [thi.ng/hiccup-svg](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/hiccup-svg), though the latter provides a [`convertTree()`](https://docs.thi.ng/umbrella/hiccup-svg/functions/convertTree.html) function for that purpose. This is only needed for some cases of dynamic in-browser SVG DOM creation... Instead, the hiccup format used here for interim interop is compatible with that used by the [thi.ng/hiccup-canvas](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/hiccup-canvas) package (see its readme for details) and avoids extraneous stringification of geometry data and attrib values. A brief example to illustrate some differences: ```ts tangle:export/readme-hiccup.ts import { circle, asSvg } from "@thi.ng/geom"; import { convertTree } from "@thi.ng/hiccup-svg"; // a circle with RGBA color attrib const a = circle([100, 200], 300, { fill: [1, 0.5, 0, 1] }); // invocation of the IToHiccup interface (all shapes support it) console.log(a.toHiccup()); // [ "circle", { fill: [ 1, 0, 0, 1 ] }, [ 100, 200 ], 300 ] // convert shape into to a SVG compatible hiccup format // (i.e. stringify attributes, convert colors etc.) console.log(convertTree(a)); // [ "circle", { fill: "#ff8000", cx: "100", cy: "200", r: "300" } ] // asSvg() automatically uses convertTree() when serializing shape(s) to SVG console.log(asSvg(a)); // ``` ### SVG support For 2D shape types only, SVG conversion is included via the [`asSvg()`](https://docs.thi.ng/umbrella/geom/functions/asSvg.html) and [`svgDoc()`](https://docs.thi.ng/umbrella/geom/functions/svgDoc.html) functions. ### Polymorphic operations The following operations are provided (many also applicable to shape groups directly and/or perform automatic resampling/conversion if needed). | Operation | Description | |-----------------------------------------------------------------------------------------------------|--------------------------------------------------------------------| | [`applyTransforms()`](https://docs.thi.ng/umbrella/geom/functions/applyTransforms.html) | applies any spatial transformation attributes | | [`arcLength()`](https://docs.thi.ng/umbrella/geom/functions/arcLength.html) | compute arc length / perimeter of shape boundary | | [`area()`](https://docs.thi.ng/umbrella/geom/functions/area.html) | signed/unsigned surface area | | [`asCubic()`](https://docs.thi.ng/umbrella/geom/functions/asCubic.html) | convert shape boundary to cubic bezier segments | | [`asPath()`](https://docs.thi.ng/umbrella/geom/functions/asPath.html) | convert shape to path | | [`asPolygon()`](https://docs.thi.ng/umbrella/geom/functions/asPolygon.html) | convert shape to polygon(s) | | [`asPolyline()`](https://docs.thi.ng/umbrella/geom/functions/asPolyline.html) | convert shape to polyline(s) | | [`asSector()`](https://docs.thi.ng/umbrella/geom/functions/asSector.html) | convert arc to sector (path) | | [`asSvg()`](https://docs.thi.ng/umbrella/geom/functions/asSvg.html) | serialize shape/group/hierarchy to SVG | | [`bounds()`](https://docs.thi.ng/umbrella/geom/functions/bounds.html) | compute bounding box | | [`center()`](https://docs.thi.ng/umbrella/geom/functions/center.html) | center shape around origin or point | | [`centroid()`](https://docs.thi.ng/umbrella/geom/functions/centroid.html) | compute shape centroid | | [`classifyPoint()`](https://docs.thi.ng/umbrella/geom/functions/classifyPoint.html) | classify point in relation to shape boundary (in/out) | | [`clipConvex()`](https://docs.thi.ng/umbrella/geom/functions/clipConvex.html) | clip shape against convex boundary | | [`closestPoint()`](https://docs.thi.ng/umbrella/geom/functions/closestPoint.html) | compute closest point on shape boundary | | [`convexHull()`](https://docs.thi.ng/umbrella/geom/functions/convexHull.html) | compute convex hull (2d only) | | [`convolve()`](https://docs.thi.ng/umbrella/geom/functions/convolve.html) | kernel based vertex convolution/filtering | | [`edges()`](https://docs.thi.ng/umbrella/geom/functions/edges.html) | extract