svg_path

svg_path is a utility for parsing, serializing, inspecting, and performing simple geometric manipulations on SVG paths and transforms.

The package tries to provide a flexible API for the construction of valid SVG paths from imperfectly matching segments.

gleam add svg_path@0

import svg_path/parse
import svg_path/serialize

pub fn tidy_path_data(input: String) -> String {
  let assert Ok(path) = parse.path(input)

  serialize.path(path)
}

Typical workflows compose parsing, path editing, transforms, conversion, and serialization:

import gleam/result
import svg_path
import svg_path/parse
import svg_path/serialize
import svg_path/transform

pub fn prepare_for_arc_averse_consumer(
  input: String,
) -> Result(String, parse.Error) {
  use path <- result.try(parse.path(input))

  let assert Ok(path) =
    path
    |> transform.scale_path(factor: 2.0)

  path
  |> svg_path.path_arcs_to_cubic_beziers
  |> serialize.path
  |> Ok
}

Core Model

The root svg_path module models SVG path data with four main types: Point, Segment, Subpath, and Path.

Points

A Point is borrowed from the vec package:

pub type Point =
  Vec2(Float)

Use svg_path.point to create points without importing vec directly:

svg_path.point(10.0, 20.0)

Segments

A Segment is one drawing instruction with explicit start and end points. These are the public segment variants:

svg_path.Line(start:, end:)
svg_path.QuadraticBezier(start:, control:, end:)
svg_path.CubicBezier(start:, control1:, control2:, end:)
svg_path.Arc(start:, radius:, x_axis_rotation:, large_arc:, sweep:, end:)

The lower-case helper functions construct the same values with ordinary function-call syntax:

svg_path.line(start:, end:)
svg_path.quadratic_bezier(start:, control:, end:)
svg_path.cubic_bezier(start:, control1:, control2:, end:)
svg_path.arc(start:, radius:, x_axis_rotation:, large_arc:, sweep:, end:)

Segments can be evaluated and split by their local parameter t, where 0.0 is the segment start and 1.0 is the segment end:

svg_path.segment_point(segment, at: 0.5)
svg_path.segment_derivative(segment, at: 0.5)
svg_path.split_segment(segment, at: 0.5)

These helpers work for lines, quadratic Beziers, cubic Beziers, and arcs. Values outside 0.0..1.0 extrapolate along the same segment. Use split_segment_inside when outside values should return an error instead.

Subpaths

A Subpath is a continuous list of segments plus a closed/open flag. Its constructor is opaque; internally, the type is shaped like this:

pub opaque type Subpath {
  Subpath(segments: List(Segment), closed: Bool)
}

The segments list must be continuous: every segment after the first must start at the previous segment's end point. The closed field records whether the subpath is topologically closed. A closed subpath must end where it starts, which is an invariant that the library maintains by keeping the type opaque, but a geometrically closed path need not be closed. The serialization of a Subpath ends in Z (or z if relative motions are used) if and only if closed is True.

Use svg_path.subpath to construct an open subpath from a list of already continuous segments, and svg_path.set_closed to change whether a subpath is topologically closed:

svg_path.subpath(segments)
svg_path.set_closed(subpath, closed: Bool)

Construction succeeds when the segment endpoints meet. In this example, the segments return to their starting point geometrically, but the subpath becomes topologically closed only after set_closed:

import gleam/result
import svg_path

pub fn closed_triangle() -> Result(svg_path.Subpath, svg_path.Error) {
  let a = svg_path.point(0.0, 0.0)
  let b = svg_path.point(10.0, 0.0)
  let c = svg_path.point(5.0, 10.0)

  use subpath <- result.try(svg_path.subpath([
    svg_path.line(start: a, end: b),
    svg_path.line(start: b, end: c),
    svg_path.line(start: c, end: a),
  ]))

  svg_path.set_closed(subpath, closed: True)
  // Ok(subpath)
}

Construction returns an error when the segment endpoints do not meet. Closing a subpath with set_closed(subpath, closed: True) can fail for the same reason if the final segment endpoint does not meet the first segment start point:

import svg_path

pub fn discontinuous_corner() -> Result(svg_path.Subpath, svg_path.Error) {
  let a = svg_path.point(0.0, 0.0)
  let b = svg_path.point(10.0, 0.0)
  let c = svg_path.point(10.0, 10.0)
  let d = svg_path.point(20.0, 10.0)

  svg_path.subpath([
    svg_path.line(start: a, end: b),
    svg_path.line(start: c, end: d),
  ])
  // Error(...)
}

