| Current File : /home/tradevaly/www/node_modules/svgo/plugins/_path.js |
/* global a2c */
'use strict';
var rNumber = String.raw`[-+]?(?:\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?\s*`,
rCommaWsp = String.raw`(?:\s,?\s*|,\s*)`,
rNumberCommaWsp = `(${rNumber})` + rCommaWsp,
rFlagCommaWsp = `([01])${rCommaWsp}?`,
rCoordinatePair = String.raw`(${rNumber})${rCommaWsp}?(${rNumber})`,
rArcSeq = (rNumberCommaWsp + '?').repeat(2) + rNumberCommaWsp + rFlagCommaWsp.repeat(2) + rCoordinatePair;
var regPathInstructions = /([MmLlHhVvCcSsQqTtAaZz])\s*/,
regCoordinateSequence = new RegExp(rNumber, 'g'),
regArcArgumentSequence = new RegExp(rArcSeq, 'g'),
regNumericValues = /[-+]?(\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?/,
transform2js = require('./_transforms').transform2js,
transformsMultiply = require('./_transforms').transformsMultiply,
transformArc = require('./_transforms').transformArc,
collections = require('./_collections.js'),
referencesProps = collections.referencesProps,
defaultStrokeWidth = collections.attrsGroupsDefaults.presentation['stroke-width'],
cleanupOutData = require('../lib/svgo/tools').cleanupOutData,
removeLeadingZero = require('../lib/svgo/tools').removeLeadingZero,
prevCtrlPoint;
/**
* Convert path string to JS representation.
*
* @param {String} pathString input string
* @param {Object} params plugin params
* @return {Array} output array
*/
exports.path2js = function(path) {
if (path.pathJS) return path.pathJS;
var paramsLength = { // Number of parameters of every path command
H: 1, V: 1, M: 2, L: 2, T: 2, Q: 4, S: 4, C: 6, A: 7,
h: 1, v: 1, m: 2, l: 2, t: 2, q: 4, s: 4, c: 6, a: 7
},
pathData = [], // JS representation of the path data
instruction, // current instruction context
startMoveto = false;
// splitting path string into array like ['M', '10 50', 'L', '20 30']
path.attr('d').value.split(regPathInstructions).forEach(function(data) {
if (!data) return;
if (!startMoveto) {
if (data == 'M' || data == 'm') {
startMoveto = true;
} else return;
}
// instruction item
if (regPathInstructions.test(data)) {
instruction = data;
// z - instruction w/o data
if (instruction == 'Z' || instruction == 'z') {
pathData.push({
instruction: 'z'
});
}
// data item
} else {
/* jshint boss: true */
if (instruction == 'A' || instruction == 'a') {
var newData = [];
for (var args; (args = regArcArgumentSequence.exec(data));) {
for (var i = 1; i < args.length; i++) {
newData.push(args[i]);
}
}
data = newData;
} else {
data = data.match(regCoordinateSequence);
}
if (!data) return;
data = data.map(Number);
// Subsequent moveto pairs of coordinates are threated as implicit lineto commands
// http://www.w3.org/TR/SVG/paths.html#PathDataMovetoCommands
if (instruction == 'M' || instruction == 'm') {
pathData.push({
instruction: pathData.length == 0 ? 'M' : instruction,
data: data.splice(0, 2)
});
instruction = instruction == 'M' ? 'L' : 'l';
}
for (var pair = paramsLength[instruction]; data.length;) {
pathData.push({
instruction: instruction,
data: data.splice(0, pair)
});
}
}
});
// First moveto is actually absolute. Subsequent coordinates were separated above.
if (pathData.length && pathData[0].instruction == 'm') {
pathData[0].instruction = 'M';
}
path.pathJS = pathData;
return pathData;
};
/**
* Convert relative Path data to absolute.
