# all files / src/util/ delaunay.js

1.65% Statements 2/121
0% Branches 0/62
0% Functions 0/6
1.71% Lines 2/117

    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    71
    72
    73
    74
    75
    76
    77
    78
    79
    80
    81
    82
    83
    84
    85
    86
    87
    88
    89
    90
    91
    92
    93
    94
    95
    96
    97
    98
    99
    100
    101
    102
    103
    104
    105
    106
    107
    108
    109
    110
    111
    112
    113
    114
    115
    116
    117
    118
    119
    120
    121
    122
    123
    124
    125
    126
    127
    128
    129
    130
    131
    132
    133
    134
    135
    136
    137
    138
    139
    140
    141
    142
    143
    144
    145
    146
    147
    148
    149
    150
    151
    152
    153
    154
    155
    156
    157
    158
    159
    160
    161
    162
    163
    164
    165
    166
    167
    168
    169
    170
    171
    172
    173
    174
    175
    176
    177
    178
    179
    180
    181
    182
    183
    184
    185
    186
    187
    188
    189
    190
    191
    192
    193
    194
    195
    196
    197
    198
    199
    200
    201
    202
    203
    204
    205
    206
    207
    208
    209
    210
    211
    212
    213
    214
    215
    216
    217
    218
    219
    220
    221
    222
    223
    224
    225
    226
    227
    228
    229
    230
    231
    232
    233
    234
    235
    236
    237
    238
    239
    240
    241
    242
    243
    244

    1×

    1×

     // Delaunay Triangulation
    // Modified from https://github.com/ironwallaby/delaunay
    var EPSILON = 1.0 / 1048576.0;

    function supertriangle(vertices) {
        var xmin = Number.POSITIVE_INFINITY;
        var ymin = Number.POSITIVE_INFINITY;
        var xmax = Number.NEGATIVE_INFINITY;
        var ymax = Number.NEGATIVE_INFINITY;
        var i, dx, dy, dmax, xmid, ymid;

        for (i = vertices.length; i--; ) {
            if (vertices[i][0] < xmin) { xmin = vertices[i][0]; }
            if (vertices[i][0] > xmax) { xmax = vertices[i][0]; }
            if (vertices[i][1] < ymin) { ymin = vertices[i][1]; }
            if (vertices[i][1] > ymax) { ymax = vertices[i][1]; }
        }

        dx = xmax - xmin;
        dy = ymax - ymin;
        dmax = Math.max(dx, dy);
        xmid = xmin + dx * 0.5;
        ymid = ymin + dy * 0.5;

        return [
            [xmid - 20 * dmax, ymid -      dmax],
            [xmid            , ymid + 20 * dmax],
            [xmid + 20 * dmax, ymid -      dmax]
        ];
    }

    function circumcircle(vertices, i, j, k) {
        var x1 = vertices[i][0],
                y1 = vertices[i][1],
                x2 = vertices[j][0],
                y2 = vertices[j][1],
                x3 = vertices[k][0],
                y3 = vertices[k][1],
                fabsy1y2 = Math.abs(y1 - y2),
                fabsy2y3 = Math.abs(y2 - y3),
                xc, yc, m1, m2, mx1, mx2, my1, my2, dx, dy;

        /* Check for coincident points */
        if (fabsy1y2 < EPSILON && fabsy2y3 < EPSILON) {
            throw new Error('Eek! Coincident points!');
        }

        if (fabsy1y2 < EPSILON) {
            m2  = -((x3 - x2) / (y3 - y2));
            mx2 = (x2 + x3) / 2.0;
            my2 = (y2 + y3) / 2.0;
            xc  = (x2 + x1) / 2.0;
            yc  = m2 * (xc - mx2) + my2;
        }

        else if (fabsy2y3 < EPSILON) {
            m1  = -((x2 - x1) / (y2 - y1));
            mx1 = (x1 + x2) / 2.0;
            my1 = (y1 + y2) / 2.0;
            xc  = (x3 + x2) / 2.0;
            yc  = m1 * (xc - mx1) + my1;
        }

        else {
            m1  = -((x2 - x1) / (y2 - y1));
            m2  = -((x3 - x2) / (y3 - y2));
            mx1 = (x1 + x2) / 2.0;
            mx2 = (x2 + x3) / 2.0;
            my1 = (y1 + y2) / 2.0;
            my2 = (y2 + y3) / 2.0;
            xc  = (m1 * mx1 - m2 * mx2 + my2 - my1) / (m1 - m2);
            yc  = (fabsy1y2 > fabsy2y3) ?
                m1 * (xc - mx1) + my1 :
                m2 * (xc - mx2) + my2;
        }

        dx = x2 - xc;
        dy = y2 - yc;
        return {i: i, j: j, k: k, x: xc, y: yc, r: dx * dx + dy * dy};
    }

    function dedup(edges) {
        var i, j, a, b, m, n;

        for (j = edges.length; j; ) {
            b = edges[--j];
            a = edges[--j];

            for (i = j; i; ) {
                n = edges[--i];
                m = edges[--i];

                if ((a === m && b === n) || (a === n && b === m)) {
                    edges.splice(j, 2);
                    edges.splice(i, 2);
                    break;
                }
            }
        }
    }

    var delaunay = {
        triangulate: function(vertices, key) {
            var n = vertices.length;
            var i, j, indices, st, open, closed, edges, dx, dy, a, b, c;

