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Polygon Triangulation For Globe

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Is it real to fill all polygons? Codepen. As I get it ThreeGeoJSON can not fill polygons, outlines only. Also I've tried Earcut for triangulation. drawThreeGeo(data, radius, 'spher

Solution 1:

I suggest you to use better map: countries.geojson

The solution consists of following steps, for each shape:

  1. Put vertices inside of shape, so that when triangulated, it could bend around the globe,
  2. Run https://github.com/mapbox/delaunator to build triangulated mesh,
  3. Step 2 will create triangles outside the shape too, we need to remove them by looking into each triangle, and deciding if it belongs to shape or not,
  4. Bend the triangulated mesh with convertCoordinates

You can test my jsfiddle: http://jsfiddle.net/mmalex/pg5a4132/

Warning: it is quite slow because of high level of detail of input.

triangulate planet three.js with delaunay triangulation

triangulate planet three.js wireframe

hover triangulated shape with three.js

The complete solution:

/* Draw GeoJSON

Iterates through the latitude and longitude values, converts the values to XYZ coordinates, and draws the geoJSON geometries.

*/

let TRIANGULATION_DENSITY = 5; // make it smaller for more dense mesh

function verts2array(coords) {
    let flat = [];
    for (let k = 0; k < coords.length; k++) {
        flat.push(coords[k][0], coords[k][1]);
    }
    return flat;
}

function array2verts(arr) {
    let coords = [];
    for (let k = 0; k < arr.length; k += 2) {
        coords.push([arr[k], arr[k + 1]]);
    }
    return coords;
}

function findBBox(points) {
    let min = {
        x: 1e99,
        y: 1e99
    };
    let max = {
        x: -1e99,
        y: -1e99
    };
    for (var point_num = 0; point_num < points.length; point_num++) {
        if (points[point_num][0] < min.x) {
            min.x = points[point_num][0];
        }
        if (points[point_num][0] > max.x) {
            max.x = points[point_num][0];
        }
        if (points[point_num][1] < min.y) {
            min.y = points[point_num][1];
        }
        if (points[point_num][1] > max.y) {
            max.y = points[point_num][1];
        }
    }
    return {
        min: min,
        max: max
    };
}

function isInside(point, vs) {
    // ray-casting algorithm based on
    // http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html

    var x = point[0],
        y = point[1];

    var inside = false;
    for (var i = 0, j = vs.length - 1; i < vs.length; j = i++) {
        var xi = vs[i][0],
            yi = vs[i][1];
        var xj = vs[j][0],
            yj = vs[j][1];

        var intersect = ((yi > y) != (yj > y)) && (x < (xj - xi) * (y - yi) / (yj - yi) + xi);
        if (intersect) inside = !inside;
    }

    return inside;
}

function genInnerVerts(points) {
    let res = [];
    for (let k = 0; k < points.length; k++) {
        res.push(points[k]);
    }

    let bbox = findBBox(points);

    let step = TRIANGULATION_DENSITY;
    let k = 0;
    for (let x = bbox.min.x + step / 2; x < bbox.max.x; x += step) {
        for (let y = bbox.min.y + step / 2; y < bbox.max.y; y += step) {
            let newp = [x, y];
            if (isInside(newp, points)) {
                res.push(newp);
            }
            k++;
        }
    }

    return res;
}

function removeOuterTriangles(delaunator, points) {
    let newTriangles = [];
    for (let k = 0; k < delaunator.triangles.length; k += 3) {
        let t0 = delaunator.triangles[k];
        let t1 = delaunator.triangles[k + 1];
        let t2 = delaunator.triangles[k + 2];

        let x0 = delaunator.coords[2 * t0];
        let y0 = delaunator.coords[2 * t0 + 1];

        let x1 = delaunator.coords[2 * t1];
        let y1 = delaunator.coords[2 * t1 + 1];

        let x2 = delaunator.coords[2 * t2];
        let y2 = delaunator.coords[2 * t2 + 1];

        let midx = (x0 + x1 + x2) / 3;
        let midy = (y0 + y1 + y2) / 3;

        let midp = [midx, midy];

        if (isInside(midp, points)) {
            newTriangles.push(t0, t1, t2);
        }
    }
    delaunator.triangles = newTriangles;
}

var x_values = [];
var y_values = [];
var z_values = [];

var progressEl = $("#progress");
var clickableObjects = [];
var someColors = [0x909090, 0x808080, 0xa0a0a0, 0x929292, 0x858585, 0xa9a9a9];

function drawThreeGeo(json, radius, shape, options) {

    var json_geom = createGeometryArray(json);
    var convertCoordinates = getConversionFunctionName(shape);

    for (var geom_num = 0; geom_num < json_geom.length; geom_num++) {
        console.log("Processing " + geom_num + " of " + json_geom.length + " shapes");