*
* @param {Array} data input data
* @return {Array} output data
*/
var relative2absolute = exports.relative2absolute = function(data) {
var currentPoint = [0, 0],
subpathPoint = [0, 0],
i;
return data.map(function(item) {
var instruction = item.instruction,
itemData = item.data && item.data.slice();
if (instruction == 'M') {
set(currentPoint, itemData);
set(subpathPoint, itemData);
} else if ('mlcsqt'.indexOf(instruction) > -1) {
for (i = 0; i < itemData.length; i++) {
itemData[i] += currentPoint[i % 2];
}
set(currentPoint, itemData);
if (instruction == 'm') {
set(subpathPoint, itemData);
}
} else if (instruction == 'a') {
itemData[5] += currentPoint[0];
itemData[6] += currentPoint[1];
set(currentPoint, itemData);
} else if (instruction == 'h') {
itemData[0] += currentPoint[0];
currentPoint[0] = itemData[0];
} else if (instruction == 'v') {
itemData[0] += currentPoint[1];
currentPoint[1] = itemData[0];
} else if ('MZLCSQTA'.indexOf(instruction) > -1) {
set(currentPoint, itemData);
} else if (instruction == 'H') {
currentPoint[0] = itemData[0];
} else if (instruction == 'V') {
currentPoint[1] = itemData[0];
} else if (instruction == 'z') {
set(currentPoint, subpathPoint);
}
return instruction == 'z' ?
{ instruction: 'z' } :
{
instruction: instruction.toUpperCase(),
data: itemData
};
});
};
/**
* Apply transformation(s) to the Path data.
*
* @param {Object} elem current element
* @param {Array} path input path data
* @param {Object} params whether to apply transforms to stroked lines and transform precision (used for stroke width)
* @return {Array} output path data
*/
exports.applyTransforms = function(elem, path, params) {
// if there are no 'stroke' attr and references to other objects such as
// gradiends or clip-path which are also subjects to transform.
if (!elem.hasAttr('transform') || !elem.attr('transform').value ||
elem.someAttr(function(attr) {
return ~referencesProps.indexOf(attr.name) && ~attr.value.indexOf('url(');
}))
return path;
var matrix = transformsMultiply(transform2js(elem.attr('transform').value)),
stroke = elem.computedAttr('stroke'),
id = elem.computedAttr('id'),
transformPrecision = params.transformPrecision,
newPoint, scale;
if (stroke && stroke != 'none') {
if (!params.applyTransformsStroked ||
(matrix.data[0] != matrix.data[3] || matrix.data[1] != -matrix.data[2]) &&
(matrix.data[0] != -matrix.data[3] || matrix.data[1] != matrix.data[2]))
return path;
// "stroke-width" should be inside the part with ID, otherwise it can be overrided in <use>
if (id) {
var idElem = elem,
hasStrokeWidth = false;
do {
if (idElem.hasAttr('stroke-width')) hasStrokeWidth = true;
} while (!idElem.hasAttr('id', id) && !hasStrokeWidth && (idElem = idElem.parentNode));
if (!hasStrokeWidth) return path;
}
scale = +Math.sqrt(matrix.data[0] * matrix.data[0] + matrix.data[1] * matrix.data[1]).toFixed(transformPrecision);
if (scale !== 1) {
var strokeWidth = elem.computedAttr('stroke-width') || defaultStrokeWidth;
if (!elem.hasAttr('vector-effect') || elem.attr('vector-effect').value !== 'non-scaling-stroke') {
if (elem.hasAttr('stroke-width')) {
elem.attrs['stroke-width'].value = elem.attrs['stroke-width'].value.trim()
.replace(regNumericValues, function(num) {
return removeLeadingZero(num * scale);
});
} else {
elem.addAttr({
name: 'stroke-width',
prefix: '',
local: 'stroke-width',
value: strokeWidth.replace(regNumericValues, function(num) {
return removeLeadingZero(num * scale);
})
});
}
}
}
} else if (id) { // Stroke and stroke-width can be redefined with <use>
return path;
}
path.forEach(function(pathItem) {
if (pathItem.data) {
// h -> l
if (pathItem.instruction === 'h') {
pathItem.instruction = 'l';
pathItem.data[1] = 0;
// v -> l
} else if (pathItem.instruction === 'v') {
pathItem.instruction = 'l';
pathItem.data[1] = pathItem.data[0];
pathItem.data[0] = 0;
}
// if there is a translate() transform
if (pathItem.instruction === 'M' &&
(matrix.data[4] !== 0 ||
matrix.data[5] !== 0)
) {
// then apply it only to the first absoluted M
newPoint = transformPoint(matrix.data, pathItem.data[0], pathItem.data[1]);
set(pathItem.data, newPoint);
set(pathItem.coords, newPoint);
// clear translate() data from transform matrix
matrix.data[4] = 0;
matrix.data[5] = 0;
} else {
if (pathItem.instruction == 'a') {
transformArc(pathItem.data, matrix.data);
// reduce number of digits in rotation angle
if (Math.abs(pathItem.data[2]) > 80) {
var a = pathItem.data[0],
rotation = pathItem.data[2];
pathItem.data[0] = pathItem.data[1];
pathItem.data[1] = a;
pathItem.data[2] = rotation + (rotation > 0 ? -90 : 90);
}
newPoint = transformPoint(matrix.data, pathItem.data[5], pathItem.data[6]);
pathItem.data[5] = newPoint[0];
pathItem.data[6] = newPoint[1];
} else {
for (var i = 0; i < pathItem.data.length; i += 2) {
newPoint = transformPoint(matrix.data, pathItem.data[i], pathItem.data[i + 1]);
pathItem.data[i] = newPoint[0];
pathItem.data[i + 1] = newPoint[1];
}
}
pathItem.coords[0] = pathItem.base[0] + pathItem.data[pathItem.data.length - 2];
pathItem.coords[1] = pathItem.base[1] + pathItem.data[pathItem.data.length - 1];
}
}
});
// remove transform attr
elem.removeAttr('transform');
return path;
};
/**
* Apply transform 3x3 matrix to x-y point.
