2D triangulation library. Allows translating lines and polygons (both based on points) to the language of GPUs.

Overview


triangolatte

2D triangulation library. Allows translating lines and polygons (both based on points) to the language of GPUs.

Features normal and miter joint line triangulation. Handles polygons using ear clipping algorithm with hole elimination included.

screenshot

For reference: triangulates 99.76% of 75 thousand buildings in Cracow under 3.43s on average programmer notebook (single threaded).

Table of contents

Installation

Nothing surprising

go get github.com/tchayen/triangolatte

Usage

Basic example

vertices := []Point{{10, 20}, {30, 40}, {50, 60}}
t, err = triangolatte.Polygon(vertices)

Examples

In /examples you can find:

  • buildings – full-blown WebGL previewer of buildings triangulated in city example
  • city – triangulation of whole city downloaded from Open Street Map
  • gpx – GPX format parsing and triangulation of its data
  • wireframe – desktop OpenGL wireframe previewer for triangulated shapes

You will find instructions for running the code there.

Features

API

Polygon(points []Point, holes [][]Point) ([]float64, error)

Takes array of points and produces array of triangle coordinates.

Based on the following paper and inspired by EarCut.

JoinHoles(points [][]Point) ([]Point, error)

Removes holes, joining them with the rest of the polygon. Provides preprocessing for Polygon. First element of the points array is the outer polygon, the rest of them are considered as holes to be removed.

Line(joint Joint, points []Point, width int) ([]float64, error)

Takes array of points and triangulates them to resemble a line of given width. Returns array of two-coordinate CCW triangles one after another.

Types

To select method of joining line segments.

type Joint int

const (
	// No joint correction.
	Normal Joint = 0
	// Producing miter joints, i.e. extending the lines until they meet at some point.
	Miter Joint = 1
)

For calculations using points.

type Point struct {
  X, Y float64
}

A wrapper for Point used in cyclic list.

type Element struct {
	Prev, Next *Element
	Point      Point
}

Helpers

You can have a look at helpers.go file. It stores triangolatte's helper functions used mostly by tests and examples. They are not exported because I don't want to commit to supporting them in the future, but they might turn out useful for you.

Tests

Code is (more or less) covered in tests. You can run them like this:

go test -v

You can also run benchmarks for selected functions (refer to the *_test.go files for availability). For example:

go test -run NONE -bench IsInsideTriangle

Benchmarks

NOTE: This section contains work in progress. Numbers below are better reference point than nothing, but still far from perfect.

Polygon() on shape with 10 vertices takes 754ns on average.

Triangulation of 75 thousand buildings runs for around 3.43s.

Using average programmer's notebook. Expect speed up on faster CPUs or while splitting execution into separate threads.

Flame Graphs

CPU time % usage snaphost using Flame Graphs:

assets/torch.svg

Want to learn what is it or maybe you are willing to generate one yourself? Check FlameGraphs document in this repository.

Future plans

Optimizations

NOTE: this library is developed mostly with map data triangulation in mind and it will be its main performance target.

  • explore possibilities for optimizations in JoinHoles(...)
  • maybe allow reusing point array for massive allocation reduction

Content

  • provide more examples (e.g. desktop OpenGL usage, mobile app, live rendering pipeline, other unusual use cases...)
  • add benchmarks with comparison to libraries in other languages

WebAssembly

One of the core plans for this library's development is creating, as soon as it becomes possible, some kind of WebAssembly module for use in JS.

Contributing

You are welcome to create an issue or pull request if you've got an idea what to do. It is usually a good idea to visit Gitter and discuss your thoughts.

Don't have one, but still want to contribute? Get in touch with us and we can brainstorm some ideas.

License

MIT License – refer to the LICENSE file.

Comments
  • Triangulation error

    Triangulation error

    I was looking into using this library for a small side project but I am currently running into an error.