            /* Bail if there aren't enough vertices to form any triangles. */
            if (n < 3) {
                return [];
            }

            /* Slice out the actual vertices from the passed objects. (Duplicate the
                * array even if we don't, though, since we need to make a supertriangle
                * later on!) */
            vertices = vertices.slice(0);

            if (key) {
                for (i = n; i--; ) {
                    vertices[i] = vertices[i][key];
                }
            }

            /* Make an array of indices into the vertex array, sorted by the
                * vertices' x-position. Force stable sorting by comparing indices if
                * the x-positions are equal. */
            indices = new Array(n);

            for (i = n; i--; ) {
                indices[i] = i;
            }

            indices.sort(function(i, j) {
                var diff = vertices[j][0] - vertices[i][0];
                return diff !== 0 ? diff : i - j;
            });

            /* Next, find the vertices of the supertriangle (which contains all other
                * triangles), and append them onto the end of a (copy of) the vertex
                * array. */
            st = supertriangle(vertices);
            vertices.push(st[0], st[1], st[2]);

            /* Initialize the open list (containing the supertriangle and nothing
                * else) and the closed list (which is empty since we havn't processed
                * any triangles yet). */
            open   = [circumcircle(vertices, n + 0, n + 1, n + 2)];
            closed = [];
            edges  = [];

            /* Incrementally add each vertex to the mesh. */
            for (i = indices.length; i--; edges.length = 0) {
                c = indices[i];

                /* For each open triangle, check to see if the current point is
                    * inside it's circumcircle. If it is, remove the triangle and add
                    * it's edges to an edge list. */
                for (j = open.length; j--; ) {
                    /* If this point is to the right of this triangle's circumcircle,
                        * then this triangle should never get checked again. Remove it
                        * from the open list, add it to the closed list, and skip. */
                    dx = vertices[c][0] - open[j].x;
                    if (dx > 0.0 && dx * dx > open[j].r) {
                        closed.push(open[j]);
                        open.splice(j, 1);
                        continue;
                    }

                    /* If we're outside the circumcircle, skip this triangle. */
                    dy = vertices[c][1] - open[j].y;
                    if (dx * dx + dy * dy - open[j].r > EPSILON) {
                        continue;
                    }

                    /* Remove the triangle and add it's edges to the edge list. */
                    edges.push(
                        open[j].i, open[j].j,
                        open[j].j, open[j].k,
                        open[j].k, open[j].i
                    );
                    open.splice(j, 1);
                }

                /* Remove any doubled edges. */
                dedup(edges);

                /* Add a new triangle for each edge. */
                for (j = edges.length; j; ) {
                    b = edges[--j];
                    a = edges[--j];
                    open.push(circumcircle(vertices, a, b, c));
                }
            }

            /* Copy any remaining open triangles to the closed list, and then
                * remove any triangles that share a vertex with the supertriangle,
                * building a list of triplets that represent triangles. */
            for (i = open.length; i--; ) {
                closed.push(open[i]);
            }
            open.length = 0;

            for (i = closed.length; i--; ) {
                if (closed[i].i < n && closed[i].j < n && closed[i].k < n) {
                    open.push(closed[i].i, closed[i].j, closed[i].k);
                }
            }

            /* Yay, we're done! */
            return open;
        },
        contains: function(tri, p) {
            /* Bounding box test first, for quick rejections. */
            if ((p[0] < tri[0][0] && p[0] < tri[1][0] && p[0] < tri[2][0]) ||
                    (p[0] > tri[0][0] && p[0] > tri[1][0] && p[0] > tri[2][0]) ||
                    (p[1] < tri[0][1] && p[1] < tri[1][1] && p[1] < tri[2][1]) ||
                    (p[1] > tri[0][1] && p[1] > tri[1][1] && p[1] > tri[2][1])) {
                return null;
            }

            var a = tri[1][0] - tri[0][0];
            var b = tri[2][0] - tri[0][0];
            var c = tri[1][1] - tri[0][1];
            var d = tri[2][1] - tri[0][1];
            var i = a * d - b * c;

            /* Degenerate tri. */
            if (i === 0.0) {
                return null;
            }

            var u = (d * (p[0] - tri[0][0]) - b * (p[1] - tri[0][1])) / i,
                    v = (a * (p[1] - tri[0][1]) - c * (p[0] - tri[0][0])) / i;

            /* If we're outside the tri, fail. */
            if (u < 0.0 || v < 0.0 || (u + v) > 1.0) {
                return null;
            }

            return [u, v];
        }
    };

    export default delaunay;