*
* @param {Array} matrix transform 3x3 matrix
* @param {Array} point x-y point
* @return {Array} point with new coordinates
*/
function transformPoint(matrix, x, y) {
return [
matrix[0] * x + matrix[2] * y + matrix[4],
matrix[1] * x + matrix[3] * y + matrix[5]
];
}
/**
* Compute Cubic Bézie bounding box.
*
* @see http://processingjs.nihongoresources.com/bezierinfo/
*
* @param {Float} xa
* @param {Float} ya
* @param {Float} xb
* @param {Float} yb
* @param {Float} xc
* @param {Float} yc
* @param {Float} xd
* @param {Float} yd
*
* @return {Object}
*/
exports.computeCubicBoundingBox = function(xa, ya, xb, yb, xc, yc, xd, yd) {
var minx = Number.POSITIVE_INFINITY,
miny = Number.POSITIVE_INFINITY,
maxx = Number.NEGATIVE_INFINITY,
maxy = Number.NEGATIVE_INFINITY,
ts,
t,
x,
y,
i;
// X
if (xa < minx) { minx = xa; }
if (xa > maxx) { maxx = xa; }
if (xd < minx) { minx= xd; }
if (xd > maxx) { maxx = xd; }
ts = computeCubicFirstDerivativeRoots(xa, xb, xc, xd);
for (i = 0; i < ts.length; i++) {
t = ts[i];
if (t >= 0 && t <= 1) {
x = computeCubicBaseValue(t, xa, xb, xc, xd);
// y = computeCubicBaseValue(t, ya, yb, yc, yd);
if (x < minx) { minx = x; }
if (x > maxx) { maxx = x; }
}
}
// Y
if (ya < miny) { miny = ya; }
if (ya > maxy) { maxy = ya; }
if (yd < miny) { miny = yd; }
if (yd > maxy) { maxy = yd; }
ts = computeCubicFirstDerivativeRoots(ya, yb, yc, yd);
for (i = 0; i < ts.length; i++) {
t = ts[i];
if (t >= 0 && t <= 1) {
// x = computeCubicBaseValue(t, xa, xb, xc, xd);
y = computeCubicBaseValue(t, ya, yb, yc, yd);
if (y < miny) { miny = y; }
if (y > maxy) { maxy = y; }
}
}
return {
minx: minx,
miny: miny,
maxx: maxx,
maxy: maxy
};
};
// compute the value for the cubic bezier function at time=t
function computeCubicBaseValue(t, a, b, c, d) {
var mt = 1 - t;
return mt * mt * mt * a + 3 * mt * mt * t * b + 3 * mt * t * t * c + t * t * t * d;
}
// compute the value for the first derivative of the cubic bezier function at time=t
function computeCubicFirstDerivativeRoots(a, b, c, d) {
var result = [-1, -1],
tl = -a + 2 * b - c,
tr = -Math.sqrt(-a * (c - d) + b * b - b * (c + d) + c * c),
dn = -a + 3 * b - 3 * c + d;
if (dn !== 0) {
result[0] = (tl + tr) / dn;
result[1] = (tl - tr) / dn;
}
return result;
}
/**
* Compute Quadratic Bézier bounding box.
