Overview

Parametric Voronoi generator with real time editing and SVG export

Live demo

Chrome is tested as web browser, Edge might work but Firefox might show white page only

• https://voronoi-editor.web.app/
• https://websvg.github.io/voronoi/

Discussions

get support, give feedback or simply chat to brainstorm about new ideas

https://github.com/WebSVG/voronoi/discussions

3D Printed Voronoi Shapes

Photos and 3D Models available

https://www.homesmartmesh.com/3dprinting/voronoi-shapes/

User Guide

Overview

• Generate Diagram
• Edit cells
• Export SVG

We see above the user generating new sets of seeds with their resulting voronoi diagram, hiding and viewing seeds, cells and edges, changing the number of seeds with a slider while the view updates in real time, editing the cells by moving them, removing and adding cells, changing the cells shape to quadratic bezier, simple edges and back to cubic bezier, finally adjusting the space between cells before exporting in an SVG file.

Export seeds coordinates

The seeds coordinates are what allows to generate again the same voronoig diagram

• seeds can be exported as a json text file containing each seed coordinate
• the seeds.json can be imported by drag and drop on the view area
• it is possible therefore to share seeds structures and continue working on a seeds set at any point in time

cells retraction

• The cells are not scaled down, their edges are rather retracted in parallel to their original location.
• When retracting cells as a consequence some edges could become irrelevant and the shape might decrese in edges number.

• Below is another example where we see in debug mode the translated edges and the discarded one is red

cubic bezier minimum edge size

• goal is to filter small edge to avoid sharp bezier curves
• the quadratic bezier only has one control point, so using the center of the removed edge would still break the tangency alignment with the previous curve
• clean way would require ignoring the corresponding site completely and extend the left edges till the small edge is nullified, thus reducing the total number of sides of the cell
• therfore, in order to keep shapes tangent to the sides, min edge ignore is only implemented in quadratic bezier.

Shaped tesselation area

step 1 : sampling

the shape is approximated with a set of linear interpolation points along the path

step 2 : cells isolation

the naive (and not so nice) way

    <defs>
        <clipPath id="cut-off-cells">
            <path xmlns="http://www.w3.org/2000/svg" d=${path} fill="#991155" fill-opacity="0.9"></path>
        </clipPath>
    </defs>

this applies an svg mask, with the SVG clipPath function, it would result in this

• First issue, Fusion360 as example does not support clipPath
• Second issue, the cut is very sharp and breaks the bezier shape of the cells

the nicer way

Note : the higher the number of samples per seed, the more the cells will allign the shape's path

Before explaining how this works, let's inspect that the voronoi cells are natually alligned along the custom path we provided as input

Below is the revealed secret. There are seeds actually being sampled outside the path area for the sole purpose of giving support to the inside cells not to expand till the external frame. Also important that the cells are not just simply randomly sampled inside and outside the area, they are rather avoiding the path with a distance cost factor, that prevents cells from cutting the edges to a certain extent.

Seeds sampling cost map

• drag and drop a png file on the editor's window
• run sampling with preferrably a high sample count (~100 or more)

In all sampling variants, the seeds do have the neighbors distance as cost minimzation factor. Using a shape's path, the cost add up to avoid the path with a distance. Here, a png image gray scale is used as a cost map that is weighted with the neighbors distance.

In the animation below, after dropping a spiral cost map, the Map Cost Vs Dist slider is moved from 5 to 20 to concentrate the cells in the darker areas.

SVG Path Shaped area and png seeds cost map

Filters : Displacement with Turbulence

warning ! The svg filters effect, though part of the standard and viewable in browsers are not always supported by CAD programs such as Fusion360 !