Paths

A Path is a list of Subpath values:

pub type Path {
  Path(subpaths: List(Subpath))
}

You can use the public constructor directly, or the helper function with the same shape:

svg_path.Path(subpaths: [subpath])
svg_path.path([subpath])

A Path may consist of an empty list of subpaths, and an open Subpath may consist of an empty list of segments, which is intentional. Empty paths and empty open subpaths serialize to the empty string. A closed Subpath with no segments is impossible to construct.

Use path_start and path_end to get the endpoints of a full path. Empty subpaths are ignored; EmptyPath is returned for Path([]), and EmptySubpaths is returned when a path has subpaths but none contain segments:

svg_path.path_start(path)
svg_path.path_end(path)

Matching Endpoints

Helper functions in the root module let users employ an EndpointPolicy option to specify different types of error-recovery behavior for non-matching endpoints:

svg_path.Strict
svg_path.Wiggle
svg_path.Bridge
svg_path.WiggleThenBridge

Strict requires exact endpoint equality. Wiggle moves nearby endpoints together within the package's default wiggle tolerance of 0.000000001, while preserving horizontal and vertical straight-line segments. Bridge keeps existing endpoints in place and inserts a straight line segment when needed. WiggleThenBridge, as the name implies, first tries Wiggle before falling back on Bridge.

The behavior of option-free functions and constructors is EndpointPolicy.Strict. These include:

svg_path.subpath(segments)
svg_path.append_segment(subpath, segment)
svg_path.join([first_subpath, second_subpath])
svg_path.splice(subpath, start:, delete:, insert:)
svg_path.set_closed(subpath, closed: Bool)

These functions preserve Segment lists exactly while returning a Discontinuous error payload when segment endpoints fail to match up by exact floating point equality. The Discontinuous error payload names the index at which discontinuity occurs as well as the position and distance between the endpoints involved:

Discontinuous(
  previous_index: Int,
  next_index: Int,
  expected: Point,
  got: Point,
  distance: Float,
)

This is often enough to tell whether upstream geometry missed by floating-point noise or by a real modeling mistake.

The _with variants of constructor and subpath-modifying functions enable the specification of a non-Strict endpoint policy:

svg_path.subpath_with(segments, policy: svg_path.Wiggle)
svg_path.append_segment_with(subpath, segment, policy: svg_path.Bridge)
svg_path.join_with([first_subpath, second_subpath], policy: svg_path.WiggleThenBridge)
svg_path.splice_with(subpath, start:, delete:, insert:, policy: svg_path.Wiggle)
svg_path.set_closed_with(subpath, closed: Bool, policy: svg_path.Bridge)

Use the assert_ functions for hand-authored/static geometry where invalid continuity is a programmer error:

svg_path.assert_subpath(segments)
svg_path.assert_append_segment(subpath, segment)
svg_path.assert_join([first_subpath, second_subpath])
svg_path.assert_join_with([first_subpath, second_subpath], policy: svg_path.WiggleThenBridge)
svg_path.assert_splice(subpath, start:, delete:, insert:)
svg_path.assert_set_closed(subpath, closed: Bool)

Joining Subpaths

join combines open subpaths into one open subpath. With the default Strict policy, each subpath's end point must exactly equal the next subpath's start point. Empty open subpaths act as identity values, and join([]) returns an empty open subpath.

svg_path.join([first_subpath, second_subpath, third_subpath])

Closed subpaths are rejected rather than implicitly opened. This keeps closedness as explicit topology: if you want to discard it, use set_closed(subpath, closed: False) first.

Use join_with when you want another endpoint policy:

svg_path.join_with([first_subpath, second_subpath], policy: svg_path.Wiggle)
svg_path.join_with([first_subpath, second_subpath], policy: svg_path.Bridge)

Splicing Subpaths

splice replaces a range of segments while preserving the subpath invariant. start is a zero-based segment index, delete is the number of segments to remove, and insert is the replacement list.

svg_path.splice(subpath, start: 2, delete: 1, insert: replacement_segments)

If start + delete extends past the end of the subpath, everything from start onward is deleted. Negative start, negative delete, and start greater than the subpath length return InvalidSplice.