*
* @see http://processingjs.nihongoresources.com/bezierinfo/
*
* @param {Float} xa
* @param {Float} ya
* @param {Float} xb
* @param {Float} yb
* @param {Float} xc
* @param {Float} yc
*
* @return {Object}
*/
exports.computeQuadraticBoundingBox = function(xa, ya, xb, yb, xc, yc) {
var minx = Number.POSITIVE_INFINITY,
miny = Number.POSITIVE_INFINITY,
maxx = Number.NEGATIVE_INFINITY,
maxy = Number.NEGATIVE_INFINITY,
t,
x,
y;
// X
if (xa < minx) { minx = xa; }
if (xa > maxx) { maxx = xa; }
if (xc < minx) { minx = xc; }
if (xc > maxx) { maxx = xc; }
t = computeQuadraticFirstDerivativeRoot(xa, xb, xc);
if (t >= 0 && t <= 1) {
x = computeQuadraticBaseValue(t, xa, xb, xc);
// y = computeQuadraticBaseValue(t, ya, yb, yc);
if (x < minx) { minx = x; }
if (x > maxx) { maxx = x; }
}
// Y
if (ya < miny) { miny = ya; }
if (ya > maxy) { maxy = ya; }
if (yc < miny) { miny = yc; }
if (yc > maxy) { maxy = yc; }
t = computeQuadraticFirstDerivativeRoot(ya, yb, yc);
if (t >= 0 && t <=1 ) {
// x = computeQuadraticBaseValue(t, xa, xb, xc);
y = computeQuadraticBaseValue(t, ya, yb, yc);
if (y < miny) { miny = y; }
if (y > maxy) { maxy = y ; }
}
return {
minx: minx,
miny: miny,
maxx: maxx,
maxy: maxy
};
};
// compute the value for the quadratic bezier function at time=t
function computeQuadraticBaseValue(t, a, b, c) {
var mt = 1 - t;
return mt * mt * a + 2 * mt * t * b + t * t * c;
}
// compute the value for the first derivative of the quadratic bezier function at time=t
function computeQuadraticFirstDerivativeRoot(a, b, c) {
var t = -1,
denominator = a - 2 * b + c;
if (denominator !== 0) {
t = (a - b) / denominator;
}
return t;
}
/**
* Convert path array to string.
*
* @param {Array} path input path data
* @param {Object} params plugin params
* @return {String} output path string
*/
exports.js2path = function(path, data, params) {
path.pathJS = data;
if (params.collapseRepeated) {
data = collapseRepeated(data);
}
path.attr('d').value = data.reduce(function(pathString, item) {
var strData = '';
if (item.data) {
strData = cleanupOutData(item.data, params, item.instruction);
}
return pathString += item.instruction + strData;
}, '');
};
/**
* Collapse repeated instructions data
*
* @param {Array} path input path data
* @return {Array} output path data
*/
function collapseRepeated(data) {
var prev,
prevIndex;
// copy an array and modifieds item to keep original data untouched
data = data.reduce(function(newPath, item) {
if (
prev && item.data &&
item.instruction == prev.instruction
) {
// concat previous data with current
if (item.instruction != 'M') {
prev = newPath[prevIndex] = {
instruction: prev.instruction,
data: prev.data.concat(item.data),
coords: item.coords,
base: prev.base
};
} else {
prev.data = item.data;
prev.coords = item.coords;
}
} else {
newPath.push(item);
prev = item;
prevIndex = newPath.length - 1;
}
return newPath;
}, []);
return data;
}
function set(dest, source) {
dest[0] = source[source.length - 2];
dest[1] = source[source.length - 1];
return dest;
}
/**
* Checks if two paths have an intersection by checking convex hulls
* collision using Gilbert-Johnson-Keerthi distance algorithm
* http://entropyinteractive.com/2011/04/gjk-algorithm/
*
* @param {Array} path1 JS path representation
* @param {Array} path2 JS path representation
* @return {Boolean}
*/
exports.intersects = function(path1, path2) {
if (path1.length < 3 || path2.length < 3) return false; // nothing to fill
// Collect points of every subpath.
var points1 = relative2absolute(path1).reduce(gatherPoints, []),
points2 = relative2absolute(path2).reduce(gatherPoints, []);
// Axis-aligned bounding box check.
