example code that works (at least in one test case):

var c = projection.lobes().map(d => d3.merge(d.map(q => {
  var centroid = d3.geoCentroid({type:"MultiPoint", coordinates:q});
  return q.map(p => d3.geoInterpolate(p,centroid)(1e-7)); // pull inside each lobe
})));
c = d3.merge([c[0], c[1].reverse()]); // north, south
projection.preclip(d3.geoClipPolygon({ type: "Polygon", coordinates: [c] }));

    var lobes = [
      [
        [[-180, 0], [-130, 90], [-95, 0]],
        [[-95, 0], [-30, 90], [55, 0]],
        [[55, 0], [120, 90], [180, 0]]
      ],
      [
        [[-180, 0], [-120, -90], [-60, 0]],
        [[-60, 0], [20, -90], [85, 0]],
        [[85, 0], [140, -90], [180, 0]]
      ]
    ];
    projection = d3.geoInterrupt(d3.geoHomolosineRaw, lobes).rotate([-204, 0])
    .fitExtent([[10, 10], [width-10, height-10]], {type: "Sphere"});

The issue is described here: d3/d3-geo-projection#125

To sum up this would need to:

• introduce geoCahill1909 (which would be geoPolyhedralWaterman but with the inferior choice of angles from Cahill's original — and that could be a parameter of course), and be mindful of the face projection used in 1909
• create a "true" geoWaterman with Antarctica cut out (see also #11)
• obsolete geoPolyhedralWaterman

We could use the Schwarz-Christoffel transformation. http://www.genekeyes.com/CAHILL-VARIANTS/Cahill-Conformal.html shows one made by @jrus

Hello,

the inverse of the Tetrahedral Lee does not seem to work.
I’ve used the script by @cambecc – see here – to try this. Here is a demo, on top is the Imago projection where the inverse works (everything’s filled with blue pixels) but on the Lee, I only get a red triangle.

Am I doing something wrong or is the inverse broken?

Kind regards,
Tobias

The Imago projection needs to use polygon clipping; but it seems a bit absurd that we are doing spherical clipping (with 200 control points computed as the inverse of 200 planar points) just to do what is in the end a simple rectangular clipping. The thing is tricky because, so close to the limit, the spherical interpolation between control points might jump from one side to the other.

https://github.com/mourner/robust-predicates

Can we use this to cut (instead of clipping) to the polygon.

Would be useful to avoid disappearing points that are just on the edge of the polygon in polyhedral projections.
See d3/d3-geo-projection#132 (comment)

In https://observablehq.com/@fil/oronce-fines-triangle-projection the graticule was properly clipped until [email protected], but it failed with release 1.8.0.
I think the offending commit is eb1e663 (#160).

Test @ https://observablehq.com/@fil/clipping-bug-39

This is also the reason why #60 (rhombic) had a small rotation. Same bug appears in https://observablehq.com/d/8085f693f9972f0e (#9)

See https://beta.observablehq.com/@fil/an-equal-area-projection-for-the-cubic-earth

Is there any interest in integrating this equal-area square face projection? (It can be fun to use on something else than the 1/6th square face of the cube.) If so, should it be integrated in this module or in d3-geo-projection?

Hi,

I was messing around again and created a v2 geoDesic projection. I starts of with the icosahedron and splits up the triangle in sub triangles. For a v2 a triangle is split up into 4 sub triangles.

Here is an example

I am currently working on making the projection parametric so geoDesic(2) would create a v2 and geoDesic(3) would create a v3.

If you are interested in adding this I can create a pull request.

http://blockbuilder.org/Fil/90c1d39fa1b92281fd119c02188da858 shows how to use this plugin. It calls a modified version of d3.polyhedral (in d3-geo-projection) that in turn uses d3.geoClipPolygon(). More soon on this.

Older examples are available from https://bl.ocks.org/Fil/fc967d8ac6aa246863c6f2a4b7dbe41c and will be updated progressively.

Examples should go in the README when they're ready.

Hi,

i created a deltoidal hexecontahedron projection which can be seen here.

https://observablehq.com/d/881a8431e638b408

would this be a welcome addition to the project? I based it on d3.geoPolyhedralVoronoi()

South aspect of Lee’s conformal projection in a tetrahedron shows all black.

From the tweet exchange @Fil has verified that

it doesn't happen with [email protected] but with [email protected]

The equator is broken (missing some parts, and bleeding out in other parts) at
http://blockbuilder.org/Fil/ee9bf16bf8b2fa56057733c443832c5d

Because we reexport some projections (say, geoGingery) under the same name, when combining the UMD bundles for d3-geo-polygon and d3-geo-projection, we get either the unclipped projection from d3-geo-projection (if it was loaded after d3-geo-polygon), or a recursion loop (if it was loaded before).