    This is a reproducible unit test:

    func TestTriangulationError(t *testing.T) {
    	vertices := []triangolatte.Point{
    		{X: 512.00, Y: 30.00},
    		{X: 512.00, Y: 145.04},
    		{X: 596.96, Y: 145.04},
    		{X: 596.96, Y: 85.05},
    		{X: 636.96, Y: 85.05},
    		{X: 636.96, Y: 30.00},
    		{X: 512.00, Y: 30.00},
    	}
    
    	_, err := triangolatte.Polygon(vertices)
    	if err != nil {
    		t.Fatal(err)
    	}
    }
    
    === RUN   TestTriangulationError
    --- FAIL: TestTriangulationError (0.00s)
        shape_test.go:22: oops
    FAIL
    
    Process finished with exit code 1
    

    I have no experience with doing polygon triangulation so maybe I am doing something stupid? What resources would you recommend to learn more about the algorithm in detail?

    opened by fgrosse 3
  • Bump dns-packet from 1.3.1 to 1.3.4 in /examples/buildings

    Bump dns-packet from 1.3.1 to 1.3.4 in /examples/buildings

    Bumps dns-packet from 1.3.1 to 1.3.4.

    Commits

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  • Bump hosted-git-info from 2.7.1 to 2.8.9 in /examples/buildings

    Bump hosted-git-info from 2.7.1 to 2.8.9 in /examples/buildings

    Bumps hosted-git-info from 2.7.1 to 2.8.9.

    Changelog

    Sourced from hosted-git-info's changelog.

    2.8.9 (2021-04-07)

    Bug Fixes

    2.8.8 (2020-02-29)

    Bug Fixes

    • #61 & #65 addressing issues w/ url.URL implmentation which regressed node 6 support (5038b18), closes #66

    2.8.7 (2020-02-26)

    Bug Fixes

    • Do not attempt to use url.URL when unavailable (2d0bb66), closes #61 #62
    • Do not pass scp-style URLs to the WhatWG url.URL (f2cdfcf), closes #60

    2.8.6 (2020-02-25)

    2.8.5 (2019-10-07)

    Bug Fixes

    • updated pathmatch for gitlab (e8325b5), closes #51
    • updated pathmatch for gitlab (ffe056f)

    2.8.4 (2019-08-12)

    ... (truncated)

    Commits
    • 8d4b369 chore(release): 2.8.9
    • 29adfe5 fix: backport regex fix from #76
    • afeaefd chore(release): 2.8.8
    • 5038b18 fix: #61 & #65 addressing issues w/ url.URL implmentation which regressed nod...
    • 7440afa chore(release): 2.8.7
    • 2d0bb66 fix: Do not attempt to use url.URL when unavailable
    • f2cdfcf fix: Do not pass scp-style URLs to the WhatWG url.URL
    • e1b83df chore(release): 2.8.6
    • ff259a6 Ensure passwords in hosted Git URLs are correctly escaped
    • 624fd6f chore(release): 2.8.5
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  • Bump lodash from 4.17.20 to 4.17.21 in /examples/buildings

    Bump lodash from 4.17.20 to 4.17.21 in /examples/buildings

    Bumps lodash from 4.17.20 to 4.17.21.

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    • c4847eb Improve performance of toNumber, trim and trimEnd on large input strings
    • 3469357 Prevent command injection through _.template's variable option
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  • Bump ua-parser-js from 0.7.18 to 0.7.28 in /examples/buildings

    Bump ua-parser-js from 0.7.18 to 0.7.28 in /examples/buildings

    Bumps ua-parser-js from 0.7.18 to 0.7.28.

    Commits
    • 1d3c98a Revert breaking fix #279 and release as 0.7.28
    • 535f11b Delete redundant code
    • 642c039 Fix #492 LG TV WebOS detection
    • 3edacdd Merge branch 'master' into develop
    • acc0b91 Update contributor list
    • f726dcd Merge branch 'master' into develop
    • 383ca58 More test for tablet devices
    • 7c8aa43 Minor rearrangement
    • 09aa910 Add new device & browser: Tesla
    • 557cc21 More test for latest phones with unique form factor (fold/flip/qwerty/swivel)
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  • Bump yargs-parser from 5.0.0 to 5.0.1 in /examples/buildings

    Bump yargs-parser from 5.0.0 to 5.0.1 in /examples/buildings

    Bumps yargs-parser from 5.0.0 to 5.0.1.

    Release notes

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    yargs-parser v5.0.1

    Bug Fixes

    • security: address GHSA-p9pc-299p-vxgp (#362) (1c417bd)
    Changelog

    Sourced from yargs-parser's changelog.