if (points1.maxX <= points2.minX || points2.maxX <= points1.minX ||
points1.maxY <= points2.minY || points2.maxY <= points1.minY ||
points1.every(function (set1) {
return points2.every(function (set2) {
return set1[set1.maxX][0] <= set2[set2.minX][0] ||
set2[set2.maxX][0] <= set1[set1.minX][0] ||
set1[set1.maxY][1] <= set2[set2.minY][1] ||
set2[set2.maxY][1] <= set1[set1.minY][1];
});
})
) return false;
// Get a convex hull from points of each subpath. Has the most complexity O(n·log n).
var hullNest1 = points1.map(convexHull),
hullNest2 = points2.map(convexHull);
// Check intersection of every subpath of the first path with every subpath of the second.
return hullNest1.some(function(hull1) {
if (hull1.length < 3) return false;
return hullNest2.some(function(hull2) {
if (hull2.length < 3) return false;
var simplex = [getSupport(hull1, hull2, [1, 0])], // create the initial simplex
direction = minus(simplex[0]); // set the direction to point towards the origin
var iterations = 1e4; // infinite loop protection, 10 000 iterations is more than enough
while (true) {
if (iterations-- == 0) {
console.error('Error: infinite loop while processing mergePaths plugin.');
return true; // true is the safe value that means “do nothing with paths”
}
// add a new point
simplex.push(getSupport(hull1, hull2, direction));
// see if the new point was on the correct side of the origin
if (dot(direction, simplex[simplex.length - 1]) <= 0) return false;
// process the simplex
if (processSimplex(simplex, direction)) return true;
}
});
});
function getSupport(a, b, direction) {
return sub(supportPoint(a, direction), supportPoint(b, minus(direction)));
}
// Computes farthest polygon point in particular direction.
// Thanks to knowledge of min/max x and y coordinates we can choose a quadrant to search in.
// Since we're working on convex hull, the dot product is increasing until we find the farthest point.
function supportPoint(polygon, direction) {
var index = direction[1] >= 0 ?
direction[0] < 0 ? polygon.maxY : polygon.maxX :
direction[0] < 0 ? polygon.minX : polygon.minY,
max = -Infinity,
value;
while ((value = dot(polygon[index], direction)) > max) {
max = value;
index = ++index % polygon.length;
}
return polygon[(index || polygon.length) - 1];
}
};
function processSimplex(simplex, direction) {
/* jshint -W004 */
// we only need to handle to 1-simplex and 2-simplex
if (simplex.length == 2) { // 1-simplex
var a = simplex[1],
b = simplex[0],
AO = minus(simplex[1]),
AB = sub(b, a);
// AO is in the same direction as AB
if (dot(AO, AB) > 0) {
// get the vector perpendicular to AB facing O
set(direction, orth(AB, a));
} else {
set(direction, AO);
// only A remains in the simplex
simplex.shift();
}
} else { // 2-simplex
var a = simplex[2], // [a, b, c] = simplex
b = simplex[1],
c = simplex[0],
AB = sub(b, a),
AC = sub(c, a),
AO = minus(a),
ACB = orth(AB, AC), // the vector perpendicular to AB facing away from C
ABC = orth(AC, AB); // the vector perpendicular to AC facing away from B
if (dot(ACB, AO) > 0) {
if (dot(AB, AO) > 0) { // region 4
set(direction, ACB);
simplex.shift(); // simplex = [b, a]
} else { // region 5
set(direction, AO);
simplex.splice(0, 2); // simplex = [a]
}
} else if (dot(ABC, AO) > 0) {
if (dot(AC, AO) > 0) { // region 6
set(direction, ABC);
simplex.splice(1, 1); // simplex = [c, a]
} else { // region 5 (again)
set(direction, AO);
simplex.splice(0, 2); // simplex = [a]
}
} else // region 7
return true;
}
return false;
}
function minus(v) {