        // if (geom_num !== 17) continue;
        // if (geom_num > 10) break;

        if (json_geom[geom_num].type == 'Point') {
            convertCoordinates(json_geom[geom_num].coordinates, radius);
            drawParticle(y_values[0], z_values[0], x_values[0], options);

        } else if (json_geom[geom_num].type == 'MultiPoint') {
            for (let point_num = 0; point_num < json_geom[geom_num].coordinates.length; point_num++) {
                convertCoordinates(json_geom[geom_num].coordinates[point_num], radius);
                drawParticle(y_values[0], z_values[0], x_values[0], options);
            }

        } else if (json_geom[geom_num].type == 'LineString') {

            for (let point_num = 0; point_num < json_geom[geom_num].coordinates.length; point_num++) {
                convertCoordinates(json_geom[geom_num].coordinates[point_num], radius);
            }
            drawLine(y_values, z_values, x_values, options);

        } else if (json_geom[geom_num].type == 'Polygon') {
            let group = createGroup(geom_num);
            let randomColor = someColors[Math.floor(someColors.length * Math.random())];

            for (let segment_num = 0; segment_num < json_geom[geom_num].coordinates.length; segment_num++) {

                let coords = json_geom[geom_num].coordinates[segment_num];
                let refined = genInnerVerts(coords);
                let flat = verts2array(refined);
                let d = new Delaunator(flat);
                removeOuterTriangles(d, coords);

                let delaunayVerts = array2verts(d.coords);
                for (let point_num = 0; point_num < delaunayVerts.length; point_num++) {
                    // convertCoordinates(refined[point_num], radius);
                    convertCoordinates(delaunayVerts[point_num], radius);
                }
                // drawLine(y_values, z_values, x_values, options);
                drawMesh(group, y_values, z_values, x_values, d.triangles, randomColor);
            }

        } else if (json_geom[geom_num].type == 'MultiLineString') {
            for (let segment_num = 0; segment_num < json_geom[geom_num].coordinates.length; segment_num++) {
                let coords = json_geom[geom_num].coordinates[segment_num];
                for (let point_num = 0; point_num < coords.length; point_num++) {
                    convertCoordinates(json_geom[geom_num].coordinates[segment_num][point_num], radius);
                }
                drawLine(y_values, z_values, x_values);
            }

        } else if (json_geom[geom_num].type == 'MultiPolygon') {
            let group = createGroup(geom_num);
            let randomColor = someColors[Math.floor(someColors.length * Math.random())];

            for (let polygon_num = 0; polygon_num < json_geom[geom_num].coordinates.length; polygon_num++) {
                for (let segment_num = 0; segment_num < json_geom[geom_num].coordinates[polygon_num].length; segment_num++) {

                    let coords = json_geom[geom_num].coordinates[polygon_num][segment_num];
                    let refined = genInnerVerts(coords);
                    let flat = verts2array(refined);
                    let d = new Delaunator(flat);
                    removeOuterTriangles(d, coords);

                    let delaunayVerts = array2verts(d.coords);
                    for (let point_num = 0; point_num < delaunayVerts.length; point_num++) {
                        // convertCoordinates(refined[point_num], radius);
                        convertCoordinates(delaunayVerts[point_num], radius);
                    }
                    // drawLine(y_values, z_values, x_values, options);
                    drawMesh(group, y_values, z_values, x_values, d.triangles, randomColor)
                }
            }
        } else {
            throw new Error('The geoJSON is not valid.');
        }