Features details

• Generate Voronoi Diagram

• Export to SVG file

• Shaped Tesselation area with an SVG path

• Cost map for Seeds sampling from a png file

  seeds

• Edit seeds : add, move, remove

• Export and import seeds (drag and drop seeds.json) and continue editing of an existing seeds set

  • seeds contain window size info since 26.04.2020, prio formats with seeds array only have to have window size adjust manually before import

• Parametric Seeds generation

  • Controlled seeds spread regularity with multiple sampling and keeping best candidate (farthest from neighbors)
  • Optionally include distance from walls to the sampling selection cost

• Range slider with interactive update for adding and removing seeds to and out of existing set

• rearrange seeds when modifying window size

• Shaped tesselation area

  • sampling points inside an SVG path with document.elementFromPoint(x, y);

• Concentration cost map for seeds sampling

  cells

• different cells types

  • bezier quadratic
  • bezier cubic
  • simple geometric edges

• cells edges retraction. Not cells scale but edges parallel rertraction with handling of closed edges discard

• Shaped tesselation area

  • display of cells which seeds are within an SVG path
  • the option is available to simply cut cells with an SVG mask

  gui

• grid based, responsive svg and menu areas

• Show/hide (cells, edges, seeds) and independently configure the SVG export

• Browser local storage of config parameters (No storage of SVG nor seeds as they can be saved separately)

• SVG filters for displacement and turbulence, but note that they can only be seen on the browser and they're not supported by tools such as Fusion360

• display of width and height with unit ratio

  • transform scale possible but Fusion360 ignores the scale transform

  cost map

• display / hide cost map

• slider to weight cost map vs distance

Planned features

• edges cells filet effect
• add irregularities to the edges thickness (randomize retraction)
• improve error alerts by using boostrap auto vanishing alerts
• random colors for cells

discarded features

• export scale with a ratio (adjusting to a given unit)

  • feature brings an ambiguous usage as svg is supposed to be scalable and should not require a fixed scale
  • extremely difficult, due to dependency to shape input that is svg and which size has to match, could be exported
  • cost map is png with pixel units, so would also deviate from map view
  • simple svg scale function not recognised by Fusion360
  • modifying seeds coordinates to deviate them far away from pixels values might result in floating precision errors, resulting in unhandled voronoi cases
  • could have been possible to copy all of the cells, edges structures and scale them one by one before export
  • as a workaround, provided view with ratio unit

• detract quadratic bezier short edges

  • cells retraction "Space between cells" is providing a good enough short edges removal, combined with space though. It is hard to differentiate the effect of both, and it would break the Voronoi equalities

• edit seed weight to modify cells size (? requires a new engine, or use cells retraction technique) (editing singe seed weight,cartographic seeds weight)

  • Would break the voronoi intuitive equality, and requires a new engine. Also wuold require the user to tweak each cell separately. The cost map is a good solution how to achieve the last point (cartographic seeds weight), as the cells size is a one to one match to the seeds dispertion.

License

MIT

Issues

https://github.com/WebSVG/voronoi/issues

Dependencies

node dependencies are not required to serve the project locally, but only to reference the used dependencies

Vornoi js Library

• 'gorhill' Javascript Voronoi library
  • github repo
  • live demo
  • used rhill-voronoi-core.js from commit 3fe2165
  • modified for ES2015 module import

Vector module from matter.js

• modified ./node_modules/matter-js/src/geometry/Vector.js for ES2015 module import

bootstrap

• https://getbootstrap.com/docs/4.4/getting-started/introduction/
• https://gitbrent.github.io/bootstrap4-toggle/
• issue with bootstrap toggle adding event listeners with js not possible

Export / Download

• Filesaver

  npm install file-saver --save
  [email protected]

• to be replaced with 'a' download attribute : https://www.w3schools.com/tags/att_a_download.asp

References

• 'stg' voronoi SVG vectorisation :
  • also baed on gorhill's library
  • github stg repo
  • forked added live demo
• http://alexbeutel.com/webgl/voronoi.html
• http://cfbrasz.github.io/VoronoiColoring.html
• https://www.jasondavies.com/maps/voronoi/
• wikipedia - lines intersection

• Bezier curves https://pomax.github.io/bezierinfo/
• Closest point on path approximation : https://bl.ocks.org/mbostock/8027637
• https://docs.w3cub.com/svg/
• SVG Displacement map