return [-v[0], -v[1]];
}
function sub(v1, v2) {
return [v1[0] - v2[0], v1[1] - v2[1]];
}
function dot(v1, v2) {
return v1[0] * v2[0] + v1[1] * v2[1];
}
function orth(v, from) {
var o = [-v[1], v[0]];
return dot(o, minus(from)) < 0 ? minus(o) : o;
}
function gatherPoints(points, item, index, path) {
var subPath = points.length && points[points.length - 1],
prev = index && path[index - 1],
basePoint = subPath.length && subPath[subPath.length - 1],
data = item.data,
ctrlPoint = basePoint;
switch (item.instruction) {
case 'M':
points.push(subPath = []);
break;
case 'H':
addPoint(subPath, [data[0], basePoint[1]]);
break;
case 'V':
addPoint(subPath, [basePoint[0], data[0]]);
break;
case 'Q':
addPoint(subPath, data.slice(0, 2));
prevCtrlPoint = [data[2] - data[0], data[3] - data[1]]; // Save control point for shorthand
break;
case 'T':
if (prev.instruction == 'Q' || prev.instruction == 'T') {
ctrlPoint = [basePoint[0] + prevCtrlPoint[0], basePoint[1] + prevCtrlPoint[1]];
addPoint(subPath, ctrlPoint);
prevCtrlPoint = [data[0] - ctrlPoint[0], data[1] - ctrlPoint[1]];
}
break;
case 'C':
// Approximate quibic Bezier curve with middle points between control points
addPoint(subPath, [.5 * (basePoint[0] + data[0]), .5 * (basePoint[1] + data[1])]);
addPoint(subPath, [.5 * (data[0] + data[2]), .5 * (data[1] + data[3])]);
addPoint(subPath, [.5 * (data[2] + data[4]), .5 * (data[3] + data[5])]);
prevCtrlPoint = [data[4] - data[2], data[5] - data[3]]; // Save control point for shorthand
break;
case 'S':
if (prev.instruction == 'C' || prev.instruction == 'S') {
addPoint(subPath, [basePoint[0] + .5 * prevCtrlPoint[0], basePoint[1] + .5 * prevCtrlPoint[1]]);
ctrlPoint = [basePoint[0] + prevCtrlPoint[0], basePoint[1] + prevCtrlPoint[1]];
}
addPoint(subPath, [.5 * (ctrlPoint[0] + data[0]), .5 * (ctrlPoint[1]+ data[1])]);
addPoint(subPath, [.5 * (data[0] + data[2]), .5 * (data[1] + data[3])]);
prevCtrlPoint = [data[2] - data[0], data[3] - data[1]];
break;
case 'A':
// Convert the arc to bezier curves and use the same approximation
var curves = a2c.apply(0, basePoint.concat(data));
for (var cData; (cData = curves.splice(0,6).map(toAbsolute)).length;) {
addPoint(subPath, [.5 * (basePoint[0] + cData[0]), .5 * (basePoint[1] + cData[1])]);
addPoint(subPath, [.5 * (cData[0] + cData[2]), .5 * (cData[1] + cData[3])]);
addPoint(subPath, [.5 * (cData[2] + cData[4]), .5 * (cData[3] + cData[5])]);
if (curves.length) addPoint(subPath, basePoint = cData.slice(-2));
}
break;
}
// Save final command coordinates
if (data && data.length >= 2) addPoint(subPath, data.slice(-2));
return points;
function toAbsolute(n, i) { return n + basePoint[i % 2] }
// Writes data about the extreme points on each axle
function addPoint(path, point) {
if (!path.length || point[1] > path[path.maxY][1]) {
path.maxY = path.length;
points.maxY = points.length ? Math.max(point[1], points.maxY) : point[1];
}
if (!path.length || point[0] > path[path.maxX][0]) {
path.maxX = path.length;
points.maxX = points.length ? Math.max(point[0], points.maxX) : point[0];
}
if (!path.length || point[1] < path[path.minY][1]) {
path.minY = path.length;
points.minY = points.length ? Math.min(point[1], points.minY) : point[1];
}
if (!path.length || point[0] < path[path.minX][0]) {
path.minX = path.length;
points.minX = points.length ? Math.min(point[0], points.minX) : point[0];
}
path.push(point);
}
}
/**
* Forms a convex hull from set of points of every subpath using monotone chain convex hull algorithm.