    }

    progressEl.text("Complete!");
}

function createGeometryArray(json) {
    var geometry_array = [];

    if (json.type == 'Feature') {
        geometry_array.push(json.geometry);
    } else if (json.type == 'FeatureCollection') {
        for (var feature_num = 0; feature_num < json.features.length; feature_num++) {
            geometry_array.push(json.features[feature_num].geometry);
        }
    } else if (json.type == 'GeometryCollection') {
        for (var geom_num = 0; geom_num < json.geometries.length; geom_num++) {
            geometry_array.push(json.geometries[geom_num]);
        }
    } else {
        throw new Error('The geoJSON is not valid.');
    }
    //alert(geometry_array.length);
    return geometry_array;
}

function getConversionFunctionName(shape) {
    var conversionFunctionName;

    if (shape == 'sphere') {
        conversionFunctionName = convertToSphereCoords;
    } else if (shape == 'plane') {
        conversionFunctionName = convertToPlaneCoords;
    } else {
        throw new Error('The shape that you specified is not valid.');
    }
    return conversionFunctionName;
}


function convertToSphereCoords(coordinates_array, sphere_radius) {
    var lon = coordinates_array[0];
    var lat = coordinates_array[1];

    x_values.push(Math.cos(lat * Math.PI / 180) * Math.cos(lon * Math.PI / 180) * sphere_radius);
    y_values.push(Math.cos(lat * Math.PI / 180) * Math.sin(lon * Math.PI / 180) * sphere_radius);
    z_values.push(Math.sin(lat * Math.PI / 180) * sphere_radius);
}

function convertToPlaneCoords(coordinates_array, radius) {
    var lon = coordinates_array[0];
    var lat = coordinates_array[1];
    var plane_offset = radius / 2;

    z_values.push((lat / 180) * radius);
    y_values.push((lon / 180) * radius);

}

function drawParticle(x, y, z, options) {
    var particle_geom = new THREE.Geometry();
    particle_geom.vertices.push(new THREE.Vector3(x, y, z));

    var particle_material = new THREE.ParticleSystemMaterial(options);

    var particle = new THREE.ParticleSystem(particle_geom, particle_material);
    scene.add(particle);

    clearArrays();
}

function drawLine(x_values, y_values, z_values, options) {
    var line_geom = new THREE.Geometry();
    createVertexForEachPoint(line_geom, x_values, y_values, z_values);

    var line_material = new THREE.LineBasicMaterial(options);
    var line = new THREE.Line(line_geom, line_material);
    scene.add(line);

    clearArrays();
}

function createGroup(idx) {
    var group = new THREE.Group();
    group.userData.userText = "_" + idx;
    scene.add(group);
    return group;
}

function drawMesh(group, x_values, y_values, z_values, triangles, color) {
    var geometry = new THREE.Geometry();

    for (let k = 0; k < x_values.length; k++) {
        geometry.vertices.push(
            new THREE.Vector3(x_values[k], y_values[k], z_values[k])
        );
    }

    for (let k = 0; k < triangles.length; k += 3) {
        geometry.faces.push(new THREE.Face3(triangles[k], triangles[k + 1], triangles[k + 2]));
    }

    geometry.computeVertexNormals()

    var mesh = new THREE.Mesh(geometry, new THREE.MeshLambertMaterial({
        side: THREE.DoubleSide,
        color: color,
        wireframe: true
    }));
    clickableObjects.push(mesh);
    group.add(mesh);

    clearArrays();
}

function createVertexForEachPoint(object_geometry, values_axis1, values_axis2, values_axis3) {
    for (var i = 0; i < values_axis1.length; i++) {
        object_geometry.vertices.push(new THREE.Vector3(values_axis1[i],
            values_axis2[i], values_axis3[i]));
    }
}

function clearArrays() {
    x_values.length = 0;
    y_values.length = 0;
    z_values.length = 0;
}

var scene = new THREE.Scene();
var raycaster = new THREE.Raycaster();
var camera = new THREE.PerspectiveCamera(32, window.innerWidth / window.innerHeight, 0.5, 1000);
var radius = 200;

camera.position.x = 140.7744005681177;
camera.position.y = 160.30950538100814;
camera.position.z = 131.8637122564268;

var renderer = new THREE.WebGLRenderer();
renderer.setSize(window.innerWidth, window.innerHeight);
renderer.setPixelRatio(window.devicePixelRatio);
document.body.appendChild(renderer.domElement);

var light = new THREE.HemisphereLight(0xffffbb, 0x080820, 1);
scene.add(light);

var light = new THREE.AmbientLight(0x505050); // soft white light
scene.add(light);

var geometry = new THREE.SphereGeometry(radius, 32, 32);

var material = new THREE.MeshPhongMaterial({
    color: 0x1e90ff
});
var sphere = new THREE.Mesh(geometry, material);
scene.add(sphere);
var test_json = $.getJSON("https://raw.githubusercontent.com/datasets/geo-countries/master/data/countries.geojson", function(data) {
    drawThreeGeo(data, radius + 1, 'sphere', {
        color: 'yellow'
    })