If someone really cannot upgrade their environment to ESM and must have a reclipped gingery, they will have to manually copy the code from https://github.com/d3/d3-geo-polygon/blob/main/src/reclip.js

For example:

<script src="https://cdn.jsdelivr.net/npm/d3-array@3"></script>
<script src="https://cdn.jsdelivr.net/npm/d3-geo@3"></script>
<script src="https://cdn.jsdelivr.net/npm/d3-geo-polygon@2"></script>
<script src="https://cdn.jsdelivr.net/npm/d3-geo-projection@3"></script>
<script>

function reclip(projection, vertical = false) {
  const {lobes} = projection;
  function reset(projection) {
    const rotate = projection.rotate();
    const scale = projection.scale();
    const translate = projection.translate();
    projection.rotate([0, 0]).translate([0, 0]);
    projection.lobes = function (_) {
      return !arguments.length ? lobes() : reset(lobes(_));
    };

    projection.preclip((stream) => stream); // clipNone
    const R = 1 - 1e-7;
    const Rx = vertical ? 1 : R;
    let points = [];
    projection
      .stream({
        point(x, y) {
          points.push([x * Rx, y * R]);
        },
        lineStart() {},
        lineEnd() {},
        polygonStart() {},
        polygonEnd() {},
        sphere() {},
      })
      .sphere();

    projection.scale(scale);
    points = points.map(projection.invert);
    points.push(points[0]);

    return projection
      .rotate(rotate)
      .translate(translate)
      .preclip(d3.geoClipPolygon({ type: "Polygon", coordinates: [points] }));
  }
  return reset(projection);
}

const projection = reclip(d3.geoGingery());

</script>

Sorry noob question here...how do i inverse the clipping of d3.geoClipPolygon with preclip?...any example would be appreciate

First, thanks for your great contributions regarding projections in D3. I have been playing with your new added projections in this d3-geo-polygon extension in combination with vega. Firstly I used the airocean projection to cut and engrave some wood using laser and liked the result¹.

But now having seen these maps on https://beta.observablehq.com/@fil/speed-of-the-voronoi-projection I would love to play with this projection as well.

I used the method as mentioned in the notebook:

The following map was made with the Voronoi projection — available as d3.geoVoronoi() in d3-geo-polygon.

When I try to use this:
projection = d3.geoVoronoi()

I receive:
TypeError: d3.geoVoronoi is not a function

Question: I'm trying features that are not yet available? or do I call them wrongly?

I was playing around and got some clipping problem.
This code map(d3.geoCubic().parents([-1, 2, 0, 2, 5, 2]).rotate([0,0,45])) produces some artefacts:

map() as per https://beta.observablehq.com/@fil/polyhedral-projections-with-d3-geo-polygon

Trying to bundle this in a webpack-based app, I find it breaks because it assumes a hardcoded location for node_modules in many places, eg (from here).

import {abs, degrees, epsilon, radians} from "../../node_modules/d3-geo-projection/src/math";
import {default as matrix, multiply, inverse} from "../../node_modules/d3-geo-projection/src/polyhedral/matrix";

ERROR in ./node_modules/d3-geo-polygon/src/polyhedral/waterman.js
Module not found: Error: Can't resolve '../../node_modules/d3-geo-projection/src/math' in '/home/bschmidt/project/node_modules/d3-geo-polygon/src/polyhedral'

~/project/node_modules/d3-geo-polygon/ find . -name "*.js" | xargs -I {} -n 1 perl -pi -e 's/\..\/\..\/node_modules\///g' {}

Hi, many of the links to examples on scratchpad don't work. In particular, I want the https://beta.observablehq.com/@fil/icosahedral-projection

This package is constrained to node ">=6.0.0 <=10.17.0". Using this package with maintained node versions without ignoring engines constraint isn't possible. Is there any reason why this constraint is present in d3-geo-polygon package.json?

Part of API doesn't seem to rely on node internals eg. geoArcIntersect. Maybe if part of API needs old node version it'll be good idea to move independent code parts into other package.

i can only draw the first face by setting .parents([-1])

but if i only wanted to draw for example the first 3 faces of a cube would that be possible?

i have this question as i like to laser cut the faces out of would an turn them into a globe.
Drawing only a few faces would make it easier to fit on the laser cutter.

see https://beta.observablehq.com/@fil/speed-of-the-voronoi-projection

The projection is 100x faster if it can use geovoronoi.find() to know to which face a point belongs. In my local branch, I've solved this by allowing to pass a faceFind function.

But should we limit ourselves to this, or be bolder and pass a full geoVoronoi object (which would also help in finding shared edges much faster, by using the delaunay topology)?

https://beta.observablehq.com/@fil/cahill-keyes-projection#Antarctica

Namely, d3.geoAlbers? I am trying to use preclipping and am getting very strange results.