* http://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain
*
* @param points An array of [X, Y] coordinates
*/
function convexHull(points) {
/* jshint -W004 */
points.sort(function(a, b) {
return a[0] == b[0] ? a[1] - b[1] : a[0] - b[0];
});
var lower = [],
minY = 0,
bottom = 0;
for (var i = 0; i < points.length; i++) {
while (lower.length >= 2 && cross(lower[lower.length - 2], lower[lower.length - 1], points[i]) <= 0) {
lower.pop();
}
if (points[i][1] < points[minY][1]) {
minY = i;
bottom = lower.length;
}
lower.push(points[i]);
}
var upper = [],
maxY = points.length - 1,
top = 0;
for (var i = points.length; i--;) {
while (upper.length >= 2 && cross(upper[upper.length - 2], upper[upper.length - 1], points[i]) <= 0) {
upper.pop();
}
if (points[i][1] > points[maxY][1]) {
maxY = i;
top = upper.length;
}
upper.push(points[i]);
}
// last points are equal to starting points of the other part
upper.pop();
lower.pop();
var hull = lower.concat(upper);
hull.minX = 0; // by sorting
hull.maxX = lower.length;
hull.minY = bottom;
hull.maxY = (lower.length + top) % hull.length;
return hull;
}
function cross(o, a, b) {
return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0]);
}
/* Based on code from Snap.svg (Apache 2 license). http://snapsvg.io/
* Thanks to Dmitry Baranovskiy for his great work!
*/
// jshint ignore: start
function a2c(x1, y1, rx, ry, angle, large_arc_flag, sweep_flag, x2, y2, recursive) {
// for more information of where this Math came from visit:
// http://www.w3.org/TR/SVG11/implnote.html#ArcImplementationNotes
var _120 = Math.PI * 120 / 180,
rad = Math.PI / 180 * (+angle || 0),
res = [],
rotateX = function(x, y, rad) { return x * Math.cos(rad) - y * Math.sin(rad) },
rotateY = function(x, y, rad) { return x * Math.sin(rad) + y * Math.cos(rad) };
if (!recursive) {
x1 = rotateX(x1, y1, -rad);
y1 = rotateY(x1, y1, -rad);
x2 = rotateX(x2, y2, -rad);
y2 = rotateY(x2, y2, -rad);
var x = (x1 - x2) / 2,
y = (y1 - y2) / 2;
var h = (x * x) / (rx * rx) + (y * y) / (ry * ry);
if (h > 1) {
h = Math.sqrt(h);
rx = h * rx;
ry = h * ry;
}
var rx2 = rx * rx,
ry2 = ry * ry,
k = (large_arc_flag == sweep_flag ? -1 : 1) *
Math.sqrt(Math.abs((rx2 * ry2 - rx2 * y * y - ry2 * x * x) / (rx2 * y * y + ry2 * x * x))),
cx = k * rx * y / ry + (x1 + x2) / 2,
cy = k * -ry * x / rx + (y1 + y2) / 2,
f1 = Math.asin(((y1 - cy) / ry).toFixed(9)),
f2 = Math.asin(((y2 - cy) / ry).toFixed(9));
f1 = x1 < cx ? Math.PI - f1 : f1;
f2 = x2 < cx ? Math.PI - f2 : f2;
f1 < 0 && (f1 = Math.PI * 2 + f1);
f2 < 0 && (f2 = Math.PI * 2 + f2);
if (sweep_flag && f1 > f2) {
f1 = f1 - Math.PI * 2;
}
if (!sweep_flag && f2 > f1) {
f2 = f2 - Math.PI * 2;
}
} else {
f1 = recursive[0];
f2 = recursive[1];
cx = recursive[2];
cy = recursive[3];
}
var df = f2 - f1;
if (Math.abs(df) > _120) {
var f2old = f2,
x2old = x2,
y2old = y2;
f2 = f1 + _120 * (sweep_flag && f2 > f1 ? 1 : -1);
x2 = cx + rx * Math.cos(f2);
y2 = cy + ry * Math.sin(f2);
res = a2c(x2, y2, rx, ry, angle, 0, sweep_flag, x2old, y2old, [f2, f2old, cx, cy]);
}
df = f2 - f1;
var c1 = Math.cos(f1),
s1 = Math.sin(f1),
c2 = Math.cos(f2),
s2 = Math.sin(f2),
t = Math.tan(df / 4),
hx = 4 / 3 * rx * t,
hy = 4 / 3 * ry * t,
m = [
- hx * s1, hy * c1,
x2 + hx * s2 - x1, y2 - hy * c2 - y1,
x2 - x1, y2 - y1
];
if (recursive) {
return m.concat(res);
} else {
res = m.concat(res);
var newres = [];
for (var i = 0, n = res.length; i < n; i++) {
newres[i] = i % 2 ? rotateY(res[i - 1], res[i], rad) : rotateX(res[i], res[i + 1], rad);
}
return newres;
}
}
// jshint ignore: end