With the default Strict policy, the edited subpath must still be continuous, otherwise Discontinuous is returned with segment indices, points, and distance. Closed subpaths preserve their closed state; a splice that would turn a closed subpath into an empty subpath returns ClosedEmptySubpath.

Use splice_with when the splice should use a different endpoint policy:

svg_path.splice_with(
  subpath,
  start: 2,
  delete: 1,
  insert: replacement_segments,
  policy: svg_path.Wiggle,
)

Converting Arcs to Beziers

Some SVG consumers and geometry workflows prefer to avoid elliptical Arc segments. Use the _arcs_to_cubic_beziers function family to replace arcs with cubic Bezier curves while preserving lines, quadratic Beziers, and existing cubic Beziers:

svg_path.segment_arcs_to_cubic_beziers(segment)
svg_path.subpath_arcs_to_cubic_beziers(subpath)
svg_path.path_arcs_to_cubic_beziers(path)

Elliptical arcs are approximated with one or more cubic Beziers, split into chunks of at most a quarter turn. The conversion preserves subpath closed/open state. If an arc is degenerate, it falls back to the straight-line cubic Bezier between the arc endpoints.

There is no tolerance option for this conversion. The approximation policy is deterministic: each arc chunk spans no more than 90 degrees. This is the common practical SVG arc-to-cubic approximation and is usually more than adequate for rendering and interchange.

If you want every segment represented as cubic Bezier curves, use the stricter helpers instead. Lines and quadratic Beziers are converted exactly.

svg_path.segment_to_cubic_beziers(segment)
svg_path.subpath_to_cubic_beziers(subpath)
svg_path.path_to_cubic_beziers(path)

Geometry Helpers

The root module provides a few geometry helpers that work directly with the Segment, Subpath, and Path model.

Bounding Boxes

Use segment_bounding_box, subpath_bounding_box, and path_bounding_box to compute exact axis-aligned bounding boxes:

import svg_path

pub fn box_path(path: svg_path.Path) -> Result(svg_path.BoundingBox, svg_path.Error) {
  svg_path.path_bounding_box(path)
}

Line, quadratic Bezier, cubic Bezier, and arc extrema are included. Empty subpaths return EmptySubpath; empty paths return EmptyPath; paths whose subpaths are all empty return EmptySubpaths.

For callers working at the lower-level curve modules, svg_path/bezier exposes bezier_bounding_box, and svg_path/ellipse exposes arc_bounding_box.

Segment Crossings

Use segment_crossings to find parameter values where a scalar predicate changes sign along a segment:

import svg_path

pub fn horizontal_crossings(
  segment: svg_path.Segment,
  y: Float,
) -> Result(List(Float), svg_path.Error) {
  svg_path.segment_crossings(segment, where: fn(point) {
    point.y -. y
  })
}

The returned values are segment parameters in 0.0..1.0. You can pass them to segment_point or split_segment.

Crossing detection is numerical and sampling-based. It finds sign-change crossings visible at the configured sampling resolution, plus endpoint/sample values that are already close to zero. It does not promise tangent roots or multiple crossings hidden inside one sample window. Use segment_crossings_with and CrossingOptions to tune samples, tolerance, and max_iterations.

The scalar solver behind this lives in svg_path/root.gleam as a small self-contained bisection helper for bracketed Float -> Float functions.

Parsing

svg_path/parse accepts normal SVG path data syntax, including:

comma separators
whitespace separators
compact signed numbers such as M0-1
implicit line commands after M
repeated command argument groups
relative and absolute commands
closepath commands Z and z

import gleam/result
import svg_path/parse
import svg_path/serialize

pub fn canonicalize() -> Result(String, parse.Error) {
  use path <- result.try(parse.path("M0,0 10,10z"))

  Ok(serialize.path(path))
}

The parsed object is not just a token stream. It is normalized into this package's path model. For example, an implicit line after M becomes a Line segment internally.

Closepath is also represented semantically. If parsing Z needs a straight line back to the subpath start, the parser inserts that line and marks the subpath closed. If the subpath is already back at its start, no extra line is inserted; the subpath is just marked closed.