edges | | [`edgesFromTessellation()`](https://docs.thi.ng/umbrella/geom/functions/edgesFromTessellation.html) | extract unique edges from tessellation results | | [`fitIntoBounds2()`](https://docs.thi.ng/umbrella/geom/functions/fitIntoBounds2.html) | rescale/reposition a 2D shape into a destination boundary | | [`fitIntoBounds3()`](https://docs.thi.ng/umbrella/geom/functions/fitIntoBounds3.html) | rescale/reposition a 3D shape into a destination boundary | | [`fitAllIntoBounds2()`](https://docs.thi.ng/umbrella/geom/functions/fitAllIntoBounds2.html) | rescale/reposition multiple 2D shapes into a boundary | | [`flip()`](https://docs.thi.ng/umbrella/geom/functions/flip.html) | reverse order (vertices or direction) | | [`graphFromTessellation()`](https://docs.thi.ng/umbrella/geom/functions/graphFromTessellation.html) | create graph from tessellation results | | [`intersects()`](https://docs.thi.ng/umbrella/geom/functions/intersects.html) | pairwise shape intersection (various types) | | [`mapPoint()`](https://docs.thi.ng/umbrella/geom/functions/mapPoint.html) | transform world space point into local shape UV space | | [`offset()`](https://docs.thi.ng/umbrella/geom/functions/offset.html) | shape/path offsetting | | [`pointAt()`](https://docs.thi.ng/umbrella/geom/functions/pointAt.html) | compute point on shape boundary at parametric position | | [`pointInside()`](https://docs.thi.ng/umbrella/geom/functions/pointInside.html) | check if point is inside shape | | [`proximity()`](https://docs.thi.ng/umbrella/geom/functions/proximity.html) | distance from point to shape boundary | | [`resample()`](https://docs.thi.ng/umbrella/geom/functions/resample.html) | resample/convert shape | | [`rotate()`](https://docs.thi.ng/umbrella/geom/functions/rotate.html) | rotate shape (2D only) | | [`rotateAroundAxis()`](https://docs.thi.ng/umbrella/geom/functions/rotateAroundAxis.html) | rotate shape (3D only) | | [`rotateX()`](https://docs.thi.ng/umbrella/geom/functions/rotateX.html) | rotate shape (3D only) | | [`rotateY()`](https://docs.thi.ng/umbrella/geom/functions/rotateY.html) | rotate shape (3D only) | | [`rotateZ()`](https://docs.thi.ng/umbrella/geom/functions/rotateZ.html) | rotate shape (3D only) | | [`scale()`](https://docs.thi.ng/umbrella/geom/functions/scale.html) | scale shape (uniformly/non-uniformly) | | [`scaleWithCenter()`](https://docs.thi.ng/umbrella/geom/functions/scaleWithCenter.html) | scale shape with pivot point | | [`scatter()`](https://docs.thi.ng/umbrella/geom/functions/scatter.html) | create random points inside a shape boundary | | [`simplify()`](https://docs.thi.ng/umbrella/geom/functions/simplify.html) | simplify shape/boundary (Douglas-Peucker) | | [`splitArcLength()`](https://docs.thi.ng/umbrella/geom/functions/splitArcLength.html) | split shapes & groups based on max. arc length | | [`splitAt()`](https://docs.thi.ng/umbrella/geom/functions/splitAt.html) | split shape/boundary at parametric position | | [`splitNearPoint()`](https://docs.thi.ng/umbrella/geom/functions/splitNearPoint.html) | split shape/boundary near world position | | [`subdivCurve()`](https://docs.thi.ng/umbrella/geom/functions/subdivCurve.html) | recursively apply curve subdivision kernel | | [`tangentAt()`](https://docs.thi.ng/umbrella/geom/functions/tangentAt.html) | compute tangent at parametric position | | [`tessellate()`](https://docs.thi.ng/umbrella/geom/functions/tessellate.html) | (recursively) tessellate shape | | [`transformVertices()`](https://docs.thi.ng/umbrella/geom/functions/transformVertices.html) | apply custom function to each vertex | | [`transform()`](https://docs.thi.ng/umbrella/geom/functions/transform.html) | apply transformation matrix | | [`translate()`](https://docs.thi.ng/umbrella/geom/functions/translate.html) | translate shape | | [`union()`](https://docs.thi.ng/umbrella/geom/functions/union.html) | compute shape union | | [`unmapPoint()`](https://docs.thi.ng/umbrella/geom/functions/unmapPoint.html) | transform local shape UV point into world space | | [`vertices()`](https://docs.thi.ng/umbrella/geom/functions/vertices.html) | extract/sample vertices from shape boundary | | [`volume()`](https://docs.thi.ng/umbrella/geom/functions/volume.html) | compute shape volume (3D only) | | [`warpPoint()`](https://docs.thi.ng/umbrella/geom/functions/warpPoint.html) | transfer single point between the local spaces defined by 2 shapes | | [`warpPoints()`](https://docs.thi.ng/umbrella/geom/functions/warpPoints.html) | transfer points between the local spaces defined by 2 shapes | | [`warpPointsBPatch()`](https://docs.thi.ng/umbrella/geom/functions/warpPointsBPatch.html) | transfer points to the local spaces of a bezier patch | | [`withAttribs()`](https://docs.thi.ng/umbrella/geom/functions/withAttribs.html) | shallow copy of given shape with new `attribs` assigned | ### Shape factory functions In addition to the [above listed direct shape type functions](#shape-types), the following additional shape creation helpers are provided: #### AABB - [aabbFromMinMax()](https://docs.thi.ng/umbrella/geom/functions/aabbFromMinMax.html) - [aabbFromMinMaxWithMargin()](https://docs.thi.ng/umbrella/geom/functions/aabbFromMinMaxWithMargin.html) - [aabbFromCentroid()](https://docs.thi.ng/umbrella/geom/functions/aabbFromCentroid.html) - [aabbWithCentroidAndMargin()](https://docs.thi.ng/umbrella/geom/functions/aabbWithCentroidAndMargin.html) - [intersectionAABB()](https://docs.thi.ng/umbrella/geom/functions/intersectionAABB.html) - [inscribedAABB()](https://docs.thi.ng/umbrella/geom/functions/inscribedAABB.html) #### Arc - [arcFrom2Points()](https://docs.thi.ng/umbrella/geom/functions/arcFrom2Points.html) #### Bezier patch - [bpatchFromQuad()](https://docs.thi.ng/umbrella/geom/functions/bpatchFromQuad.html) - [bpatchFromHex()](https://docs.thi.ng/umbrella/geom/functions/bpatchFromHex.html) #### Circle - [circleFrom2Points()](https://docs.thi.ng/umbrella/geom/functions/circleFrom2Points.html) - [circleFrom3Points()](https://docs.thi.ng/umbrella/geom/functions/circleFrom3Points.html) - [invertCircle()](https://docs.thi.ng/umbrella/geom/functions/invertCircle.html) - [invertCirclePoint()](https://docs.thi.ng/umbrella/geom/functions/invertCirclePoint.html) #### Cubic - [cubicFromArc()](https://docs.thi.ng/umbrella/geom/functions/cubicFromArc.html) - [cubicFromLine()](https://docs.thi.ng/umbrella/geom/functions/cubicFromLine.html) - [cubicFromLine3()](https://docs.thi.ng/umbrella/geom/functions/cubicFromLine3.html) - [cubicFromQuadratic()](https://docs.thi.ng/umbrella/geom/functions/cubicFromQuadratic.html) - [cubicFromQuadratic3()](https://docs.thi.ng/umbrella/geom/functions/cubicFromQuadratic3.html) #### Group - [groupFromTessellation()](https://docs.thi.ng/umbrella/geom/functions/groupFromTessellation.html) #### Line - [clippedLine()](https://docs.thi.ng/umbrella/geom/functions/clippedLine.html) #### Path - [pathBuilder()](https://docs.thi.ng/umbrella/geom/functions/pathBuilder-1.html) - [pathBuilder3()](https://docs.thi.ng/umbrella/geom/functions/pathBuilder3.html) - [pathFromSvg()](https://docs.thi.ng/umbrella/geom/functions/pathFromSvg.html) - [pathFromCubics()](https://docs.thi.ng/umbrella/geom/functions/pathFromCubics.html) - [normalizedPath()](https://docs.thi.ng/umbrella/geom/functions/normalizedPath.html) - [roundedRect()](https://docs.thi.ng/umbrella/geom/functions/roundedRect.html) #### Plane - [planeWithPoint()](https://docs.thi.ng/umbrella/geom/functions/planeWithPoint.html) - [planeFrom3Points()](https://docs.thi.ng/umbrella/geom/functions/planeFrom3Points.html) - [planeFromRay()](https://docs.thi.ng/umbrella/geom/functions/planeFromRay.html) #### Polygon - [smoothPolygon()](https://docs.thi.ng/umbrella/geom/functions/smoothPolygon.html) - [star()](https://docs.thi.ng/umbrella/geom/functions/star.html) - [starWithCentroid()](https://docs.thi.ng/umbrella/geom/functions/starWithCentroid.html) #### Polyline - [smoothPolyline()](https://docs.thi.ng/umbrella/geom/functions/smoothPolyline.html) - [spiral()](https://docs.thi.ng/umbrella/geom/functions/spiral.html) #### Quad - [quadOnPlane()](https://docs.thi.ng/umbrella/geom/functions/quadOnPlane.html) #### Rect - [rectFromMinMax()](https://docs.thi.ng/umbrella/geom/functions/rectFromMinMax.html) - [rectFromMinMaxWithMargin()](https://docs.thi.ng/umbrella/geom/functions/rectFromMinMaxWithMargin.html) - [rectWithCentroid()](https://docs.thi.ng/umbrella/geom/functions/rectWithCentroid.html) - [rectWithCentroidAndMargin()](https://docs.thi.ng/umbrella/geom/functions/rectWithCentroidAndMargin.html) - [intersectionRect()](https://docs.thi.ng/umbrella/geom/functions/intersectionRect.html) - [inscribedSquare()](https://docs.thi.ng/umbrella/geom/functions/inscribedSquare.html) - [inscribedSquareHex()](https://docs.thi.ng/umbrella/geom/functions/inscribedSquareHex.html) #### Sphere - [sphereFrom2Points()](https://docs.thi.ng/umbrella/geom/functions/sphereFrom2Points.html) #### Triangle - [equilateralTriangle()](https://docs.thi.ng/umbrella/geom/functions/equilateralTriangle.html) ### Constants & presets Some of the shape operations require configuration with specific algorithms and/or constants. In all cases this relies on a completely extensible mechanism, but the package provides presets for common options/implementations: #### Curve subdivision kernels To be used with [`subdivideCurve()`](https://docs.thi.ng/umbrella/geom/functions/subdivCurve.html): - [SUBDIV_CHAIKIN](https://docs.thi.ng/umbrella/geom/variables/SUBDIV_CHAIKIN.html) - [SUBDIV_CUBIC](https://docs.thi.ng/umbrella/geom/variables/SUBDIV_CUBIC.html) - [SUBDIV_DISPLACE](https://docs.thi.ng/umbrella/geom/functions/SUBDIV_DISPLACE.html) - [SUBDIV_DLG](https://docs.thi.ng/umbrella/geom/variables/SUBDIV_DLG.html) - [SUBDIV_MID](https://docs.thi.ng/umbrella/geom/variables/SUBDIV_MID.html) - [SUBDIV_THIRDS](https://docs.thi.ng/umbrella/geom/variables/SUBDIV_THIRDS.html) #### Polygon tessellation algorithms To be used with [`tessellate()`](https://docs.thi.ng/umbrella/geom/functions/tessellate.html): See [thi.ng/geom-tessellate readme](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-tessellate/README.md#tessellators) for diagrams/illustrations of each algorithm! - [TESSELLATE_EARCUT](https://docs.thi.ng/umbrella/geom/functions/TESSELLATE_EARCUT.html) - [TESSELLATE_EARCUT_COMPLEX](https://docs.thi.ng/umbrella/geom/functions/TESSELLATE_EARCUT_COMPLEX.html) - [TESSELLATE_EDGE_SPLIT](https://docs.thi.ng/umbrella/geom/functions/TESSELLATE_EDGE_SPLIT.html) - [TESSELLATE_INSET](https://docs.thi.ng/umbrella/geom/functions/TESSELLATE_INSET.html) - [TESSELLATE_QUAD_FAN](https://docs.thi.ng/umbrella/geom/functions/TESSELLATE_QUAD_FAN.html) - [TESSELLATE_RIM_TRIS](https://docs.thi.ng/umbrella/geom/functions/TESSELLATE_RIM_TRIS.html) - [TESSELLATE_TRI_FAN](https://docs.thi.ng/umbrella/geom/functions/TESSELLATE_TRI_FAN.html) - [TESSELLATE_TRI_FAN_BOUNDARY](https://docs.thi.ng/umbrella/geom/functions/TESSELLATE_TRI_FAN_BOUNDARY.html) - [TESSELLATE_TRI_FAN_SPLIT](https://docs.thi.ng/umbrella/geom/functions/TESSELLATE_TRI_FAN_SPLIT.html) Tessellation behaviors: - [basicTessellation()](https://docs.thi.ng/umbrella/geom/functions/basicTessellation.html): default impl - [meshTessellation()](https://docs.thi.ng/umbrella/geom/functions/meshTessellation.html): uses kD-tree to deduplicate result points Tessellation post-processing: - [edgesFromTessellation()](https://docs.thi.ng/umbrella/geom/functions/edgesFromTessellation.html) - [edgePointsFromTessellation()](https://docs.thi.ng/umbrella/geom/functions/edgePointsFromTessellation.html) - [graphFromTessellation()](https://docs.thi.ng/umbrella/geom/functions/graphFromTessellation.html) - [groupFromTessellation()](https://docs.thi.ng/umbrella/geom/functions/groupFromTessellation.html) #### Vertex convolution kernels To be used with [`convolve()`](https://docs.thi.ng/umbrella/geom/functions/convolve.html): - [KERNEL_BOX](https://docs.thi.ng/umbrella/geom/functions/KERNEL_BOX.html) - [KERNEL_GAUSSIAN](https://docs.thi.ng/umbrella/geom/functions/KERNEL_GAUSSIAN.html) - [KERNEL_TRIANGLE](https://docs.thi.ng/umbrella/geom/functions/KERNEL_TRIANGLE.html) --- This package acts as a higher-level frontend for most of the following related packages (which are more low-level, lightweight and usable by themselves too): ## Support packages - [@thi.ng/geom-accel](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-accel) - n-D spatial indexing data structures with a shared ES6 Map/Set-like API - [@thi.ng/geom-arc](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-arc) - 2D circular / elliptic arc operations - [@thi.ng/geom-axidraw](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-axidraw) - Conversion and preparation of thi.ng/geom shapes & shape groups to/from AxiDraw pen plotter draw commands - [@thi.ng/geom-clip-line](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-clip-line) - 2D line clipping (Liang-Barsky) - [@thi.ng/geom-clip-poly](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-clip-poly) - 2D polygon clipping / offsetting (Sutherland-Hodgeman, Grainer-Hormann) - [@thi.ng/geom-closest-point](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-closest-point) - 2D / 3D closest point / proximity helpers - [@thi.ng/geom-fuzz](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-fuzz) - Highly configurable, fuzzy line & polygon creation with presets and composable fill & stroke styles. Canvas & SVG support - [@thi.ng/geom-hull](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-hull) - Fast 2D convex hull (Graham Scan) - [@thi.ng/geom-io-obj](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-io-obj) - Wavefront OBJ parser (& exporter soon) - [@thi.ng/geom-isec](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-isec) - 2D/3D shape intersection checks - [@thi.ng/geom-isoline](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-isoline) - Fast 2D contour line extraction / generation - [@thi.ng/geom-poly-utils](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-poly-utils) - 2D polygon/polyline analysis & processing utilities - [@thi.ng/geom-resample](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-resample) - Customizable nD polyline interpolation, re-sampling, splitting & nearest point computation - [@thi.ng/geom-sdf](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-sdf) - 2D Signed Distance Field creation from [@thi.ng/geom](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom) shapes, conversions, sampling, combinators - [@thi.ng/geom-splines](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-splines) - nD cubic & quadratic curve analysis, conversion, interpolation, splitting - [@thi.ng/geom-subdiv-curve](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-subdiv-curve) - Freely customizable, iterative nD subdivision curves for open / closed geometries - [@thi.ng/geom-tessellate](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-tessellate) - 2D/3D convex polygon tessellators - [@thi.ng/geom-trace-bitmap](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-trace-bitmap) - Bitmap image to hairline vector and point cloud conversions - [@thi.ng/geom-voronoi](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-voronoi) - Fast, incremental 2D Delaunay & Voronoi mesh implementation - [@thi.ng/geom-webgl](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-webgl) - WebGL geometry/shape conversion & interop ## Related packages - [@thi.ng/axidraw](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/axidraw) - Minimal AxiDraw plotter/drawing machine controller for Node.js - [@thi.ng/color](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/color) - Array-based color types, CSS parsing, conversions, transformations, declarative theme generation, gradients, presets - [@thi.ng/hiccup](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/hiccup) - HTML/SVG/XML serialization of nested data structures, iterables & closures - [@thi.ng/hiccup-canvas](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/hiccup-canvas) - Hiccup shape tree renderer for vanilla Canvas 2D contexts - [@thi.ng/hiccup-svg](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/hiccup-svg) - SVG element functions for [@thi.ng/hiccup](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/hiccup) & related tooling - [@thi.ng/viz](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/viz) - Declarative, functional & multi-format data visualization toolkit based around [@thi.ng/hiccup](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/hiccup) - [@thi.ng/webgl](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/webgl) - WebGL & GLSL abstraction layer ## Status **STABLE** - used in production [Search or submit any issues for this package](https://codeberg.org/thi.ng/umbrella/issues?q=%5Bgeom%5D) ## Installation ```bash yarn add @thi.ng/geom ``` ESM import: ```ts import * as geom from "@thi.ng/geom"; ``` Browser ESM import: ```html ``` [JSDelivr documentation](https://www.jsdelivr.com/) For Node.js REPL: ```js const geom = await import("@thi.ng/geom"); ``` Package sizes (brotli'd, pre-treeshake): ESM: 17.61 KB ## Dependencies - [@thi.ng/adjacency](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/adjacency) - [@thi.ng/api](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/api) - [@thi.ng/arrays](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/arrays) - [@thi.ng/checks](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/checks) - [@thi.ng/defmulti](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/defmulti) - [@thi.ng/equiv](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/equiv) - [@thi.ng/errors](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/errors) - [@thi.ng/geom-arc](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-arc) - [@thi.ng/geom-clip-line](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-clip-line) - [@thi.ng/geom-clip-poly](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-clip-poly) - [@thi.ng/geom-closest-point](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-closest-point) - [@thi.ng/geom-hull](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-hull) - [@thi.ng/geom-isec](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-isec) - [@thi.ng/geom-poly-utils](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-poly-utils) - [@thi.ng/geom-resample](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-resample) - [@thi.ng/geom-splines](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-splines) - [@thi.ng/geom-subdiv-curve](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-subdiv-curve) - [@thi.ng/geom-tessellate](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/geom-tessellate) - [@thi.ng/hiccup](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/hiccup) - [@thi.ng/hiccup-svg](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/hiccup-svg) - [@thi.ng/math](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/math) - [@thi.ng/matrices](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/matrices) - [@thi.ng/object-utils](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/object-utils) - [@thi.ng/random](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/random) - [@thi.ng/strings](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/strings) - [@thi.ng/transducers](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/transducers) - [@thi.ng/vectors](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/vectors) Note: @thi.ng/api is in _most_ cases a type-only import (not used at runtime) ## Usage examples 40 projects in this repo's [/examples](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples) directory are using this package: | Screenshot | Description | Live demo | Source | |:------------------------------------------------------------------------------------------------------------------------------|:---------------------------------------------------------------------------------|:-------------------------------------------------------------|:--------------------------------------------------------------------------------------------------| | | Basic 2D boid simulation and spatial indexing neighbor lookups | [Demo](https://demo.thi.ng/umbrella/boid-basics/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/boid-basics) | | | Parametrically design calibration sheet for B&W photography | [Demo](https://demo.thi.ng/umbrella/calibration-sheet/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/calibration-sheet) | | | Self-modifying, animated typographic grid with emergent complex patterns | [Demo](https://demo.thi.ng/umbrella/canvas-recorder/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/canvas-recorder) | | | Fiber-based cooperative multitasking basics | [Demo](https://demo.thi.ng/umbrella/fiber-basics/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/fiber-basics) | | | Polygon point classification (inside/boundary/outside) | [Demo](https://demo.thi.ng/umbrella/geom-classify-point/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-classify-point) | | | Shape conversions & operations using polygons with holes | [Demo](https://demo.thi.ng/umbrella/geom-complex-poly/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-complex-poly) | | | Convex hull & shape clipping of 2D polygons | [Demo](https://demo.thi.ng/umbrella/geom-convex-hull/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-convex-hull) | | | Piechart visualization of CSV data | [Demo](https://demo.thi.ng/umbrella/geom-csv-piechart/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-csv-piechart) | | | Embedding thi.ng/hiccup data/elements in thi.ng/geom shape hierarchies | [Demo](https://demo.thi.ng/umbrella/geom-extra-hiccup/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-extra-hiccup) | | | geom-fuzz basic shape & fill examples | [Demo](https://demo.thi.ng/umbrella/geom-fuzz-basics/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-fuzz-basics) | | | Hex grid generation & tessellations | [Demo](https://demo.thi.ng/umbrella/geom-hexgrid/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-hexgrid) | | | (Re)Constructing the thi.ng logo using a 2D signed-distance field | [Demo](https://demo.thi.ng/umbrella/geom-sdf-logo/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-sdf-logo) | | | SVG path to SDF, applying deformation and converting back to SVG | [Demo](https://demo.thi.ng/umbrella/geom-sdf-path/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-sdf-path) | | | 2.5D hidden line visualization of digital elevation files (DEM) | [Demo](https://demo.thi.ng/umbrella/geom-terrain-viz/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-terrain-viz) | | | Animated, recursive polygon tessellations | [Demo](https://demo.thi.ng/umbrella/geom-tessel/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-tessel) | | | Iterating the unique edges of a tessellation | [Demo](https://demo.thi.ng/umbrella/geom-unique-edges/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-unique-edges) | | | Poisson-disk shape-aware sampling, Voronoi & Minimum Spanning Tree visualization | [Demo](https://demo.thi.ng/umbrella/geom-voronoi-mst/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-voronoi-mst) | | | Augmenting thi.ng/geom shapes for WebGL, using instancing & attribute buffers | [Demo](https://demo.thi.ng/umbrella/geom-webgl-attrib-pool/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-webgl-attrib-pool) | | | Converting thi.ng/geom shape types for WebGL | [Demo](https://demo.thi.ng/umbrella/geom-webgl-basics/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/geom-webgl-basics) | | | Mouse gesture / stroke analysis, simplification, corner detection | [Demo](https://demo.thi.ng/umbrella/gesture-analysis/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/gesture-analysis) | | | 2D Bezier curve-guided particle system | [Demo](https://demo.thi.ng/umbrella/hdom-canvas-particles/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/hdom-canvas-particles) | | | Animated arcs & drawing using hiccup-canvas | [Demo](https://demo.thi.ng/umbrella/hiccup-canvas-arcs/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/hiccup-canvas-arcs) | | | Canvas based Immediate Mode GUI components | [Demo](https://demo.thi.ng/umbrella/imgui/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/imgui) | | | Animated sine plasma effect visualized using contour lines | [Demo](https://demo.thi.ng/umbrella/iso-plasma/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/iso-plasma) | | | k-means clustering visualization | [Demo](https://demo.thi.ng/umbrella/kmeans-viz/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/kmeans-viz) | | | Live coding playground for 2D geometry generation using @thi.ng/pointfree-lang | [Demo](https://demo.thi.ng/umbrella/pointfree-geom/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/pointfree-geom) | | | 2D Poisson-disc sampler with procedural gradient map | [Demo](https://demo.thi.ng/umbrella/poisson-circles/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/poisson-circles) | | | Polygon to cubic curve conversion & visualization | [Demo](https://demo.thi.ng/umbrella/poly-spline/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/poly-spline) | | | Animated, iterative polygon subdivisions & visualization | [Demo](https://demo.thi.ng/umbrella/poly-subdiv/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/poly-subdiv) | | | Quasi-random lattice generator | [Demo](https://demo.thi.ng/umbrella/quasi-lattice/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/quasi-lattice) | | | Minimal rdom-canvas animation | [Demo](https://demo.thi.ng/umbrella/rdom-canvas-basics/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/rdom-canvas-basics) | | | Animated Voronoi diagram, cubic splines & SVG download | [Demo](https://demo.thi.ng/umbrella/rotating-voronoi/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/rotating-voronoi) | | | 2D scenegraph & shape picking | [Demo](https://demo.thi.ng/umbrella/scenegraph/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/scenegraph) | | | 2D scenegraph & image map based geometry manipulation | [Demo](https://demo.thi.ng/umbrella/scenegraph-image/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/scenegraph-image) | | | Basic 2D scenegraph example with pan/zoom functionality | [Demo](https://demo.thi.ng/umbrella/scenegraph-pan-zoom/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/scenegraph-pan-zoom) | | | Compute cubic spline position & tangent using Dual Numbers | [Demo](https://demo.thi.ng/umbrella/spline-tangent/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/spline-tangent) | | | SVG path parsing & dynamic resampling | [Demo](https://demo.thi.ng/umbrella/svg-resample/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/svg-resample) | | | 3D wireframe textmode demo | [Demo](https://demo.thi.ng/umbrella/text-canvas/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/text-canvas) | | | Multi-layer vectorization & dithering of bitmap images | [Demo](https://demo.thi.ng/umbrella/trace-bitmap/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/trace-bitmap) | | | Animated t-SNE visualization of 4D data | [Demo](https://demo.thi.ng/umbrella/tsne-colors/) | [Source](https://codeberg.org/thi.ng/umbrella/src/branch/develop/examples/tsne-colors) | ## API [Generated API docs](https://docs.thi.ng/umbrella/geom/) ## Authors - [Karsten Schmidt](https://thi.ng) If this project contributes to an academic publication, please cite it as: ```bibtex @misc{thing-geom, title = "@thi.ng/geom", author = "Karsten Schmidt", note = "https://thi.ng/geom", year = 2013 } ``` ## License © 2013 - 2026 Karsten Schmidt // Apache License 2.0