    5.0.0 (2017-02-18)

    Bug Fixes

    • environment variables should take precedence over config file (#81) (76cee1f)

    BREAKING CHANGES

    • environment variables will now override config files (args, env, config-file, config-object)

    5.0.1 (2021-03-10)

    Bug Fixes

    • security: address GHSA-p9pc-299p-vxgp (#362) (1c417bd)

    4.2.1 (2017-01-02)

    Bug Fixes

    4.2.0 (2016-12-01)

    Bug Fixes

    • inner objects in configs had their keys appended to top-level key when dot-notation was disabled (#72) (0b1b5f9)

    Features

    • allow multiple arrays to be provided, rather than always combining (#71) (0f0fb2d)

    4.1.0 (2016-11-07)

    ... (truncated)

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  • Bump y18n from 3.2.1 to 3.2.2 in /examples/buildings

    Bump y18n from 3.2.1 to 3.2.2 in /examples/buildings

    Bumps y18n from 3.2.1 to 3.2.2.

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  • Bump ini from 1.3.5 to 1.3.7 in /examples/buildings

    Bump ini from 1.3.5 to 1.3.7 in /examples/buildings

    Bumps ini from 1.3.5 to 1.3.7.

    Commits
    • c74c8af 1.3.7
    • 024b8b5 update deps, add linting
    • 032fbaf Use Object.create(null) to avoid default object property hazards
    • 2da9039 1.3.6
    • cfea636 better git push script, before publish instead of after
    • 56d2805 do not allow invalid hazardous string as section name
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    This version was pushed to npm by isaacs, a new releaser for ini since your current version.


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  • Bump http-proxy from 1.17.0 to 1.18.1 in /examples/buildings

    Bump http-proxy from 1.17.0 to 1.18.1 in /examples/buildings

    Bumps http-proxy from 1.17.0 to 1.18.1.

    Changelog

    Sourced from http-proxy's changelog.

    v1.18.1 - 2020-05-17

    Merged

    1.18.0 - 2019-09-18

    Merged

    Commits

    • [dist] New test fixtures. 7e4a0e5
    • [dist] End of an era. a9b09cc
    • [dist] Version bump. 1.18.0 9bbe486
    • [fix] Latest versions. 59c4403
    • [fix test] Update tests. dd1d08b
    • [dist] Update dependency ws to v3 [SECURITY] b00911c
    • [dist] .gitattributes all the things. fc93520
    • [dist] Regenerate package-lock.json. 16d4f8a
    Commits
    • 9b96cd7 1.18.1
    • 335aeeb Skip sending the proxyReq event when the expect header is present (#1447)
    • dba3966 Remove node6 support, add node12 to build (#1397)
    • 9bbe486 [dist] Version bump. 1.18.0
    • 6e4bef4 Added in auto-changelog module set to keepachangelog format (#1373)
    • d056241 fix 'Modify Response' readme section to avoid unnecessary array copying (#1300)
    • 244303b Fix incorrect target name for reverse proxy example (#1135)
    • b4028ba Fix modify response middleware example (#1139)
    • 77a9815 [dist] Update dependency async to v3 (#1359)
    • c662f9e Fix path to local http-proxy in examples. (#1072)
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  • Bump node-sass from 4.9.2 to 4.13.1 in /examples/buildings

    Bump node-sass from 4.9.2 to 4.13.1 in /examples/buildings

    Bumps node-sass from 4.9.2 to 4.13.1.

    Release notes

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    v4.13.1

    Community

    Supported Environments

    OS Architecture Node
    Windows x86 & x64 0.10, 0.12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
    OSX x64 0.10, 0.12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
    Linux* x86 & x64 0.10, 0.12, 1, 2, 3, 4, 5, 6, 7, 8**, 9**, 10**^, 11**^, 12**^, 13**^
    Alpine Linux x64 6, 8, 10, 11, 12, 13
    FreeBSD i386 amd64 8, 10, 12, 13

