Voronoï playground : interactive weighted Voronoï study II

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Voronoï playground : interactive weighted Voronoï study II

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Last edited Dec 3, 2018

Created on Mar 2, 2017

This interactive visualization explores the 2D additive weighted power diagram, showing how two draggable sites partition a rectangular area into concave cells whose borders shift as sliders adjust each site’s weight. The diagram is computed via a convex hull algorithm (ConvexHull.js, PowerDiagram.js) that lifts sites to a paraboloid, with the resulting polygons clipped using a Sutherland–Hodgman implementation from d3-polygon-clip. Rendered in SVG with D3 v4, the display updates live, and circles around each site scale with the square root of the weight to visualize its influence.

AI-generated description

This block experiments weighted Voronoï diagram, and is a continuation of a previous block. Weighted Voronoï diagram comes in severall flavours (additive/multiplicative, powered/not-powered, 2D/3D and highier dimensions, ...), but this block focuses on the 2D additive weighted power diagram, which provides a tessellation made of concave polygons/cells with straight borders, as the default Voronoï diagram does.

What are you seeing ?

there is 2 sites (one blue and one green), with their corresponding influence areas (i.e. cells)
if weights are big enough, circles around sites give a sense of the weight of each site

User interactions :

you can change the weight of each site with the corresponding slider
you can drag and drop each site

Code details :

Code essentially comes from <a href='http://bl.ocks.org/mkedwards/'>mkedwards</a>'s block: <a href='http://bl.ocks.org/mkedwards/759e719eefe36cf9c8ab'>Treemap</a>, which is an implementation of the technique describe in Computing Voronoi Treemaps : Faster, Simpler, and Resolution-independent. I extracted the code which produces the power diagram, and updated it for D3v4:

reuse ConvexHull.js,
reuse PowerDiagram.js,
remove VoronoiTreemap.js,
remove VoronoiTreemapD3.js,
remove Vertex's percentage,
dummy bounding sites related to clipping polygon (ie. available area), instead of depending on extremes sites
in linearDependant function, bug fix p1.x==0 || p2.x==0 (insteaf of p1.x==0 || p1.x==0)
add epsilonesque function
rename GraphEdge as ConflictListNode

Furthermore, as d3 v4 no longer provides polygon clipping, code for polygon clipping comes from <a href='http://bl.ocks.org/mbostock/'>mbostock</a>'s block: <a href='https://bl.ocks.org/mbostock/ece50c027bdf8cc20003a17d93e4f60e'>Polygon Clipping III</a>, which he introduces as 'a trivial port of Sutherland–Hodgman clipping from v3'.

For a more up-to-date version of the code, please refer to the [Weighted Voronoi Treemap in D3v4] (https://bl.ocks.org/kcnarf/15d54f4ccae6a3710cd3029546664eec) block.

Acknowledgments to:

<a href='https://d3js.org/'>D3.js</a> (v.4)
<a href='http://blockbuilder.org'>blockbuilder.org</a>
<a href='http://bl.ocks.org/mkedwards/'>mkedwards</a>'s block: <a href='http://bl.ocks.org/mkedwards/759e719eefe36cf9c8ab'>Treemap</a>

gpl-3.0 Licensed

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