Path Serialization

svg_path/serialize emits canonical SVG path data.

By default it uses:

absolute commands
up to 5 decimal places
stripped trailing decimal zeroes
readable whitespace
repeated command letters
H and V for horizontal and vertical lines when possible
Z for closed subpaths

import svg_path/parse
import svg_path/serialize

pub fn tidy_path_data(input: String) -> String {
  let assert Ok(path) = parse.path(input)

  serialize.path(path)
}

Serialization options can use relative commands, remove optional whitespace, round numbers, keep fixed decimal places, and omit repeated command letters.

import svg_path/parse
import svg_path/serialize

pub fn compact_path_data(input: String) -> String {
  let assert Ok(path) = parse.path(input)
  let options =
    serialize.relative_decimal_options(2)
    |> serialize.minimize_whitespace
    |> serialize.repeat_commands(False)

  serialize.path_with_options(path, options:)
}

Repeated Command Letters

SVG allows repeated commands of the same type to omit later command letters. Pass False to repeat_commands to use this form.

serialize.default_options()
|> serialize.repeat_commands(False)

For example, repeated line commands may serialize as:

M 0 0 L 10 10 20 20 30 30

instead of:

M 0 0 L 10 10 L 20 20 L 30 30

Closepath and Final Lines

Closed subpaths serialize with Z.

If a closed subpath ends with a non-zero-length straight line back to the subpath start, the serializer drops that final line command and uses Z to represent the closure.

For example, this internal subpath:

Line(0,0 -> 10,0)
Line(10,0 -> 10,20)
Line(10,20 -> 0,0)
closed

serializes as:

M 0 0 H 10 V 20 Z

not:

M 0 0 H 10 V 20 L 0 0 Z

This is intentional. Z is the SVG-native representation of closing the subpath, and including both the final straight line and Z would be redundant.

Zero-length final lines are different. If the final segment is Line(A, A), the serializer keeps it visible:

M 0 0 H 0 Z

This is also intentional. A zero-length line is often evidence of unusual upstream geometry. The serializer does not hide that from the user.

The same rule applies in relative mode:

m 10 10 h 10 h -10 h 0 Z

The final h 0 remains visible because it is a zero-length line.

Cleaning Zero-Length Lines

Serialization is not a general cleanup pass. It only uses Z to avoid a redundant non-zero-length final closing line.

If you want to remove zero-length straight lines from a subpath, use clean_subpath.

import svg_path

pub fn clean(subpath: svg_path.Subpath) -> svg_path.Subpath {
  svg_path.clean_subpath(subpath)
}

clean_subpath removes zero-length Line segments while preserving the subpath's closed/open state. If a subpath consists only of zero-length lines, one zero-length line is retained so the subpath does not become empty.

This distinction is deliberate:

serialize.subpath preserves odd zero-length lines so the output still shows that the object contains them.
svg_path.clean_subpath is an explicit user-requested cleanup.

Transforming Paths

svg_path/transform applies SVG-style affine transforms to segments, subpaths, and paths.

import svg_path/parse
import svg_path/serialize
import svg_path/transform

pub fn move_path_data(input: String) -> String {
  let assert Ok(path) = parse.path(input)
  let matrix = transform.translate(x: 10.0, y: 20.0)
  let assert Ok(path) = transform.path(path, by: matrix)

  serialize.path(path)
}

Transforms use the SVG six-value affine matrix:

matrix(a b c d e f)

which corresponds to:

x' = a*x + c*y + e
y' = b*x + d*y + f

Matrix values can be constructed and inspected as tuples:

import svg_path/transform

pub fn inspect_transform() -> #(Float, Float, Float, Float, Float, Float) {
  transform.rotate(degrees: 30.0)
  |> transform.to_tuple
}

Use chain(first:, then:) when thinking in application order. Use multiply(left:, right:) when thinking in matrix multiplication order.

import svg_path/transform

pub fn scale_then_move() -> transform.Matrix {
  let scale = transform.scale(factor: 2.0)
  let move = transform.translate(x: 10.0, y: 20.0)

  // Applying scale, then move, is move * scale.
  transform.chain(first: scale, then: move)
  // transform.multiply(left: move, right: scale)
}