    *Linux support refers to Ubuntu, Debian, and CentOS 5+ ** Not available on CentOS 5 ^ Only available on x64

    v4.13.0

    Features

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    Supported Environments

    OS Architecture Node
    Windows x86 & x64 0.10, 0.12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
    OSX x64 0.10, 0.12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
    Linux* x86 & x64 0.10, 0.12, 1, 2, 3, 4, 5, 6, 7, 8**, 9**, 10**^, 11**^, 12**^, 13**^
    Alpine Linux x64 6, 8, 10, 11, 12, 13
    FreeBSD i386 amd64 6, 8, 10, 12, 13

    *Linux support refers to Ubuntu, Debian, and CentOS 5+

    Changelog

    Sourced from node-sass's changelog.

    v4.13.1

    https://github.com/sass/node-sass/releases/tag/v4.13.1

    v4.13.0

    https://github.com/sass/node-sass/releases/tag/v4.13.0

    v4.12.0

    https://github.com/sass/node-sass/releases/tag/v4.12.0

    v4.11.0

    https://github.com/sass/node-sass/releases/tag/v4.11.0

    v4.10.0

    https://github.com/sass/node-sass/releases/tag/v4.10.0

    v4.9.4

    https://github.com/sass/node-sass/releases/tag/v4.9.4

    v4.9.3

    https://github.com/sass/node-sass/releases/tag/v4.9.3

    Commits

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    dependencies 
    opened by dependabot[bot] 1
  • Bump elliptic from 6.4.0 to 6.5.3 in /examples/buildings

    Bump elliptic from 6.4.0 to 6.5.3 in /examples/buildings

    Bumps elliptic from 6.4.0 to 6.5.3.

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    dependencies 
    opened by dependabot[bot] 1
  • Bump url-parse from 1.4.7 to 1.5.1 in /examples/buildings

    Bump url-parse from 1.4.7 to 1.5.1 in /examples/buildings

    Bumps url-parse from 1.4.7 to 1.5.1.

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    dependencies 
    opened by dependabot[bot] 1
  • Bump elliptic from 6.5.3 to 6.5.4 in /examples/buildings

    Bump elliptic from 6.5.3 to 6.5.4 in /examples/buildings

    Bumps elliptic from 6.5.3 to 6.5.4.

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    dependencies 
    opened by dependabot[bot] 1
  • Ear cutting may terminate too early?

    Ear cutting may terminate too early?

    Thank you for creating this helpful library! I have just started playing around with it and may have come across a bug. As I'm just coming to grips with it I would appreciate another set of eyes

    Here is a reproducing example:

    outer = []triangolatte.Point{
        {0.0, 0.0},
        {-10.0, 0.0},
        {-10.0, -10.0},
        {0.0, -10.0},
    }
    
    hole = []triangolatte.Point{
        {-1.8813725490196056, -4.059803921568627},
        {-3.663725490196078, -2.0794117647058803},
        {-2.1784313725490176, -3.465686274509803},
        {-2.0794117647058803, -3.5647058823529405},
    }
    
    poly, err := triangolatte.JoinHoles([][]triangolatte.Point{outer, hole})
    if err != nil {
        panic(fmt.Sprintf("JoinHoles failed: %s", err))
    }
    
    fmt.Println("Poly is", poly)
    _, err = triangolatte.Polygon(poly)
    if err != nil {
        panic(fmt.Sprintf("Polygon failed: %s", err))
    }
    

    The above will fail to triangulate the resulting polygon. In my opinion this is because it terminates too early. This proposed change fixes the example above:

    diff --git a/polygon.go b/polygon.go
    index 1c3fe48..825813c 100644
    --- a/polygon.go
    +++ b/polygon.go
    @@ -292,7 +292,7 @@ func Polygon(points []Point) ([]float64, error) {
    
                            ear.Remove()
                            ear = ear.Next
    -                       stop = stop.Next
    +                       stop = ear
                            continue
                    }
    

    With the fix applied it does, however, still fail to triangulate the more complete polygon from which I created the above example. The original polygon I was trying to triangulate is reproduced in this gist

    Sadly the original example is quite large and I don't have good insights where it fails. I did find that tripy manages to triangulate the original polygon.

    I would appreciate any insights on where things break.

    opened by danieltwagner 1
Owner
Tomasz Czajęcki
React (Native) dev. SECCLO @AaltoUniversity. He/him.
Tomasz Czajęcki
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