More to the point.
Polygon 1:
[ [ [ 30, 60 ], [ 90, 60 ], [ 90, 30 ], [ 30, 30 ], [ 30, 60 ] ] ]
Polygon 2:
[ [ [ 45, 75 ], [ 75, 75 ], [ 75, 15 ], [ 45, 15 ], [ 45, 75 ] ] ]

Projection:
d3.geoAlbers() .rotate([-105, 0]) .center([-10, 65]) .parallels([52, 64]);

Below is a picture made in qGis, cyan polygon (P2) is being clipped, green is the one doing the clipping (P1) (the one passed to geoClipPolygon and the result passed to preclip). Both polygons are already projected (but not preclipped).

After projecting, P2 is null.

Hi,

i made some changes to TetrahedralLee so i can add parents and it also supports setting the root of the tree in other places than faces[0]. I added it to my fork here if you want to see.

Here are some images created whith the snapshot unittests

i also tried generating svg's but that is not working flawless yet.

From Jason Davies's code (ported in 82d9481#diff-1955ba130f17ffd3f1a5db97ee798e02R13 ), there was an epsilon2 test in this function.

Somehow it allowed lines to escape the clipping on some occasions, so I lowered it to epsilon3 in 202e604 and got much less errors.

But it still happens, and the fix is to get rid of any epsilon and compare the values with 0.

I wonder what I'm missing (in which cases this value should be st. positive), but testing in all my examples seems to be OK with 0 instead of epsilon3.

It’d be nice if this library were easier to use when saving spherically-clipped GeoJSON. For example:

https://beta.observablehq.com/d/d706c7f9c6e46907

The tedious parts are:

• You need to wrap the d3.geoClipPolygon instance with an object that has a stream method.

• You need to compose the d3.geoClipPolygon instance with streams that transform from degrees to radians and then back again.

Part of me wonders if it’s worth revisiting a more composable geographic projection pipeline…

(Also, I think d3.geoProject sometimes breaks polygon semantics, but that’s a separate issue.)

So i was trying to create a rhombic dodecahedron projection but there is something weird going on with the clipping

rhombic_f = {
  var degrees = 180 / Math.PI;
  var phi1 = Math.atan(Math.SQRT1_2) * degrees;
  var vertices = [
    [0, 90],      // 0
    [0, phi1],    // 1
    [90, phi1],   // 2
    [180, phi1],  // 3
    [-90, phi1],  // 4
    [45, 0],      // 5
    [135, 0],     // 6
    [-135, 0],     // 7
    [-45, 0],     // 8
    [0, -phi1],   // 9
    [90, -phi1],  // 10
    [180, -phi1], // 11
    [-90, -phi1], // 12
    [0, -90]      // 13
  ];
    
  // rhombic dodecahedron
  var polyhedron = [
    [0, 1, 8, 4],
    [0, 2, 5, 1],
    [0, 3, 6, 2],
    [0, 4, 7, 3],

    [1, 5, 9, 8],
    [2, 6, 10, 5],
    [3, 7, 11, 6],
    [4, 8, 12, 7],

    [8, 9, 13, 12],
    [5, 10, 13, 9],
    [6, 11, 13, 10],
    [7, 12, 13, 11]
  ].map(function(face) {
          return face.map(function(i) {
            return vertices[i];
          });
  });

  var polygons = {
    type: "FeatureCollection",
    features: polyhedron.map(function(face) {
      face.push(face[0]);
      return {
        properties: { sitecoordinates: d3.geoCentroid({type:"MultiPoint", coordinates: face}) },
        geometry: {
          type: "Polygon",
          coordinates: [ face ]
        }
      };
    })
  };

var parents = [
      -1, // 0
      0, // 1
      6, // 2
      2, // 3
      1, // 4
      9, // 5
      11, // 6
      3, // 7
      4, // 8
      8, // 9
      5, // 10
      10, // 11
    ];

  //return polygons;
  return d3.geoPolyhedralVoronoi()
   .parents(parents)
   .polygons(polygons);
};

i numbered the faces in the image below and there should be red lines around all the faces. This is a combination of the cubic and the octahedron projection.

https://github.com/d3/d3-geo-projection#geoHealpix could use a clipPolygon

The multipolygon branch is a first step towards #9 and #11.

There is a demo here:
https://beta.observablehq.com/d/368627e7d1bcc0cb

each polygon is processed in turn.

There are still a few bugs though — as you can see if you rotate the map in the demo, there are sometimes mix-ups in the variables that control the points' visibility, resulting in dots for points that should belong to a polygon, or in full-white surfaces that should be full-black.

unit test	reality (edit: on Chrome)

(I am completely puzzled)

https://observablehq.com/@fil/markley

https://beta.observablehq.com/@fil/cahill-keyes-projection

while these first two could be solved by clipping to the sphere, the last one shows we still sometimes have inversions:

(reported by @mootari @ https://imgur.com/a/Km2wK6m)