Transform Attributes

SVG transform attributes can be parsed and serialized separately from paths.

import svg_path/transform/parse
import svg_path/transform/serialize

pub fn tidy_transform_attribute(input: String) -> String {
  let assert Ok(matrix) = parse.attribute(input)

  serialize.to_string(matrix)
}

The transform parser accepts normal SVG transform syntax, including compound attributes such as:

translate(10)scale(2) skewX(3)

Transform serialization prefers readable SVG forms when the matrix can be recognized clearly:

translate(10 20)
translate(10 20)scale(2)
rotate(30)
translate(10 20)rotate(30)scale(2 3)

If no clearer representation is available, it falls back to:

matrix(a b c d e f)

Use force_matrix when you want the raw matrix form even if a shorter transform expression could be detected.

import svg_path/transform
import svg_path/transform/serialize

pub fn raw_transform_attribute() -> String {
  transform.translate(x: 10.0, y: 20.0)
  |> serialize.to_string_with_options(
    options: serialize.default_options() |> serialize.force_matrix,
  )
}

Inspecting Paths

svg_path/inspect prints path data structures for debugging and tests. It is not the SVG d serializer.

Human-readable structural inspection:

import svg_path
import svg_path/inspect

pub fn inspect_line() -> String {
  svg_path.line(
    start: svg_path.point(0.0, 0.0),
    end: svg_path.point(12.0, 10.0),
  )
  |> inspect.segment
}

Example output:

Line(start=0,0 end=12,10)

Copy-pasteable Gleam inspection:

import svg_path
import svg_path/inspect

pub fn inspect_code(path: svg_path.Path) -> String {
  inspect.path_code(path)
}

Example output:

svg_path.path([
  svg_path.assert_subpath([
    svg_path.line(start: svg_path.point(0.0, 0.0), end: svg_path.point(12.0, 10.0))
  ])
])

Inspection options support decimal rounding, fixed decimal places, and left-padding for visual alignment.

import svg_path
import svg_path/inspect

pub fn inspect_aligned(path: svg_path.Path) -> String {
  let options =
    inspect.fixed_decimal_options(1)
    |> inspect.with_left_padding(inspect.AutoLeftPadding)

  inspect.path_code_with_options(path, options:)
}

AutoLeftPadding pre-scans the value being inspected and chooses a shared left-side width for the numbers in that output. LeftPadding(Int) lets you choose the width yourself. NoLeftPadding disables it.

Converting Matrices From `matrix_gleam`

svg_path does not depend on matrix_gleam, but the tuple helpers make the conversion small if your application uses both packages.

import matrix/mat3f
import svg_path/transform

pub fn to_mat3f(matrix: transform.Matrix) -> mat3f.Mat3f {
  let #(a, b, c, d, e, f) = transform.to_tuple(matrix)

  mat3f.new(
    a, b, 0.0,
    c, d, 0.0,
    e, f, 1.0,
  )
}

import matrix/mat3f
import svg_path/transform

pub type MatrixConversionError {
  NonAffineMatrix
}

pub fn from_mat3f(
  matrix: mat3f.Mat3f,
) -> Result(transform.Matrix, MatrixConversionError) {
  case matrix.x.z == 0.0 && matrix.y.z == 0.0 && matrix.z.z == 1.0 {
    False -> Error(NonAffineMatrix)
    True -> {
      Ok(transform.from_tuple(#(
        matrix.x.x,
        matrix.x.y,
        matrix.y.x,
        matrix.y.y,
        matrix.z.x,
        matrix.z.y,
      )))
    }
  }
}

Further documentation can be found at https://hexdocs.pm/svg_path.

Development

gleam test
gleam docs build

svg_path

Core Model

Points

Segments

Subpaths

Paths

Matching Endpoints

Joining Subpaths

Splicing Subpaths

Converting Arcs to Beziers

Geometry Helpers

Bounding Boxes

Segment Crossings

Parsing

Path Serialization

Repeated Command Letters

Closepath and Final Lines

Cleaning Zero-Length Lines

Transforming Paths

Transform Attributes

Inspecting Paths

Converting Matrices From matrix_gleam

Development

Converting Matrices From `matrix_gleam`