});

var controls = new THREE.TrackballControls(camera);
controls.rotateSpeed *= 0.5;
controls.zoomSpeed *= 0.5;
controls.panSpeed *= 0.5;
controls.minDistance = 10;
controls.maxDistance = 5000;

function render() {
    controls.update();
    requestAnimationFrame(render);
    renderer.setClearColor(0x1e90ff, 1);
    renderer.render(scene, camera);
}

render()

function convert_lat_lng(lat, lng, radius) {
    var phi = (90 - lat) * Math.PI / 180,
        theta = (180 - lng) * Math.PI / 180,
        position = new THREE.Vector3();

    position.x = radius * Math.sin(phi) * Math.cos(theta);
    position.y = radius * Math.cos(phi);
    position.z = radius * Math.sin(phi) * Math.sin(theta);

    return position;
}

// this will be 2D coordinates of the current mouse position, [0,0] is middle of the screen.
var mouse = new THREE.Vector2();

var hoveredObj; // this objects is hovered at the moment

// Following two functions will convert mouse coordinates
// from screen to three.js system (where [0,0] is in the middle of the screen)
function updateMouseCoords(event, coordsObj) {
    coordsObj.x = ((event.clientX - renderer.domElement.offsetLeft + 0.5) / window.innerWidth) * 2 - 1;
    coordsObj.y = -((event.clientY - renderer.domElement.offsetTop + 0.5) / window.innerHeight) * 2 + 1;
}

function onMouseMove(event) {
    updateMouseCoords(event, mouse);

    latestMouseProjection = undefined;
    clickedObj = undefined;

    raycaster.setFromCamera(mouse, camera); {
        var intersects = raycaster.intersectObjects(clickableObjects);

        let setGroupColor = function(group, colorHex) {
            for (let i = 0; i < group.children.length; i++) {
                if (!group.children[i].userData.color) {
                    group.children[i].userData.color = hoveredObj.parent.children[i].material.color.clone();
                    group.children[i].material.color.set(colorHex);
                    group.children[i].material.needsUpdate = true;
                }
            }
        }

        let resetGroupColor = function(group) {
            // set all shapes of the group to initial color
            for (let i = 0; i < group.children.length; i++) {
                if (group.children[i].userData.color) {
                    group.children[i].material.color = group.children[i].userData.color;
                    delete group.children[i].userData.color;
                    group.children[i].material.needsUpdate = true;
                }
            }
        }

        if (intersects.length > 0) {
            latestMouseProjection = intersects[0].point;
            // reset colors for previously hovered group
            if (hoveredObj) {
                resetGroupColor(hoveredObj.parent);
            }

            hoveredObj = intersects[0].object;
            if (!hoveredObj.parent) return;
            // set colors for hovered group
            setGroupColor(hoveredObj.parent, 0xff0000);
        } else {
            if (!hoveredObj || !hoveredObj.parent) return;

            // nothing is hovered => just reset colors on the last group
            resetGroupColor(hoveredObj.parent);
            hoveredObj = undefined;
            console.log("<deselected>");
        }
    }
}

window.addEventListener('mousemove', onMouseMove, false);

Solution 2:

You'd need to split each country into a separate geometry, use a raycaster to find out which country the mouse is over, then change its material.color. You can see raycasting in action in this example with source code available on the bottom-right corner. The key lines in that example are:

function onDocumentMouseMove( event ) {
    event.preventDefault();
    mouse.x = ( event.clientX / window.innerWidth ) * 2 - 1;
    mouse.y = - ( event.clientY / window.innerHeight ) * 2 + 1;
}

function render() {
    // find intersections
    raycaster.setFromCamera( mouse, camera );
    var intersects = raycaster.intersectObjects( scene.children );
    if ( intersects.length > 0 ) {
        if ( INTERSECTED != intersects[ 0 ].object ) {
            if ( INTERSECTED ) INTERSECTED.material.emissive.setHex( INTERSECTED.currentHex );
            INTERSECTED = intersects[ 0 ].object;
            INTERSECTED.currentHex = INTERSECTED.material.emissive.getHex();
            INTERSECTED.material.emissive.setHex( 0xff0000 );
        }
    } else {
        if ( INTERSECTED ) INTERSECTED.material.emissive.setHex( INTERSECTED.currentHex );
        INTERSECTED = null;
    }
    renderer.render( scene, camera );
}

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